A solution algorithm for fluid–particle flows across all flow regimes

DOE PAGES

Kong, Bo; Fox, Rodney O.

2017-05-12

Many fluid–particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are closepacked as well as very dilute regions where particle–particle collisions are rare. Thus, in order to simulate such fluid–particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in themore » flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas–particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid–particle flows.« less

A solution algorithm for fluid-particle flows across all flow regimes

NASA Astrophysics Data System (ADS)

Kong, Bo; Fox, Rodney O.

2017-09-01

Many fluid-particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are close-packed as well as very dilute regions where particle-particle collisions are rare. Thus, in order to simulate such fluid-particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in the flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas-particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid-particle flows.

A solution algorithm for fluid–particle flows across all flow regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kong, Bo; Fox, Rodney O.

Many fluid–particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are closepacked as well as very dilute regions where particle–particle collisions are rare. Thus, in order to simulate such fluid–particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in themore » flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas–particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid–particle flows.« less

Development of a hip joint model for finite volume simulations.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

2014-01-01

This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Implementation of a Pseudo-Bending Seismic Travel-Time Calculator in a Distributed Parallel Computing Environment

DTIC Science & Technology

2008-09-01

algorithms that have been proposed to accomplish it fall into three broad categories. Eikonal solvers (e.g., Vidale, 1988, 1990; Podvin and Lecomte, 1991...difference eikonal solvers, the FMM algorithm works by following a wavefront as it moves across a volume of grid points, updating the travel times in...the grid according to the eikonal differential equation, using a second-order finite-difference scheme. We chose to use FMM for our comparison because

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

NASA Astrophysics Data System (ADS)

Jayakumar, J. S.; Kumar, Inder; Eswaran, V.

2010-12-01

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Near-Field Noise Computation for a Supersonic Circular Jet

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Hultgren, Lennart S.

2005-01-01

A fully expanded, high-Reynolds-number, supersonic circular jet of Mach number 1.4 is simulated, using a 3-D finite-volume Navier-Stokes solver, with emphasis on the near field noise. The numerical results are generally in good agreement with existing experimental findings.

Characteristics of the Shuttle Orbiter Leeside Flow During A Reentry Condition

NASA Technical Reports Server (NTRS)

Kleb, William L.; Weilmuenster, K. James

1992-01-01

A study of the leeside flow characteristics of the Shuttle Orbiter is presented for a reentry flight condition. The flow is computed using a point-implicit, finite-volume scheme known as the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). LAURA is a second-order accurate, laminar Navier-Stokes solver, incorporating finite-rate chemistry with a radiative equilibrium wall temperature distribution and finite-rate wall catalysis. The resulting computational solution is analyzed in terms of salient flow features and the surface quantities are compared with flight data.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Dumbser, Michael

2015-10-01

Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on unstructured meshes. Several stringent two- and three-dimensional problems are shown to work well with the methods presented here.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Moving and adaptive grid methods for compressible flows

NASA Technical Reports Server (NTRS)

Trepanier, Jean-Yves; Camarero, Ricardo

1995-01-01

This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology.

Gpu Implementation of a Viscous Flow Solver on Unstructured Grids

NASA Astrophysics Data System (ADS)

Xu, Tianhao; Chen, Long

2016-06-01

Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

Calm water resistance prediction of a bulk carrier using Reynolds averaged Navier-Stokes based solver

NASA Astrophysics Data System (ADS)

Rahaman, Md. Mashiur; Islam, Hafizul; Islam, Md. Tariqul; Khondoker, Md. Reaz Hasan

2017-12-01

Maneuverability and resistance prediction with suitable accuracy is essential for optimum ship design and propulsion power prediction. This paper aims at providing some of the maneuverability characteristics of a Japanese bulk carrier model, JBC in calm water using a computational fluid dynamics solver named SHIP Motion and OpenFOAM. The solvers are based on the Reynolds average Navier-Stokes method (RaNS) and solves structured grid using the Finite Volume Method (FVM). This paper comprises the numerical results of calm water test for the JBC model with available experimental results. The calm water test results include the total drag co-efficient, average sinkage, and trim data. Visualization data for pressure distribution on the hull surface and free water surface have also been included. The paper concludes that the presented solvers predict the resistance and maneuverability characteristics of the bulk carrier with reasonable accuracy utilizing minimum computational resources.

Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959)

USGS Publications Warehouse

George, D.L.

2011-01-01

The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

Four-way coupling of a three-dimensional debris flow solver to a Lagrangian Particle Simulation: method and first results

NASA Astrophysics Data System (ADS)

von Boetticher, Albrecht; Rickenmann, Dieter; McArdell, Brian; Kirchner, James W.

2017-04-01

Debris flows are dense flowing mixtures of water, clay, silt, sand and coarser particles. They are a common natural hazard in mountain regions and frequently cause severe damage. Modeling debris flows to design protection measures is still challenging due to the complex interactions within the inhomogeneous material mixture, and the sensitivity of the flow process to the channel geometry. The open-source, OpenFOAM-based finite-volume debris flow model debrisInterMixing (von Boetticher et al, 2016) defines rheology parameters based on the material properties of the debris flow mixture to reduce the number of free model parameters. As a simplification in this first model version, gravel was treated as a Coulomb-viscoplastic fluid, neglecting grain-to-grain collisions and the coupling between the coarser gravel grains and the interstitial fluid. Here we present an extension of that solver, accounting for the particle-to-particle and particle-to-boundary contacts with a Lagrangian Particle Simulation composed of spherical grains and a user-defined grain size distribution. The grain collisions of the Lagrangian particles add granular flow behavior to the finite-volume simulation of the continuous phases. The two-way coupling exchanges momentum between the phase-averaged flow in a finite volume cell, and among all individual particles contained in that cell, allowing the user to choose from a number of different drag models. The momentum exchange is implemented in the momentum equation and in the pressure equation (ensuring continuity) of the so-called PISO-loop, resulting in a stable 4-way coupling (particle-to-particle, particle-to-boundary, particle-to-fluid and fluid-to-particle) that represents the granular and viscous flow behavior of debris flow material. We will present simulations that illustrate the relative benefits and drawbacks of explicitly representing grain collisions, compared to the original debrisInterMixing solver.

Using a multifrontal sparse solver in a high performance, finite element code

NASA Technical Reports Server (NTRS)

King, Scott D.; Lucas, Robert; Raefsky, Arthur

1990-01-01

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Molvik, G. A.

1991-01-01

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Euler equation computations for the flow over a hovering helicopter rotor

NASA Technical Reports Server (NTRS)

Roberts, Thomas Wesley

1988-01-01

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

The piecewise parabolic method for Riemann problems in nonlinear elasticity.

PubMed

Zhang, Wei; Wang, Tao; Bai, Jing-Song; Li, Ping; Wan, Zhen-Hua; Sun, De-Jun

2017-10-18

We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD ("D" denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC ("C" denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid "stick" problem with the same material at the two sides of contact interface and the solid/solid "slip" problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

TransCut: interactive rendering of translucent cutouts.

PubMed

Li, Dongping; Sun, Xin; Ren, Zhong; Lin, Stephen; Tong, Yiying; Guo, Baining; Zhou, Kun

2013-03-01

We present TransCut, a technique for interactive rendering of translucent objects undergoing fracturing and cutting operations. As the object is fractured or cut open, the user can directly examine and intuitively understand the complex translucent interior, as well as edit material properties through painting on cross sections and recombining the broken pieces—all with immediate and realistic visual feedback. This new mode of interaction with translucent volumes is made possible with two technical contributions. The first is a novel solver for the diffusion equation (DE) over a tetrahedral mesh that produces high-quality results comparable to the state-of-art finite element method (FEM) of Arbree et al. but at substantially higher speeds. This accuracy and efficiency is obtained by computing the discrete divergences of the diffusion equation and constructing the DE matrix using analytic formulas derived for linear finite elements. The second contribution is a multiresolution algorithm to significantly accelerate our DE solver while adapting to the frequent changes in topological structure of dynamic objects. The entire multiresolution DE solver is highly parallel and easily implemented on the GPU. We believe TransCut provides a novel visual effect for heterogeneous translucent objects undergoing fracturing and cutting operations.

An assessment of unstructured grid technology for timely CFD analysis

NASA Technical Reports Server (NTRS)

Kinard, Tom A.; Schabowski, Deanne M.

1995-01-01

An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.

CFD analysis of a twin scroll radial turbine

NASA Astrophysics Data System (ADS)

Fürst, Jiří; Žák, Zdenĕk

2018-06-01

The contribution deals with the application of coupled implicit solver for compressible flows to CFD analysis of a twin scroll radial turbine. The solver is based on the finite volume method, convective terms are approximated using AUSM+up scheme, viscous terms use central approximation and the time evolution is achieved with lower-upper symmetric Gauss-Seidel (LU-SGS) method. The solver allows steady simulation with the so called frozen rotor approach as well as the fully unsteady solution. Both approaches are at first validated for the case of ERCOFTAC pump [1]. Then the CFD analysis of the flow through a twin scroll radial turbine and the predictions of the efficiency and turbine power is performed and the results are compared to experimental data obtained in the framework of Josef Božek - Competence Centre for Automotive Industry.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

Acceleration of FDTD mode solver by high-performance computing techniques.

PubMed

Han, Lin; Xi, Yanping; Huang, Wei-Ping

2010-06-21

A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.

The fundamentals of adaptive grid movement

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.

1990-01-01

Basic grid point movement schemes are studied. The schemes are referred to as adaptive grids. Weight functions and equidistribution in one dimension are treated. The specification of coefficients in the linear weight, attraction to a given grid or a curve, and evolutionary forces are considered. Curve by curve and finite volume methods are described. The temporal coupling of partial differential equations solvers and grid generators was discussed.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Drekar v.2.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Coupled Modeling of Hydrodynamics and Sound in Coastal Ocean for Renewable Ocean Energy Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Jung, Ki Won; Yang, Zhaoqing

An underwater sound model was developed to simulate sound propagation from marine and hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite difference methods were developed to solve the 3D Helmholtz equation for sound propagation in the coastal environment. A 3D sparse matrix solver with complex coefficients was formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method was applied to solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model was then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generatedmore » by human activities, such as construction of OSW turbines or tidal stream turbine operations, in a range-dependent setting. As a proof of concept, initial validation of the solver is presented for two coastal wedge problems. This sound model can be useful for evaluating impacts on marine mammals due to deployment of MHK devices and OSW energy platforms.« less

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Probability density function approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1994-01-01

The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

NASA Astrophysics Data System (ADS)

Qiang, Ji

2016-06-01

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

A multi-scale network method for two-phase flow in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khayrat, Karim, E-mail: khayratk@ifd.mavt.ethz.ch; Jenny, Patrick

Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces withinmore » each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver.« less

Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem

PubMed Central

Abas, Aizat; Mokhtar, N. Hafizah; Ishak, M. H. H.; Abdullah, M. Z.; Ho Tian, Ang

2016-01-01

This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required. PMID:27239221

Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Park, George Ilhwan; Moin, Parviz

2016-01-01

This paper focuses on numerical and practical aspects associated with a parallel implementation of a two-layer zonal wall model for large-eddy simulation (LES) of compressible wall-bounded turbulent flows on unstructured meshes. A zonal wall model based on the solution of unsteady three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations on a separate near-wall grid is implemented in an unstructured, cell-centered finite-volume LES solver. The main challenge in its implementation is to couple two parallel, unstructured flow solvers for efficient boundary data communication and simultaneous time integrations. A coupling strategy with good load balancing and low processors underutilization is identified. Face mapping and interpolation procedures at the coupling interface are explained in detail. The method of manufactured solution is used for verifying the correct implementation of solver coupling, and parallel performance of the combined wall-modeled LES (WMLES) solver is investigated. The method has successfully been applied to several attached and separated flows, including a transitional flow over a flat plate and a separated flow over an airfoil at an angle of attack.

Performance of a parallel thermal-hydraulics code TEMPEST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fann, G.I.; Trent, D.S.

The authors describe the parallelization of the Tempest thermal-hydraulics code. The serial version of this code is used for production quality 3-D thermal-hydraulics simulations. Good speedup was obtained with a parallel diagonally preconditioned BiCGStab non-symmetric linear solver, using a spatial domain decomposition approach for the semi-iterative pressure-based and mass-conserved algorithm. The test case used here to illustrate the performance of the BiCGStab solver is a 3-D natural convection problem modeled using finite volume discretization in cylindrical coordinates. The BiCGStab solver replaced the LSOR-ADI method for solving the pressure equation in TEMPEST. BiCGStab also solves the coupled thermal energy equation. Scalingmore » performance of 3 problem sizes (221220 nodes, 358120 nodes, and 701220 nodes) are presented. These problems were run on 2 different parallel machines: IBM-SP and SGI PowerChallenge. The largest problem attains a speedup of 68 on an 128 processor IBM-SP. In real terms, this is over 34 times faster than the fastest serial production time using the LSOR-ADI solver.« less

A 1D-2D Shallow Water Equations solver for discontinuous porosity field based on a Generalized Riemann Problem

NASA Astrophysics Data System (ADS)

Ferrari, Alessia; Vacondio, Renato; Dazzi, Susanna; Mignosa, Paolo

2017-09-01

A novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D Shallow Water Equation (SWE) models is presented. With the aim of accurately approximating the porosity source term, a Generalized Riemann Problem is derived by adding an additional fictitious equation to the SWEs system and imposing mass and momentum conservation across the porosity discontinuity. The modified Shallow Water Equations are theoretically investigated, and the implementation of an augmented Roe Solver in a 1D Godunov-type finite volume scheme is presented. Robust treatment of transonic flows is ensured by introducing an entropy fix based on the wave pattern of the Generalized Riemann Problem. An Exact Riemann Solver is also derived in order to validate the numerical model. As an extension of the 1D scheme, an analogous 2D numerical model is also derived and validated through test cases with radial symmetry. The capability of the 1D and 2D numerical models to capture different wave patterns is assessed against several Riemann Problems with different wave patterns.

Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver

NASA Astrophysics Data System (ADS)

Lee, Hee Dong; Kwon, Oh Joon

The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.

Flow solution on a dual-block grid around an airplane

NASA Technical Reports Server (NTRS)

Eriksson, Lars-Erik

1987-01-01

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

NASA Astrophysics Data System (ADS)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.

2017-06-01

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D., E-mail: jregele@iastate.edu

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kuttamore » method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.« less

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Kwak, Dochan; Rogers, Stuart E.

2002-01-01

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

Three-dimensional forward solver and its performance analysis for magnetic resonance electrical impedance tomography (MREIT) using recessed electrodes.

PubMed

Lee, Byung Il; Oh, Suk Hoon; Woo, Eung Je; Lee, Soo Yeol; Cho, Min Hyoung; Kwon, Ohin; Seo, Jin Keun; Lee, June-Yub; Baek, Woon Sik

2003-07-07

In magnetic resonance electrical impedance tomography (MREIT), we try to reconstruct a cross-sectional resistivity (or conductivity) image of a subject. When we inject a current through surface electrodes, it generates a magnetic field. Using a magnetic resonance imaging (MRI) scanner, we can obtain the induced magnetic flux density from MR phase images of the subject. We use recessed electrodes to avoid undesirable artefacts near electrodes in measuring magnetic flux densities. An MREIT image reconstruction algorithm produces cross-sectional resistivity images utilizing the measured internal magnetic flux density in addition to boundary voltage data. In order to develop such an image reconstruction algorithm, we need a three-dimensional forward solver. Given injection currents as boundary conditions, the forward solver described in this paper computes voltage and current density distributions using the finite element method (FEM). Then, it calculates the magnetic flux density within the subject using the Biot-Savart law and FEM. The performance of the forward solver is analysed and found to be enough for use in MREIT for resistivity image reconstructions and also experimental designs and validations. The forward solver may find other applications where one needs to compute voltage, current density and magnetic flux density distributions all within a volume conductor.

Evaluation of Resuspension from Propeller Wash in DoD Harbors

DTIC Science & Technology

2016-09-01

Environmental Research and Development Center FANS FOV ICP-MS Finite Analytical Navier-Stoker Solver Field of View Inductively Coupled Plasma with...Model (1984) and the Finite Analytical Navier- Stoker Solver (FANS) model (Chen et al., 2003) were set up to simulate and evaluate flow velocities and...model for evaluating the resuspension potential of propeller wash by a tugboat and the FANS model for a DDG. The Finite -Analytic Navier-Stokes (FANS

Numerical Simulations for Landing Gear Noise Generation and Radiation

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Long, Lyle N.

2002-01-01

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kenjeres, S.; Hanjalic, K.; Renaudier, S.

2006-12-15

Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); A. Gailitis et al., Physics of Plasmas 11, 2838 (2004)], consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeledmore » by a finite-volume Navier-Stokes solver using a Reynolds-averaged-Navier-Stokes turbulence model. The magnetic field is computed by an Adams-Bashforth finite-difference solver. The coupling of the two computational codes, although performed sequentially, provides an improved understanding of the interaction between the fluid velocity and magnetic fields in the saturation regime of the Riga dynamo experiment under realistic working conditions.« less

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Flowfield predictions for multiple body launch vehicles

NASA Technical Reports Server (NTRS)

Deese, Jerry E.; Pavish, D. L.; Johnson, Jerry G.; Agarwal, Ramesh K.; Soni, Bharat K.

1992-01-01

A method is developed for simulating inviscid and viscous flow around multicomponent launch vehicles. Grids are generated by the GENIE general-purpose grid-generation code, and the flow solver is a finite-volume Runge-Kutta time-stepping method. Turbulence effects are simulated using Baldwin and Lomax (1978) turbulence model. Calculations are presented for three multibody launch vehicle configurations: one with two small-diameter solid motors, one with nine small-diameter solid motors, and one with three large-diameter solid motors.

Equilibrium Wall Model Implementation in a Nodal Finite Element Flow Solver JENRE for Large Eddy Simulations

DTIC Science & Technology

2017-11-13

condition is applied to the inviscid and viscous fluxes on the wall to satisfy the surface physical condition, but a non -zero surface tangential...velocity profiles and turbulence quantities predicted by the current wall-model implementation agree well with available experimental data and...implementations. The volume and surface integrals based on the non -zero surface velocity in a cell adjacent to the wall show a good agreement with those

LES of Swirling Reacting Flows via the Unstructured scalar-FDF Solver

NASA Astrophysics Data System (ADS)

Ansari, Naseem; Pisciuneri, Patrick; Strakey, Peter; Givi, Peyman

2011-11-01

Swirling flames pose a significant challenge for computational modeling due to the presence of recirculation regions and vortex shedding. In this work, results are presented of LES of two swirl stabilized non-premixed flames (SM1 and SM2) via the FDF methodology. These flames are part of the database for validation of turbulent-combustion models. The scalar-FDF is simulated on a domain discretized by unstructured meshes, and is coupled with a finite volume flow solver. In the SM1 flame (with a low swirl number) chemistry is described by the flamelet model based on the full GRI 2.11 mechanism. The SM2 flame (with a high swirl number) is simulated via a 46-step 17-species mechanism. The simulated results are assessed via comparison with experimental data.

Conjugate Heat Transfer Study in Hypersonic Flows

NASA Astrophysics Data System (ADS)

Sahoo, Niranjan; Kulkarni, Vinayak; Peetala, Ravi Kumar

2018-04-01

Coupled and decoupled conjugate heat transfer (CHT) studies are carried out to imitate experimental studies for heat transfer measurement in hypersonic flow regime. The finite volume based solvers are used for analyzing the heat interaction between fluid and solid domains. Temperature and surface heat flux signals are predicted by both coupled and decoupled CHT analysis techniques for hypersonic Mach numbers. These two methodologies are also used to study the effect of different wall materials on surface parameters. Effectiveness of these CHT solvers has been verified for the inverse problem of wall heat flux recovery using various techniques reported in the literature. Both coupled and decoupled CHT techniques are seen to be equally useful for prediction of local temperature and heat flux signals prior to the experiments in hypersonic flows.

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Modeling of photon migration in the human lung using a finite volume solver

NASA Astrophysics Data System (ADS)

Sikorski, Zbigniew; Furmanczyk, Michal; Przekwas, Andrzej J.

2006-02-01

The application of the frequency domain and steady-state diffusive optical spectroscopy (DOS) and steady-state near infrared spectroscopy (NIRS) to diagnosis of the human lung injury challenges many elements of these techniques. These include the DOS/NIRS instrument performance and accurate models of light transport in heterogeneous thorax tissue. The thorax tissue not only consists of different media (e.g. chest wall with ribs, lungs) but its optical properties also vary with time due to respiration and changes in thorax geometry with contusion (e.g. pneumothorax or hemothorax). This paper presents a finite volume solver developed to model photon migration in the diffusion approximation in heterogeneous complex 3D tissues. The code applies boundary conditions that account for Fresnel reflections. We propose an effective diffusion coefficient for the void volumes (pneumothorax) based on the assumption of the Lambertian diffusion of photons entering the pleural cavity and accounting for the local pleural cavity thickness. The code has been validated using the MCML Monte Carlo code as a benchmark. The code environment enables a semi-automatic preparation of 3D computational geometry from medical images and its rapid automatic meshing. We present the application of the code to analysis/optimization of the hybrid DOS/NIRS/ultrasound technique in which ultrasound provides data on the localization of thorax tissue boundaries. The code effectiveness (3D complex case computation takes 1 second) enables its use to quantitatively relate detected light signal to absorption and reduced scattering coefficients that are indicators of the pulmonary physiologic state (hemoglobin concentration and oxygenation).

Scalable direct Vlasov solver with discontinuous Galerkin method on unstructured mesh.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, J.; Ostroumov, P. N.; Mustapha, B.

2010-12-01

This paper presents the development of parallel direct Vlasov solvers with discontinuous Galerkin (DG) method for beam and plasma simulations in four dimensions. Both physical and velocity spaces are in two dimesions (2P2V) with unstructured mesh. Contrary to the standard particle-in-cell (PIC) approach for kinetic space plasma simulations, i.e., solving Vlasov-Maxwell equations, direct method has been used in this paper. There are several benefits to solving a Vlasov equation directly, such as avoiding noise associated with a finite number of particles and the capability to capture fine structure in the plasma. The most challanging part of a direct Vlasov solvermore » comes from higher dimensions, as the computational cost increases as N{sup 2d}, where d is the dimension of the physical space. Recently, due to the fast development of supercomputers, the possibility has become more realistic. Many efforts have been made to solve Vlasov equations in low dimensions before; now more interest has focused on higher dimensions. Different numerical methods have been tried so far, such as the finite difference method, Fourier Spectral method, finite volume method, and spectral element method. This paper is based on our previous efforts to use the DG method. The DG method has been proven to be very successful in solving Maxwell equations, and this paper is our first effort in applying the DG method to Vlasov equations. DG has shown several advantages, such as local mass matrix, strong stability, and easy parallelization. These are particularly suitable for Vlasov equations. Domain decomposition in high dimensions has been used for parallelization; these include a highly scalable parallel two-dimensional Poisson solver. Benchmark results have been shown and simulation results will be reported.« less

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Turbulent Bubbly Flow in a Vertical Pipe Computed By an Eddy-Resolving Reynolds Stress Model

DTIC Science & Technology

2014-09-19

the numerical code OpenFOAM R©. 1 Introduction Turbulent bubbly flows are encountered in many industrially relevant applications, such as chemical in...performed using the OpenFOAM -2.2.2 computational code utilizing a cell- center-based finite volume method on an unstructured numerical grid. The...the mean Courant number is always below 0.4. The utilized turbulence models were implemented into the so-called twoPhaseEulerFoam solver in OpenFOAM , to

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vay, Jean-Luc, E-mail: jlvay@lbl.gov; Haber, Irving; Godfrey, Brendan B.

Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of themore » wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods.« less

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

Spectral modeling of radiation in combustion systems

NASA Astrophysics Data System (ADS)

Pal, Gopalendu

Radiation calculations are important in combustion due to the high temperatures encountered but has not been studied in sufficient detail in the case of turbulent flames. Radiation calculations for such problems require accurate, robust, and computationally efficient models for the solution of radiative transfer equation (RTE), and spectral properties of radiation. One more layer of complexity is added in predicting the overall heat transfer in turbulent combustion systems due to nonlinear interactions between turbulent fluctuations and radiation. The present work is aimed at the development of finite volume-based high-accuracy thermal radiation modeling, including spectral radiation properties in order to accurately capture turbulence-radiation interactions (TRI) and predict heat transfer in turbulent combustion systems correctly and efficiently. The turbulent fluctuations of temperature and chemical species concentrations have strong effects on spectral radiative intensities, and TRI create a closure problem when the governing partial differential equations are averaged. Recently, several approaches have been proposed to take TRI into account. Among these attempts the most promising approaches are the probability density function (PDF) methods, which can treat nonlinear coupling between turbulence and radiative emission exactly, i.e., "emission TRI". The basic idea of the PDF method is to treat physical variables as random variables and to solve the PDF transport equation stochastically. The actual reacting flow field is represented by a large number of discrete stochastic particles each carrying their own random variable values and evolving with time. The mean value of any function of those random variables, such as the chemical source term, can be evaluated exactly by taking the ensemble average of particles. The local emission term belongs to this class and thus, can be evaluated directly and exactly from particle ensembles. However, the local absorption term involves interactions between the local particle and energy emitted by all other particles and, hence, cannot be obtained from particle ensembles directly. To close the nonlinear coupling between turbulence and absorption, i.e., "absorption TRI", an optically thin fluctuation approximation can be applied to virtually all combustion problems and obtain acceptable accuracy. In the present study a composition-PDF method is applied, in which only the temperature and the species concentrations are treated as random variables. A closely coupled hybrid finite-volume/Monte Carlo scheme is adopted, in which the Monte Carlo method is used to solve the composition-PDF for chemical reactions and the finite volume method is used to solve for the flow field and radiation. Spherical harmonics method-based finite volume solvers (P-1 and P-3) are developed using the data structures of the high fidelity open-source code flow software OpenFOAM. Spectral radiative properties of the participating medium are modeled using full-spectrum k-distribution methods. Advancements of basic k-distribution methods are performed for nongray nonhomogeneous gas- and particulate-phase (soot, fuel droplets, ash, etc.) participating media using multi-scale and multi-group based approaches. These methods achieve close-to benchmark line-by-line (LBL) accuracy in strongly inhomogeneous media at a tiny fraction of LBL's computational cost. A portable spectral module is developed, which includes all the basic to advanced k-distribution methods along with the precompiled accurate and compact k-distribution databases. The P-1 /P-3 RTE solver coupled with the spectral module is used in conjunction with the combined Reynolds-averaged Navier-Stokes (RANS) and composition-PDF-based turbulence-chemistry solver to investigate TRI in multiphase turbulent combustion systems. The combustion solvers developed in this study is employed to simulate several turbulent jet flames, such as Sandia Flame D, and artificial nonsooting and sooting flames derived from Flame D. The effects of combustion chemistry, radiation and TRI on total heat transfer and pollutant (such as NO x) generation are studied for the above flames. The accuracy of the overall combustion solver is assessed by comparing it with the experimental data for Flame D. Comparison of the accuracy and the computational cost among various spectral models and RTE solvers is extensively done on the artificial flames derived from Flame D to demonstrate the necessity of accurate modeling of radiation in combustion problems.

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

The CRONOS Code for Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Kissmann, R.; Kleimann, J.; Krebl, B.; Wiengarten, T.

2018-06-01

We describe the magnetohydrodynamics (MHD) code CRONOS, which has been used in astrophysics and space-physics studies in recent years. CRONOS has been designed to be easily adaptable to the problem in hand, where the user can expand or exchange core modules or add new functionality to the code. This modularity comes about through its implementation using a C++ class structure. The core components of the code include solvers for both hydrodynamical (HD) and MHD problems. These problems are solved on different rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. CRONOS uses a finite-volume description with different approximate Riemann solvers that can be chosen at runtime. Here, we describe the implementation of the code with a view toward its ongoing development. We illustrate the code’s potential through several (M)HD test problems and some astrophysical applications.

Three-dimensional fluid-structure interaction case study on cubical fluid cavity with flexible bottom

NASA Astrophysics Data System (ADS)

Ghelardi, Stefano; Rizzo, Cesare; Villa, Diego

2017-12-01

In this paper, we report our study on a numerical fluid-structure interaction problem originally presented by Mok et al. (2001) in two dimensions and later studied in three dimensions by Valdés Vazquez (2007), Lombardi (2012), and Trimarchi (2012). We focus on a 3D test case in which we evaluated the sensitivity of several input parameters on the fluid and structural results. In particular, this analysis provides a starting point from which we can look deeper into specific aspects of these simulations and analyze more realistic cases, e.g., in sails design. In this study, using the commercial software ADINA™, we addressed a well-known unsteadiness problem comprising a square box representing the fluid domain with a flexible bottom modeled with structural shell elements. We compared data from previously published work whose authors used the same numerical approach, i.e., a partitioned approach coupling a finite volume solver (for the fluid domain) and a finite element solver (for the solid domain). Specifically, we established several benchmarks and made comparisons with respect to fluid and solid meshes, structural element types, and structural damping, as well as solution algorithms. Moreover, we compared our method with a monolithic finite element solution method. Our comparisons of new and old results provide an outline of best practices for such simulations.

Agglomeration Multigrid for an Unstructured-Grid Flow Solver

NASA Technical Reports Server (NTRS)

Frink, Neal; Pandya, Mohagna J.

2004-01-01

An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

A finite-volume ELLAM for three-dimensional solute-transport modeling

USGS Publications Warehouse

Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.

2003-01-01

A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

Unconfined laminar nanofluid flow and heat transfer around a rotating circular cylinder in the steady regime

NASA Astrophysics Data System (ADS)

Bouakkaz, Rafik; Salhi, Fouzi; Khelili, Yacine; Quazzazi, Mohamed; Talbi, Kamel

2017-06-01

In this work, steady flow-field and heat transfer through a copper- water nanofluid around a rotating circular cylinder with a constant nondimensional rotation rate α varying from 0 to 5 was investigated for Reynolds numbers of 5-40. Furthermore, the range of nanoparticle volume fractions considered is 0-5%. The effect of volume fraction of nanoparticles on the fluid flow and heat transfer characteristics are carried out by using a finite-volume method based commercial computational fluid dynamics solver. The variation of the local and the average Nusselt numbers with Reynolds number, volume fractions, and rotation rate are presented for the range of conditions. The average Nusselt number is found to decrease with increasing value of the rotation rate for the fixed value of the Reynolds number and volume fraction of nanoparticles. In addition, rotation can be used as a drag reduction technique.

Numerical Simulation of Shock Interaction with Deformable Particles Using a Constrained Interface Reinitialization Scheme

NASA Astrophysics Data System (ADS)

Jackson, Thomas L.; Sridharan, Prashanth; Zhang, Ju; Balachandar, S.

2015-11-01

In this work we present axisymmetric numerical simulations of shock propagating in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. The numerical method is a finite-volume based solver on a Cartesian grid, which allows for multi-material interfaces and shocks. To preserve particle mass and volume, a novel constraint reinitialization scheme is introduced. We compute the unsteady drag coefficient as a function of post-shock pressure, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations.

Efficient Implementation of Multigrid Solvers on Message-Passing Parrallel Systems

NASA Technical Reports Server (NTRS)

Lou, John

1994-01-01

We discuss our implementation strategies for finite difference multigrid partial differential equation (PDE) solvers on message-passing systems. Our target parallel architecture is Intel parallel computers: the Delta and Paragon system.

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

DOE PAGES

Vincenti, H.; Vay, J. -L.

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model -- GMG Linear Equation Solver Package Documentation

USGS Publications Warehouse

Wilson, John D.; Naff, Richard L.

2004-01-01

A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.

PDF approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1993-01-01

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Toward Verification of USM3D Extensions for Mixed Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Frink, Neal T.; Ding, Ejiang; Parlette, Edward B.

2013-01-01

The unstructured tetrahedral grid cell-centered finite volume flow solver USM3D has been recently extended to handle mixed element grids composed of hexahedral, prismatic, pyramidal, and tetrahedral cells. Presently, two turbulence models, namely, baseline Spalart-Allmaras (SA) and Menter Shear Stress Transport (SST), support mixed element grids. This paper provides an overview of the various numerical discretization options available in the newly enhanced USM3D. Using the SA model, the flow solver extensions are verified on three two-dimensional test cases available on the Turbulence Modeling Resource website at the NASA Langley Research Center. The test cases are zero pressure gradient flat plate, planar shear, and bump-inchannel. The effect of cell topologies on the flow solution is also investigated using the planar shear case. Finally, the assessment of various cell and face gradient options is performed on the zero pressure gradient flat plate case.

An effective lattice Boltzmann flux solver on arbitrarily unstructured meshes

NASA Astrophysics Data System (ADS)

Wu, Qi-Feng; Shu, Chang; Wang, Yan; Yang, Li-Ming

2018-05-01

The recently proposed lattice Boltzmann flux solver (LBFS) is a new approach for the simulation of incompressible flow problems. It applies the finite volume method (FVM) to discretize the governing equations, and the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. In the previous application of the LBFS, the structured meshes have been commonly employed, which may cause inconvenience for problems with complex geometries. In this paper, the LBFS is extended to arbitrarily unstructured meshes for effective simulation of incompressible flows. Two test cases, the lid-driven flow in a triangular cavity and flow around a circular cylinder, are carried out for validation. The obtained results are compared with the data available in the literature. Good agreement has been achieved, which demonstrates the effectiveness and reliability of the LBFS in simulating flows on arbitrarily unstructured meshes.

Far-Field Turbulent Vortex-Wake/Exhaust Plume Interaction for Subsonic and HSCT Airplanes

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Adam, Ihab; Wong, Tin-Chee

1996-01-01

Computational study of the far-field turbulent vortex-wake/exhaust plume interaction for subsonic and high speed civil transport (HSCT) airplanes is carried out. The Reynolds-averaged Navier-Stokes (NS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The two-equation shear stress transport model of Menter is implemented with the NS solver for turbulent-flow calculation. For the far-field study, the computations of vortex-wake interaction with the exhaust plume of a single engine of a Boeing 727 wing in a holding condition and two engines of an HSCT in a cruise condition are carried out using overlapping zonal method for several miles downstream. These results are obtained using the computer code FTNS3D. The results of the subsonic flow of this code are compared with those of a parabolized NS solver known as the UNIWAKE code.

THREE-DIMENSIONAL MODELING OF THE DYNAMICS OF THERAPEUTIC ULTRASOUND CONTRAST AGENTS

PubMed Central

Hsiao, Chao-Tsung; Lu, Xiaozhen; Chahine, Georges

2010-01-01

A 3-D thick-shell contrast agent dynamics model was developed by coupling a finite volume Navier-Stokes solver and a potential boundary element method flow solver to simulate the dynamics of thick-shelled contrast agents subjected to pressure waves. The 3-D model was validated using a spherical thick-shell model validated by experimental observations. We then used this model to study shell break-up during nonspherical deformations resulting from multiple contrast agent interaction or the presence of a nearby solid wall. Our simulations indicate that the thick viscous shell resists the contrast agent from forming a re-entrant jet, as normally observed for an air bubble oscillating near a solid wall. Instead, the shell thickness varies significantly from location to location during the dynamics, and this could lead to shell break-up caused by local shell thinning and stretching. PMID:20950929

Tsunami modelling with adaptively refined finite volume methods

USGS Publications Warehouse

LeVeque, R.J.; George, D.L.; Berger, M.J.

2011-01-01

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. Wayne

1992-01-01

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

NASA Technical Reports Server (NTRS)

Singh, Jatinder; Taylor, Stephen

1997-01-01

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

Numerical investigation of self-sustained oscillations in the flow over the spiked blunt body

NASA Astrophysics Data System (ADS)

Konstantin, Babarykin

2018-05-01

Numerical simulation of the supersonic turbulent flow around spike-tipped cylindrical body is carried out. The self-sustained oscillating flow picture is studied. For the simulations the ANSYS Fluent finite-volume solver is employed, the calculations are performed mainly for 2d axisymmetric case, and some simulations are made in 3d version. The freestream Mach number is 2,22, the cases of sharp and obtuse needle of different length are considered. The numerical results are obtained using different turbulence models, are compared with experimental data.

Numerical simulation of the transonic flow past the blunted wedge in the diverging channel

NASA Astrophysics Data System (ADS)

Ryabinin, Anatoly

2018-05-01

Positions of shock waves in the 2D channel with a blunted wedge are studied numerically. Solutions of the Euler equations are obtained with finite-volume solver SU2 for 15 variants of channel geometry. Numerical simulations reveal a considerable hysteresis in the shock wave position versus the supersonic Mach number given at the inlet. In the certain range of inlet Mach number, there are asymmetrical solutions of the equations. Small change in the geometry of the channel leads to shift of boundaries of the hysteresis range.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.

2016-03-01

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Celeris: A GPU-accelerated open source software with a Boussinesq-type wave solver for real-time interactive simulation and visualization

NASA Astrophysics Data System (ADS)

Tavakkol, Sasan; Lynett, Patrick

2017-08-01

In this paper, we introduce an interactive coastal wave simulation and visualization software, called Celeris. Celeris is an open source software which needs minimum preparation to run on a Windows machine. The software solves the extended Boussinesq equations using a hybrid finite volume-finite difference method and supports moving shoreline boundaries. The simulation and visualization are performed on the GPU using Direct3D libraries, which enables the software to run faster than real-time. Celeris provides a first-of-its-kind interactive modeling platform for coastal wave applications and it supports simultaneous visualization with both photorealistic and colormapped rendering capabilities. We validate our software through comparison with three standard benchmarks for non-breaking and breaking waves.

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation.

PubMed

Xie, Yang; Ying, Jinyong; Xie, Dexuan

2017-03-30

SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a PBE web server. SMPBS is designed with a dynamic, mobile-friendly user interface, and features easily accessible help text, asynchronous data submission, and an interactive, hardware-accelerated molecular visualization viewer based on the 3Dmol.js library. In particular, the viewer allows computed electrostatics to be directly mapped onto an irregular triangular mesh of a molecular surface. Due to this functionality and the fast SMPBE finite element solvers, the web server is very efficient in the calculation and visualization of electrostatics. In addition, SMPBE is reconstructed using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by SMPBE are optimal in the sense of minimizing the objective electrostatic free energy. SMPBS is available at the URL: smpbs.math.uwm.edu © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Gupta, K. K. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

Comparing Split and Unsplit Numerical Methods for Simulating Low and High Mach Number Turbulent Flows in Xrage

NASA Astrophysics Data System (ADS)

Saenz, Juan; Grinstein, Fernando; Dolence, Joshua; Rauenzahn, Rick; Masser, Thomas; Francois, Marianne; LANL Team

2017-11-01

We report progress in evaluating an unsplit hydrodynamic solver being implemented in the radiation adaptive grid Eulerian (xRAGE) code, and compare to a split scheme. xRage is a Eulerian hydrodynamics code used for implicit large eddy simulations (ILES) of multi-material, multi-physics flows where low and high Mach number (Ma) processes and instabilities interact and co-exist. The hydrodynamic solver in xRAGE uses a directionally split, second order Godunov, finite volume (FV) scheme. However, a standard, unsplit, Godunov-type FV scheme with 2nd and 3rd order reconstruction options, low Ma correction and a variety of Riemann solvers has recently become available. To evaluate the hydrodynamic solvers for turbulent low Ma flows, we use simulations of the Taylor Green Vortex (TGV), where there is a transition to turbulence via vortex stretching and production of small-scale eddies. We also simulate a high-low Ma shock-tube flow, where a shock passing over a perturbed surface generates a baroclinic Richtmyer-Meshkov instability (RMI); after the shock has passed, the turbulence in the accelerated interface region resembles Rayleigh Taylor (RT) instability. We compare turbulence spectra and decay in simulated TGV flows, and we present progress in simulating the high-low Ma RMI-RT flow. LANL is operated by LANS LLC for the U.S. DOE NNSA under Contract No. DE-AC52-06NA25396.

plasmaFoam: An OpenFOAM framework for computational plasma physics and chemistry

NASA Astrophysics Data System (ADS)

Venkattraman, Ayyaswamy; Verma, Abhishek Kumar

2016-09-01

As emphasized in the 2012 Roadmap for low temperature plasmas (LTP), scientific computing has emerged as an essential tool for the investigation and prediction of the fundamental physical and chemical processes associated with these systems. While several in-house and commercial codes exist, with each having its own advantages and disadvantages, a common framework that can be developed by researchers from all over the world will likely accelerate the impact of computational studies on advances in low-temperature plasma physics and chemistry. In this regard, we present a finite volume computational toolbox to perform high-fidelity simulations of LTP systems. This framework, primarily based on the OpenFOAM solver suite, allows us to enhance our understanding of multiscale plasma phenomenon by performing massively parallel, three-dimensional simulations on unstructured meshes using well-established high performance computing tools that are widely used in the computational fluid dynamics community. In this talk, we will present preliminary results obtained using the OpenFOAM-based solver suite with benchmark three-dimensional simulations of microplasma devices including both dielectric and plasma regions. We will also discuss the future outlook for the solver suite.

Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barker, Andrew T.; Benson, Thomas R.; Lee, Chak Shing

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Verriere, M.; Dubray, N.; ...

2015-11-30

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle amore » realistic calculation of fission dynamics.« less

Parallel Three-Dimensional Computation of Fluid Dynamics and Fluid-Structure Interactions of Ram-Air Parachutes

NASA Technical Reports Server (NTRS)

Tezduyar, Tayfun E.

1998-01-01

This is a final report as far as our work at University of Minnesota is concerned. The report describes our research progress and accomplishments in development of high performance computing methods and tools for 3D finite element computation of aerodynamic characteristics and fluid-structure interactions (FSI) arising in airdrop systems, namely ram-air parachutes and round parachutes. This class of simulations involves complex geometries, flexible structural components, deforming fluid domains, and unsteady flow patterns. The key components of our simulation toolkit are a stabilized finite element flow solver, a nonlinear structural dynamics solver, an automatic mesh moving scheme, and an interface between the fluid and structural solvers; all of these have been developed within a parallel message-passing paradigm.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Parallel Solver for H(div) Problems Using Hybridization and AMG

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Chak S.; Vassilevski, Panayot S.

2016-01-15

In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examinedmore » through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.« less

Multidisciplinary Simulation Acceleration using Multiple Shared-Memory Graphical Processing Units

NASA Astrophysics Data System (ADS)

Kemal, Jonathan Yashar

For purposes of optimizing and analyzing turbomachinery and other designs, the unsteady Favre-averaged flow-field differential equations for an ideal compressible gas can be solved in conjunction with the heat conduction equation. We solve all equations using the finite-volume multiple-grid numerical technique, with the dual time-step scheme used for unsteady simulations. Our numerical solver code targets CUDA-capable Graphical Processing Units (GPUs) produced by NVIDIA. Making use of MPI, our solver can run across networked compute notes, where each MPI process can use either a GPU or a Central Processing Unit (CPU) core for primary solver calculations. We use NVIDIA Tesla C2050/C2070 GPUs based on the Fermi architecture, and compare our resulting performance against Intel Zeon X5690 CPUs. Solver routines converted to CUDA typically run about 10 times faster on a GPU for sufficiently dense computational grids. We used a conjugate cylinder computational grid and ran a turbulent steady flow simulation using 4 increasingly dense computational grids. Our densest computational grid is divided into 13 blocks each containing 1033x1033 grid points, for a total of 13.87 million grid points or 1.07 million grid points per domain block. To obtain overall speedups, we compare the execution time of the solver's iteration loop, including all resource intensive GPU-related memory copies. Comparing the performance of 8 GPUs to that of 8 CPUs, we obtain an overall speedup of about 6.0 when using our densest computational grid. This amounts to an 8-GPU simulation running about 39.5 times faster than running than a single-CPU simulation.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Numerical and experimental investigation of the 3D free surface flow in a model Pelton turbine

NASA Astrophysics Data System (ADS)

Fiereder, R.; Riemann, S.; Schilling, R.

2010-08-01

This investigation focuses on the numerical and experimental analysis of the 3D free surface flow in a Pelton turbine. In particular, two typical flow conditions occurring in a full scale Pelton turbine - a configuration with a straight inlet as well as a configuration with a 90 degree elbow upstream of the nozzle - are considered. Thereby, the effect of secondary flow due to the 90 degree bending of the upstream pipe on the characteristics of the jet is explored. The hybrid flow field consists of pure liquid flow within the conduit and free surface two component flow of the liquid jet emerging out of the nozzle into air. The numerical results are validated against experimental investigations performed in the laboratory of the Institute of Fluid Mechanics (FLM). For the numerical simulation of the flow the in-house unstructured fully parallelized finite volume solver solver3D is utilized. An advanced interface capturing model based on the classic Volume of Fluid method is applied. In order to ensure sharp interface resolution an additional convection term is added to the transport equation of the volume fraction. A collocated variable arrangement is used and the set of non-linear equations, containing fluid conservation equations and model equations for turbulence and volume fraction, are solved in a segregated manner. For pressure-velocity coupling the SIMPLE and PISO algorithms are implemented. Detailed analysis of the observed flow patterns in the jet and of the jet geometry are presented.

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

DOE PAGES

Li, Fei; Yu, Peicheng; Xu, Xinlu; ...

2017-01-12

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k 1|, while keepsmore » additional main NCI modes well outside the range of physical interest with higher |k 1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.« less

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

NASA Astrophysics Data System (ADS)

Li, Fei; Yu, Peicheng; Xu, Xinlu; Fiuza, Frederico; Decyk, Viktor K.; Dalichaouch, Thamine; Davidson, Asher; Tableman, Adam; An, Weiming; Tsung, Frank S.; Fonseca, Ricardo A.; Lu, Wei; Mori, Warren B.

2017-05-01

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1 ˆ direction). We show that this eliminates the main NCI modes with moderate |k1 | , while keeps additional main NCI modes well outside the range of physical interest with higher |k1 | . These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1 ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Fei; Yu, Peicheng; Xu, Xinlu

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k 1|, while keepsmore » additional main NCI modes well outside the range of physical interest with higher |k 1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.« less

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Unstructured Euler flow solutions using hexahedral cell refinement

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1991-01-01

An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

A multigrid solver for the semiconductor equations

NASA Technical Reports Server (NTRS)

Bachmann, Bernhard

1993-01-01

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Comparison of cell centered and cell vertex scheme in the calculation of high speed compressible flows

NASA Astrophysics Data System (ADS)

Rahman, Syazila; Yusoff, Mohd. Zamri; Hasini, Hasril

2012-06-01

This paper describes the comparison between the cell centered scheme and cell vertex scheme in the calculation of high speed compressible flow properties. The calculation is carried out using Computational Fluid Dynamic (CFD) in which the mass, momentum and energy equations are solved simultaneously over the flow domain. The geometry under investigation consists of a Binnie and Green convergent-divergent nozzle and structured mesh scheme is implemented throughout the flow domain. The finite volume CFD solver employs second-order accurate central differencing scheme for spatial discretization. In addition, the second-order accurate cell-vertex finite volume spatial discretization is also introduced in this case for comparison. The multi-stage Runge-Kutta time integration is implemented for solving a set of non-linear governing equations with variables stored at the vertices. Artificial dissipations used second and fourth order terms with pressure switch to detect changes in pressure gradient. This is important to control the solution stability and capture shock discontinuity. The result is compared with experimental measurement and good agreement is obtained for both cases.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE PAGES

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia; ...

2015-11-01

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

A hybrid incremental projection method for thermal-hydraulics applications

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; Berndt, Markus; Francois, Marianne M.; Stagg, Alan K.; Xia, Yidong; Luo, Hong

2016-07-01

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

Finite Beta Boundary Magnetic Fields of NCSX

NASA Astrophysics Data System (ADS)

Grossman, A.; Kaiser, T.; Mioduszewski, P.

2004-11-01

The magnetic field between the plasma surface and wall of the National Compact Stellarator (NCSX), which uses quasi-symmetry to combine the best features of the tokamak and stellarator in a configuration of low aspect ratio is mapped via field line tracing in a range of finite beta in which part of the rotational transform is generated by the bootstrap current. We adopt the methodology developed for W7-X, in which an equilibrium solution is computed by an inverse equilibrium solver based on an energy minimizing variational moments code, VMEC2000[1], which solves directly for the shape of the flux surfaces given the external coils and their currents as well as a bootstrap current provided by a separate transport calculation. The VMEC solution and the Biot-Savart vacuum fields are coupled to the magnetic field solver for finite-beta equilibrium (MFBE2001)[2] code to determine the magnetic field on a 3D grid over a computational domain. It is found that the edge plasma is more stellarator-like, with a complex 3D structure, and less like the ordered 2D symmetric structure of a tokamak. The field lines make a transition from ergodically covering a surface to ergodically covering a volume, as the distance from the last closed magnetic surface is increased. The results are compared with the PIES[3] calculations. [1] S.P. Hirshman et al. Comput. Phys. Commun. 43 (1986) 143. [2] E. Strumberger, et al. Nucl. Fusion 42 (2002) 827. [3] A.H. Reiman and H.S. Greenside, Comput. Phys. Commun. 43, 157 (1986).

A hybrid incremental projection method for thermal-hydraulics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

A hybrid incremental projection method for thermal-hydraulics applications

DOE PAGES

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; ...

2016-07-01

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

GPU computing of compressible flow problems by a meshless method with space-filling curves

NASA Astrophysics Data System (ADS)

Ma, Z. H.; Wang, H.; Pu, S. H.

2014-04-01

A graphic processing unit (GPU) implementation of a meshless method for solving compressible flow problems is presented in this paper. Least-square fit is used to discretize the spatial derivatives of Euler equations and an upwind scheme is applied to estimate the flux terms. The compute unified device architecture (CUDA) C programming model is employed to efficiently and flexibly port the meshless solver from CPU to GPU. Considering the data locality of randomly distributed points, space-filling curves are adopted to re-number the points in order to improve the memory performance. Detailed evaluations are firstly carried out to assess the accuracy and conservation property of the underlying numerical method. Then the GPU accelerated flow solver is used to solve external steady flows over aerodynamic configurations. Representative results are validated through extensive comparisons with the experimental, finite volume or other available reference solutions. Performance analysis reveals that the running time cost of simulations is significantly reduced while impressive (more than an order of magnitude) speedups are achieved.

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

NASA Astrophysics Data System (ADS)

Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie; Bohm, Marvin

2018-07-01

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme).

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

SPIREs: A Finite-Difference Frequency-Domain electromagnetic solver for inhomogeneous magnetized plasma cylinders

NASA Astrophysics Data System (ADS)

Melazzi, D.; Curreli, D.; Manente, M.; Carlsson, J.; Pavarin, D.

2012-06-01

We present SPIREs (plaSma Padova Inhomogeneous Radial Electromagnetic solver), a Finite-Difference Frequency-Domain (FDFD) electromagnetic solver in one dimension for the rapid calculation of the electromagnetic fields and the deposited power of a large variety of cylindrical plasma problems. The two Maxwell wave equations have been discretized using a staggered Yee mesh along the radial direction of the cylinder, and Fourier transformed along the other two dimensions and in time. By means of this kind of discretization, we have found that mode-coupling of fast and slow branches can be fully resolved without singularity issues that flawed other well-established methods in the past. Fields are forced by an antenna placed at a given distance from the plasma. The plasma can be inhomogeneous, finite-temperature, collisional, magnetized and multi-species. Finite-temperature Maxwellian effects, comprising Landau and cyclotron damping, have been included by means of the plasma Z dispersion function. Finite Larmor radius effects have been neglected. Radial variations of the plasma parameters are taken into account, thus extending the range of applications to a large variety of inhomogeneous plasma systems. The method proved to be fast and reliable, with accuracy depending on the spatial grid size. Two physical examples are reported: fields in a forced vacuum waveguide with the antenna inside, and forced plasma oscillations in the helicon radiofrequency range.

Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

NASA Astrophysics Data System (ADS)

Raman, Venkatramanan

A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.

An Aeroelastic Analysis of a Thin Flexible Membrane

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.

2007-01-01

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2 N + 1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier-Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).

Development of new vibration energy flow analysis software and its applications to vehicle systems

NASA Astrophysics Data System (ADS)

Kim, D.-J.; Hong, S.-Y.; Park, Y.-H.

2005-09-01

The Energy flow analysis (EFA) offers very promising results in predicting the noise and vibration responses of system structures in medium-to-high frequency ranges. We have developed the Energy flow finite element method (EFFEM) based software, EFADSC++ R4, for the vibration analysis. The software can analyze the system structures composed of beam, plate, spring-damper, rigid body elements and many other components developed, and has many useful functions in analysis. For convenient use of the software, the main functions of the whole software are modularized into translator, model-converter, and solver. The translator module makes it possible to use finite element (FE) model for the vibration analysis. The model-converter module changes FE model into energy flow finite element (EFFE) model, and generates joint elements to cover the vibrational attenuation in the complex structures composed of various elements and can solve the joint element equations by using the wave tra! nsmission approach very quickly. The solver module supports the various direct and iterative solvers for multi-DOF structures. The predictions of vibration for real vehicles by using the developed software were performed successfully.

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

An unstructured mesh arbitrary Lagrangian-Eulerian unsteady incompressible flow solver and its application to insect flight aerodynamics

NASA Astrophysics Data System (ADS)

Su, Xiaohui; Cao, Yuanwei; Zhao, Yong

2016-06-01

In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.

Development of a Regional Structured and Unstructured Grid Methodology for Chemically Reactive Turbulent Flows

NASA Astrophysics Data System (ADS)

Stefanski, Douglas Lawrence

A finite volume method for solving the Reynolds Averaged Navier-Stokes (RANS) equations on unstructured hybrid grids is presented. Capabilities for handling arbitrary mixtures of reactive gas species within the unstructured framework are developed. The modeling of turbulent effects is carried out via the 1998 Wilcox k -- o model. This unstructured solver is incorporated within VULCAN -- a multi-block structured grid code -- as part of a novel patching procedure in which non-matching interfaces between structured blocks are replaced by transitional unstructured grids. This approach provides a fully-conservative alternative to VULCAN's non-conservative patching methods for handling such interfaces. In addition, the further development of the standalone unstructured solver toward large-eddy simulation (LES) applications is also carried out. Dual time-stepping using a Crank-Nicholson formulation is added to recover time-accuracy, and modeling of sub-grid scale effects is incorporated to provide higher fidelity LES solutions for turbulent flows. A switch based on the work of Ducros, et al., is implemented to transition from a monotonicity-preserving flux scheme near shocks to a central-difference method in vorticity-dominated regions in order to better resolve small-scale turbulent structures. The updated unstructured solver is used to carry out large-eddy simulations of a supersonic constrained mixing layer.

Moving Computational Domain Method and Its Application to Flow Around a High-Speed Car Passing Through a Hairpin Curve

NASA Astrophysics Data System (ADS)

Watanabe, Koji; Matsuno, Kenichi

This paper presents a new method for simulating flows driven by a body traveling with neither restriction on motion nor a limit of a region size. In the present method named 'Moving Computational Domain Method', the whole of the computational domain including bodies inside moves in the physical space without the limit of region size. Since the whole of the grid of the computational domain moves according to the movement of the body, a flow solver of the method has to be constructed on the moving grid system and it is important for the flow solver to satisfy physical and geometric conservation laws simultaneously on moving grid. For this issue, the Moving-Grid Finite-Volume Method is employed as the flow solver. The present Moving Computational Domain Method makes it possible to simulate flow driven by any kind of motion of the body in any size of the region with satisfying physical and geometric conservation laws simultaneously. In this paper, the method is applied to the flow around a high-speed car passing through a hairpin curve. The distinctive flow field driven by the car at the hairpin curve has been demonstrated in detail. The results show the promising feature of the method.

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers.

PubMed

Cooper, Christopher D; Bardhan, Jaydeep P; Barba, L A

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

NASA Astrophysics Data System (ADS)

Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is on the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

NASA Astrophysics Data System (ADS)

Schwing, Alan Michael

For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable comparisons across a range of regimes. Unsteady and steady applications are considered in both subsonic and supersonic flows. Inviscid and viscous simulations achieve similar results at a much reduced cost when employing dynamic mesh adaptation. Several techniques for guiding adaptation are compared. Detailed analysis of statistics from the instrumented solver enable understanding of the costs associated with adaptation. Adaptive mesh refinement shows promise for the test cases presented here. It can be considerably faster than using conventional grids and provides accurate results. The procedures for adapting the grid are light-weight enough to not require significant computational time and yield significant reductions in grid size.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Accelerating solutions of one-dimensional unsteady PDEs with GPU-based swept time-space decomposition

NASA Astrophysics Data System (ADS)

Magee, Daniel J.; Niemeyer, Kyle E.

2018-03-01

The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems require simulations with a level of resolution difficult to achieve in reasonable amounts of time-even in effectively parallelized solvers. Though the scale of the problem relative to available computing power is the greatest impediment to accelerating these applications, significant performance gains can be achieved through careful attention to the details of memory communication and access. The swept time-space decomposition rule reduces communication between sub-domains by exhausting the domain of influence before communicating boundary values. Here we present a GPU implementation of the swept rule, which modifies the algorithm for improved performance on this processing architecture by prioritizing use of private (shared) memory, avoiding interblock communication, and overwriting unnecessary values. It shows significant improvement in the execution time of finite-difference solvers for one-dimensional unsteady PDEs, producing speedups of 2 - 9 × for a range of problem sizes, respectively, compared with simple GPU versions and 7 - 300 × compared with parallel CPU versions. However, for a more sophisticated one-dimensional system of equations discretized with a second-order finite-volume scheme, the swept rule performs 1.2 - 1.9 × worse than a standard implementation for all problem sizes.

Clustering and pasta phases in nuclear density functional theory

DOE PAGES

Schuetrumpf, Bastian; Zhang, Chunli; Nazarewicz, Witold

2017-05-23

Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we usemore » the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schuetrumpf, Bastian; Zhang, Chunli; Nazarewicz, Witold

Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we usemore » the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.« less

Fluid-structure interaction with the entropic lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.

2018-02-01

We propose a fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show the validity of the proposed scheme for various challenging setups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with a finite element method (FEM) solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces.

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE PAGES

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; ...

2017-06-29

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

A comparison of upwind schemes for computation of three-dimensional hypersonic real-gas flows

NASA Technical Reports Server (NTRS)

Gerbsch, R. A.; Agarwal, R. K.

1992-01-01

The method of Suresh and Liou (1992) is extended, and the resulting explicit noniterative upwind finite-volume algorithm is applied to the integration of 3D parabolized Navier-Stokes equations to model 3D hypersonic real-gas flowfields. The solver is second-order accurate in the marching direction and employs flux-limiters to make the algorithm second-order accurate, with total variation diminishing in the cross-flow direction. The algorithm is used to compute hypersonic flow over a yawed cone and over the Ames All-Body Hypersonic Vehicle. The solutions obtained agree well with other computational results and with experimental data.

Euler Flow Computations on Non-Matching Unstructured Meshes

NASA Technical Reports Server (NTRS)

Gumaste, Udayan

1999-01-01

Advanced fluid solvers to predict aerodynamic performance-coupled treatment of multiple fields are described. The interaction between the fluid and structural components in the bladed regions of the engine is investigated with respect to known blade failures caused by either flutter or forced vibrations. Methods are developed to describe aeroelastic phenomena for internal flows in turbomachinery by accounting for the increased geometric complexity, mutual interaction between adjacent structural components and presence of thermal and geometric loading. The computer code developed solves the full three dimensional aeroelastic problem of-stage. The results obtained show that flow computations can be performed on non-matching finite-volume unstructured meshes with second order spatial accuracy.

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.

2015-02-01

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L 2 norm.

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

NASA Technical Reports Server (NTRS)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

NASA Technical Reports Server (NTRS)

Sun, Xian-He; Zhuang, Yu

1997-01-01

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Wang, Jun; Luo, Ray

2009-01-01

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Unstructured Mesh Methods for the Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Bibb, K. L. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite element algorithm for the solution of the viscous compressible flow equations which can solve flows all the way down to the incompressible limit and that can use higher order (quadratic) approximations leading to highly accurate answers, and 3) and iterative algebraic multigrid solution techniques.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

A new approach to flow simulation in highly heterogeneous porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rame, M.; Killough, J.E.

In this paper, applications are presented for a new numerical method - operator splittings on multiple grids (OSMG) - devised for simulations in heterogeneous porous media. A coarse-grid, finite-element pressure solver is interfaced with a fine-grid timestepping scheme. The CPU time for the pressure solver is greatly reduced and concentration fronts have minimal numerical dispersion.

BIGHORN Computational Fluid Dynamics Theory, Methodology, and Code Verification & Validation Benchmark Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Andrs, David; Martineau, Richard Charles

This document presents the theoretical background for a hybrid finite-element / finite-volume fluid flow solver, namely BIGHORN, based on the Multiphysics Object Oriented Simulation Environment (MOOSE) computational framework developed at the Idaho National Laboratory (INL). An overview of the numerical methods used in BIGHORN are discussed and followed by a presentation of the formulation details. The document begins with the governing equations for the compressible fluid flow, with an outline of the requisite constitutive relations. A second-order finite volume method used for solving the compressible fluid flow problems is presented next. A Pressure-Corrected Implicit Continuous-fluid Eulerian (PCICE) formulation for timemore » integration is also presented. The multi-fluid formulation is being developed. Although multi-fluid is not fully-developed, BIGHORN has been designed to handle multi-fluid problems. Due to the flexibility in the underlying MOOSE framework, BIGHORN is quite extensible, and can accommodate both multi-species and multi-phase formulations. This document also presents a suite of verification & validation benchmark test problems for BIGHORN. The intent for this suite of problems is to provide baseline comparison data that demonstrates the performance of the BIGHORN solution methods on problems that vary in complexity from laminar to turbulent flows. Wherever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using BIGHORN.« less

Implementation of Finite Rate Chemistry Capability in OVERFLOW

NASA Technical Reports Server (NTRS)

Olsen, M. E.; Venkateswaran, S.; Prabhu, D. K.

2004-01-01

An implementation of both finite rate and equilibrium chemistry have been completed for the OVERFLOW code, a chimera capable, complex geometry flow code widely used to predict transonic flow fields. The implementation builds on the computational efficiency and geometric generality of the solver.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

NASA Astrophysics Data System (ADS)

Schaa, R.; Gross, L.; du Plessis, J.

2016-04-01

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

Static aeroelastic analysis of wings using Euler/Navier-Stokes equations coupled with improved wing-box finite element structures

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; MacMurdy, Dale E.; Kapania, Rakesh K.

1994-01-01

Strong interactions between flow about an aircraft wing and the wing structure can result in aeroelastic phenomena which significantly impact aircraft performance. Time-accurate methods for solving the unsteady Navier-Stokes equations have matured to the point where reliable results can be obtained with reasonable computational costs for complex non-linear flows with shock waves, vortices and separations. The ability to combine such a flow solver with a general finite element structural model is key to an aeroelastic analysis in these flows. Earlier work involved time-accurate integration of modal structural models based on plate elements. A finite element model was developed to handle three-dimensional wing boxes, and incorporated into the flow solver without the need for modal analysis. Static condensation is performed on the structural model to reduce the structural degrees of freedom for the aeroelastic analysis. Direct incorporation of the finite element wing-box structural model with the flow solver requires finding adequate methods for transferring aerodynamic pressures to the structural grid and returning deflections to the aerodynamic grid. Several schemes were explored for handling the grid-to-grid transfer of information. The complex, built-up nature of the wing-box complicated this transfer. Aeroelastic calculations for a sample wing in transonic flow comparing various simple transfer schemes are presented and discussed.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

NASA Astrophysics Data System (ADS)

Kozdon, J. E.; Wilcox, L.

2013-12-01

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

NASA Technical Reports Server (NTRS)

Casper, Jay; Dorrepaal, J. Mark

1990-01-01

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

NASA Astrophysics Data System (ADS)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

Lagrangian transported MDF methods for compressible high speed flows

NASA Astrophysics Data System (ADS)

Gerlinger, Peter

2017-06-01

This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).

Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods

NASA Astrophysics Data System (ADS)

Murillo, J.; García-Navarro, P.

2012-02-01

In this work, the source term discretization in hyperbolic conservation laws with source terms is considered using an approximate augmented Riemann solver. The technique is applied to the shallow water equations with bed slope and friction terms with the focus on the friction discretization. The augmented Roe approximate Riemann solver provides a family of weak solutions for the shallow water equations, that are the basis of the upwind treatment of the source term. This has proved successful to explain and to avoid the appearance of instabilities and negative values of the thickness of the water layer in cases of variable bottom topography. Here, this strategy is extended to capture the peculiarities that may arise when defining more ambitious scenarios, that may include relevant stresses in cases of mud/debris flow. The conclusions of this analysis lead to the definition of an accurate and robust first order finite volume scheme, able to handle correctly transient problems considering frictional stresses in both clean water and debris flow, including in this last case a correct modelling of stopping conditions.

Computational Study of a McDonnell Douglas Single-Stage-to-Orbit Vehicle Concept for Aerodynamic Analysis

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.

1996-01-01

This paper presents the results of a computational flow analysis of the McDonnell Douglas single-stage-to-orbit vehicle concept designated as the 24U. This study was made to determine the aerodynamic characteristics of the vehicle with and without body flaps over an angle of attack range of 20-40 deg. Computations were made at a flight Mach number of 20 at 200,000 ft. altitude with equilibrium air, and a Mach number of 6 with CF4 gas. The software package FELISA (Finite Element Langley imperial College Sawansea Ames) was used for all the computations. The FELISA software consists of unstructured surface and volume grid generators, and inviscid flow solvers with (1) perfect gas option for subsonic, transonic, and low supersonic speeds, and (2) perfect gas, equilibrium air, and CF4 options for hypersonic speeds. The hypersonic flow solvers with equilibrium air and CF4 options were used in the present studies. Results are compared with other computational results and hypersonic CF4 tunnel test data.

Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester.

PubMed

Coughtrie, A R; Borman, D J; Sleigh, P A

2013-06-01

Flow in a gas-lift digester with a central draft-tube was investigated using computational fluid dynamics (CFD) and different turbulence closure models. The k-ω Shear-Stress-Transport (SST), Renormalization-Group (RNG) k-∊, Linear Reynolds-Stress-Model (RSM) and Transition-SST models were tested for a gas-lift loop reactor under Newtonian flow conditions validated against published experimental work. The results identify that flow predictions within the reactor (where flow is transitional) are particularly sensitive to the turbulence model implemented; the Transition-SST model was found to be the most robust for capturing mixing behaviour and predicting separation reliably. Therefore, Transition-SST is recommended over k-∊ models for use in comparable mixing problems. A comparison of results obtained using multiphase Euler-Lagrange and singlephase approaches are presented. The results support the validity of the singlephase modelling assumptions in obtaining reliable predictions of the reactor flow. Solver independence of results was verified by comparing two independent finite-volume solvers (Fluent-13.0sp2 and OpenFOAM-2.0.1). Copyright © 2013 Elsevier Ltd. All rights reserved.

A Direct Numerical Simulation of a Temporally Evolving Liquid-Gas Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Vu, Lam Xuan; Chiodi, Robert; Desjardins, Olivier

2017-11-01

Air-blast atomization occurs when streams of co-flowing high speed gas and low speed liquid shear to form drops. Air-blast atomization has numerous industrial applications from combustion engines in jets to sprays used for medical coatings. The high Reynolds number and dynamic pressure ratio of a realistic air-blast atomization case requires large eddy simulation and the use of multiphase sub-grid scale (SGS) models. A direct numerical simulations (DNS) of a temporally evolving mixing layer is presented to be used as a base case from which future multiphase SGS models can be developed. To construct the liquid-gas mixing layer, half of a channel flow from Kim et al. (JFM, 1987) is placed on top of a static liquid layer that then evolves over time. The DNS is performed using a conservative finite volume incompressible multiphase flow solver where phase tracking is handled with a discretely conservative volume of fluid method. This study presents statistics on velocity and volume fraction at different Reynolds and Weber numbers.

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vincenti, H.; Vay, J. -L.

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Air-structure coupling features analysis of mining contra-rotating axial flow fan cascade

NASA Astrophysics Data System (ADS)

Chen, Q. G.; Sun, W.; Li, F.; Zhang, Y. J.

2013-12-01

The interaction between contra-rotating axial flow fan blade and working gas has been studied by means of establishing air-structure coupling control equation and combining Computational Fluid Dynamics (CFD) and Computational solid mechanics (CSM). Based on the single flow channel model, the Finite Volume Method was used to make the field discrete. Additionally, the SIMPLE algorithm, the Standard k-ε model and the Arbitrary Lagrangian-Eulerian dynamic grids technology were utilized to get the airflow motion by solving the discrete governing equations. At the same time, the Finite Element Method was used to make the field discrete to solve dynamic response characteristics of blade. Based on weak coupling method, data exchange from the fluid solver and the solid solver was processed on the coupling interface. Then interpolation was used to obtain the coupling characteristics. The results showed that the blade's maximum amplitude was on the tip of the last-stage blade and aerodynamic force signal could reflect the blade working conditions to some extent. By analyzing the flow regime in contra-rotating axial flow fan, it could be found that the vortex core region was mainly in the blade surface, the hub and the blade clearance. In those regions, the turbulence intensity was very high. The last-stage blade's operating life is shorter than that of the pre-stage blade due to the fatigue fracture occurs much more easily on the last-stage blade which bears more stress.

Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.

3D Viscous Free-Surface Flow around a Combatant Ship Hull

NASA Astrophysics Data System (ADS)

Pacuraru, Florin; Lungu, Adrian; Maria, Viorel

2009-09-01

The prediction of the total drag experienced by an advancing ship is a complicated problem which requires a thorough understanding of the hydrodynamic forces acting on the hull, the physical processes from which these forces arise and their mutual interaction. A general numerical method to predict the hydrodynamic performance of a twin-propeller combatant ship hull is presented in the paper. For practical reasons, the technique couples a body forces method and a RANS-based finite volume solver to account for the interactions between the hull and the appendages mounted on it: propellers, rudders, shaft lines, bossings and brackets. The chimera approach has been found the most versatile way for grid generation of hull and appendages.

Source fields reconstruction with 3D mapping by means of the virtual acoustic volume concept

NASA Astrophysics Data System (ADS)

Forget, S.; Totaro, N.; Guyader, J. L.; Schaeffer, M.

2016-10-01

This paper presents the theoretical framework of the virtual acoustic volume concept and two related inverse Patch Transfer Functions (iPTF) identification methods (called u-iPTF and m-iPTF depending on the chosen boundary conditions for the virtual volume). They are based on the application of Green's identity on an arbitrary closed virtual volume defined around the source. The reconstruction of sound source fields combines discrete acoustic measurements performed at accessible positions around the source with the modal behavior of the chosen virtual acoustic volume. The mode shapes of the virtual volume can be computed by a Finite Element solver to handle the geometrical complexity of the source. As a result, it is possible to identify all the acoustic source fields at the real surface of an irregularly shaped structure and irrespective of its acoustic environment. The m-iPTF method is introduced for the first time in this paper. Conversely to the already published u-iPTF method, the m-iPTF method needs only acoustic pressure and avoids particle velocity measurements. This paper is focused on its validation, both with numerical computations and by experiments on a baffled oil pan.

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

DOE PAGES

Tezaur, I. K.; Perego, M.; Salinger, A. G.; ...

2015-04-27

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less

PuMA: the Porous Microstructure Analysis software

NASA Astrophysics Data System (ADS)

Ferguson, Joseph C.; Panerai, Francesco; Borner, Arnaud; Mansour, Nagi N.

2018-01-01

The Porous Microstructure Analysis (PuMA) software has been developed in order to compute effective material properties and perform material response simulations on digitized microstructures of porous media. PuMA is able to import digital three-dimensional images obtained from X-ray microtomography or to generate artificial microstructures. PuMA also provides a module for interactive 3D visualizations. Version 2.1 includes modules to compute porosity, volume fractions, and surface area. Two finite difference Laplace solvers have been implemented to compute the continuum tortuosity factor, effective thermal conductivity, and effective electrical conductivity. A random method has been developed to compute tortuosity factors from the continuum to rarefied regimes. Representative elementary volume analysis can be performed on each property. The software also includes a time-dependent, particle-based model for the oxidation of fibrous materials. PuMA was developed for Linux operating systems and is available as a NASA software under a US & Foreign release.

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kong, Bo; Fox, Rodney O.; Feng, Heng

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE PAGES

Kong, Bo; Fox, Rodney O.; Feng, Heng; ...

2017-02-16

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction in shockwave lithotripsy.

PubMed

Wang, Kevin G

2017-10-01

A novel multiphase fluid-solid-coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone-coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1 μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (p max  = 35.0MPa, p min  =- 10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior. Copyright © 2016 John Wiley & Sons, Ltd.

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balsara, Dinshaw S., E-mail: dbalsara@nd.edu; Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp; Garain, Sudip, E-mail: sgarain@nd.edu

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equationsmore » is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.« less

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho

2016-08-01

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge-Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.

A parallel finite-difference method for computational aerodynamics

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain

NASA Astrophysics Data System (ADS)

Ouyang, Chaojun; He, Siming; Xu, Qiang; Luo, Yu; Zhang, Wencheng

2013-03-01

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 1993 and the Nora debris flow in the Italian Alps in 2000, are executed, and the model outputs are compared with published results. It is established that the model predictions agree well with both the analytical solution as well as the field observations.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Three dimensional finite element methods: Their role in the design of DC accelerator systems

NASA Astrophysics Data System (ADS)

Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.

2013-04-01

High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Chen, E-mail: chuang3@fsu.edu

A key element in the density functional embedding theory (DFET) is the embedding potential. We discuss two major issues related to the embedding potential: (1) its non-uniqueness and (2) the numerical difficulty for solving for it, especially for the spin-polarized systems. To resolve the first issue, we extend DFET to finite temperature: all quantities, such as the subsystem densities and the total system’s density, are calculated at a finite temperature. This is a physical extension since materials work at finite temperatures. We show that the embedding potential is strictly unique at T > 0. To resolve the second issue, wemore » introduce an efficient iterative embedding potential solver. We discuss how to relax the magnetic moments in subsystems and how to equilibrate the chemical potentials across subsystems. The solver is robust and efficient for several non-trivial examples, in all of which good quality spin-polarized embedding potentials were obtained. We also demonstrate the solver on an extended periodic system: iron body-centered cubic (110) surface, which is related to the modeling of the heterogeneous catalysis involving iron, such as the Fischer-Tropsch and the Haber processes. This work would make it efficient and accurate to perform embedding simulations of some challenging material problems, such as the heterogeneous catalysis and the defects of complicated spin configurations in electronic materials.« less

Fluid-structure interaction of turbulent boundary layer over a compliant surface

NASA Astrophysics Data System (ADS)

Anantharamu, Sreevatsa; Mahesh, Krishnan

2016-11-01

Turbulent flows induce unsteady loads on surfaces in contact with them, which affect material stresses, surface vibrations and far-field acoustics. We are developing a numerical methodology to study the coupled interaction of a turbulent boundary layer with the underlying surface. The surface is modeled as a linear elastic solid, while the fluid follows the spatially filtered incompressible Navier-Stokes equations. An incompressible Large Eddy Simulation finite volume flow approach based on the algorithm of Mahesh et al. is used in the fluid domain. The discrete kinetic energy conserving property of the method ensures robustness at high Reynolds number. The linear elastic model in the solid domain is integrated in space using finite element method and in time using the Newmark time integration method. The fluid and solid domain solvers are coupled using both weak and strong coupling methods. Details of the algorithm, validation, and relevant results will be presented. This work is supported by NSWCCD, ONR.

MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

2013-01-01

A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

Nonlinearity Analysis for Efficient Modelling of Long-Term CO2 Storage

NASA Astrophysics Data System (ADS)

Li, Boxiao; Benson, Sally; Tchelepi, Hamdi

2014-05-01

Numerical simulation is widely used to predict the long-term fate of the injected CO2 in a storage formation. Performing large-scale simulations is often limited by the computational speed, where convergence failure of Newton iterations is one of the main bottlenecks. In order to design better numerical schemes and faster nonlinear solvers for modelling long-term CO2 storage, the nonlinearity in the simulations has to be analysed thoroughly, and the cause of convergence failures has to be identified clearly. We focus on the transport of CO2 and water in the presence of viscous, gravity, and heterogeneous capillary forces. We investigate the nonlinearity of the discrete transport equation obtained from finite-volume discretization with single-point phase-based upstream weighting, which is the industry standard. In particular, we study the discretized flux expressed as a function of saturations at the upstream and downstream (with respect to the total velocity) of each gridblock interface. We analyse the locations and complexity of the unit-flux, zero-flux, and inflection lines on the numerical flux. The unit- and zero-flux lines, referred to as kinks, correspond to a change of the flow direction, which often occurs when strong buoyancy and capillarity are present. We observe that these kinks and inflection lines are major sources of nonlinear convergence difficulties. We find that kinks create more challenges than inflection lines, especially when their locations depend on both the upstream and downstream saturations of the total velocity. When the flow is driven by viscous and gravity forces (e.g., during CO2 injection), one kink will occur in the numerical flux and its location depends only on the upstream saturation. However, when capillarity is dominant (e.g., during the post-injection period), two kinks will occur and both are functions of the upstream and downstream saturations, causing severe convergence difficulties particularly when heterogeneity is present. Our analysis of the numerical flux theoretically describes the cause of the convergence failures for simulating long-term CO2 storage. This understanding provides useful guidance in designing numerical schemes and nonlinear solvers that overcome the convergence bottlenecks. For example, to reduce the nonlinearity introduced by the two kinks in the presence of capillarity, we modify the method of Cances (2009) to discretize the capillary flux. Consequently, only one kink will occur even for coupled viscous, buoyancy, and heterogeneous capillary forces, and the kink depends only on the upstream saturation of the total velocity. An efficient nonlinear solver that is a significant refinement of the works of Jenny et al. (2009) and Wang and Tchelepi (2013) has also been proposed and demonstrated. References [1] C. Cances. Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities. ESAIM:M2AN., 43, 973-1001, (2009). [2] P. Jenny, H.A. Tchelepi, and S.H. Lee. Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions. J. Comput. Phys., 228, 7497-7512, (2009). [3] X. Wang and H.A. Tchelepi. Trust-region based solver for nonlinear transport in heterogeneous porous media. J. Comput. Phys., 253, 114-137, (2013).

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

DOE PAGES

Schuetrumpf, B.; Nazarewicz, W.

2015-10-21

Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at subsaturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100-m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite three-dimensional boxes assuming periodic boundary conditions. The resulting solutions are affected by spurious finite-size effects. To remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice quantum chromodynamics applications. In this work, we study the effectivenessmore » of TABC in the context of pasta phase simulations within nuclear density functional theory. We demonstrated that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range. Future applications will include the TABC extension of the adaptive multiresolution 3D Hartree-Fock solver and Hartree-Fock-Bogoliubov TABC applications to superfluid pasta phases and complex nucleonic topologies as in fission.« less

Optimization of tissue physical parameters for accurate temperature estimation from finite-element simulation of radiofrequency ablation.

PubMed

Subramanian, Swetha; Mast, T Douglas

2015-10-07

Computational finite element models are commonly used for the simulation of radiofrequency ablation (RFA) treatments. However, the accuracy of these simulations is limited by the lack of precise knowledge of tissue parameters. In this technical note, an inverse solver based on the unscented Kalman filter (UKF) is proposed to optimize values for specific heat, thermal conductivity, and electrical conductivity resulting in accurately simulated temperature elevations. A total of 15 RFA treatments were performed on ex vivo bovine liver tissue. For each RFA treatment, 15 finite-element simulations were performed using a set of deterministically chosen tissue parameters to estimate the mean and variance of the resulting tissue ablation. The UKF was implemented as an inverse solver to recover the specific heat, thermal conductivity, and electrical conductivity corresponding to the measured area of the ablated tissue region, as determined from gross tissue histology. These tissue parameters were then employed in the finite element model to simulate the position- and time-dependent tissue temperature. Results show good agreement between simulated and measured temperature.

Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture

NASA Astrophysics Data System (ADS)

Meng, Chunfang

2017-03-01

We present Defmod, an open source (linear) finite element code that enables us to efficiently model the crustal deformation due to (quasi-)static and dynamic loadings, poroelastic flow, viscoelastic flow and frictional fault slip. Ali (2015) provides the original code introducing an implicit solver for (quasi-)static problem, and an explicit solver for dynamic problem. The fault constraint is implemented via Lagrange Multiplier. Meng (2015) combines these two solvers into a hybrid solver that uses failure criteria and friction laws to adaptively switch between the (quasi-)static state and dynamic state. The code is capable of modeling episodic fault rupture driven by quasi-static loadings, e.g. due to reservoir fluid withdraw or injection. Here, we focus on benchmarking the Defmod results against some establish results.

Thermal radiation heat transfer in participating media by finite volume discretization using collimated beam incidence

NASA Astrophysics Data System (ADS)

Harijishnu, R.; Jayakumar, J. S.

2017-09-01

The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.

Development of mapped stress-field boundary conditions based on a Hill-type muscle model.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Flavin, R; Ivanković, A

2014-09-01

Forces generated in the muscles and tendons actuate the movement of the skeleton. Accurate estimation and application of these musculotendon forces in a continuum model is not a trivial matter. Frequently, musculotendon attachments are approximated as point forces; however, accurate estimation of local mechanics requires a more realistic application of musculotendon forces. This paper describes the development of mapped Hill-type muscle models as boundary conditions for a finite volume model of the hip joint, where the calculated muscle fibres map continuously between attachment sites. The applied muscle forces are calculated using active Hill-type models, where input electromyography signals are determined from gait analysis. Realistic muscle attachment sites are determined directly from tomography images. The mapped muscle boundary conditions, implemented in a finite volume structural OpenFOAM (ESI-OpenCFD, Bracknell, UK) solver, are employed to simulate the mid-stance phase of gait using a patient-specific natural hip joint, and a comparison is performed with the standard point load muscle approach. It is concluded that physiological joint loading is not accurately represented by simplistic muscle point loading conditions; however, when contact pressures are of sole interest, simplifying assumptions with regard to muscular forces may be valid. Copyright © 2014 John Wiley & Sons, Ltd.

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Clawpack: Building an open source ecosystem for solving hyperbolic PDEs

USGS Publications Warehouse

Iverson, Richard M.; Mandli, K.T.; Ahmadia, Aron J.; Berger, M.J.; Calhoun, Donna; George, David L.; Hadjimichael, Y.; Ketcheson, David I.; Lemoine, Grady L.; LeVeque, Randall J.

2016-01-01

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model. Clawpack: building an open source ecosystem for solving hyperbolic PDEs.

On the supersonic three-dimensional flow over an axisymmetric body with a forward-facing annular step

NASA Astrophysics Data System (ADS)

Simonenko, Mikhail; Zubkov, Alexander; Kuzmin, Alexander

2018-05-01

The 3D turbulent supersonic flow over a body of revolution at various angles of attack α is studied numerically and experimentally. The body surface incorporates a forward-facing step near its midpart and a nose cone. Experiments were conducted in a wind tunnel of the Research Institute of Mechanics, Moscow State University, at the Mach number of 3 for various lengths L of the distance between the step and nose cone. Numerical simulations were performed with a finite-volume solver ANSYS CFX-15. The study reveals bands of α and L in which the pressure on the leeward side of step abruptly increases and exceeds the pressure on the windward side.

Direct numerical simulations of mack-mode damping on porous coated cones

NASA Astrophysics Data System (ADS)

Lüdeke, H.; Wartemann, V.

2013-06-01

The flow field over a 3 degree blunt cone is investigated with respect to a hypersonic stability analysis of the boundary-layer flow at Mach 6 with porous as well as smooth walls by comparing local direct numerical simulations (DNS) and linear stability theory (LST) data. The original boundary-layer profile is generated by a finite volume solver, using shock capturing techniques to generate an axisymmetric flow field. Local boundary-layer profiles are extracted from this flow field and hypersonic Mack-modes are superimposed for cone-walls with and without a porous surface used as a passive transition-reduction device. Special care is taken of curvature effects of the wall on the mode development over smooth and porous walls.

Multi-physics optimization of three-dimensional microvascular polymeric components

NASA Astrophysics Data System (ADS)

Aragón, Alejandro M.; Saksena, Rajat; Kozola, Brian D.; Geubelle, Philippe H.; Christensen, Kenneth T.; White, Scott R.

2013-01-01

This work discusses the computational design of microvascular polymeric materials, which aim at mimicking the behavior found in some living organisms that contain a vascular system. The optimization of the topology of the embedded three-dimensional microvascular network is carried out by coupling a multi-objective constrained genetic algorithm with a finite-element based physics solver, the latter validated through experiments. The optimization is carried out on multiple conflicting objective functions, namely the void volume fraction left by the network, the energy required to drive the fluid through the network and the maximum temperature when the material is subjected to thermal loads. The methodology presented in this work results in a viable alternative for the multi-physics optimization of these materials for active-cooling applications.

A narrow-band k-distribution model with single mixture gas assumption for radiative flows

NASA Astrophysics Data System (ADS)

Jo, Sung Min; Kim, Jae Won; Kwon, Oh Joon

2018-06-01

In the present study, the narrow-band k-distribution (NBK) model parameters for mixtures of H2O, CO2, and CO are proposed by utilizing the line-by-line (LBL) calculations with a single mixture gas assumption. For the application of the NBK model to radiative flows, a radiative transfer equation (RTE) solver based on a finite-volume method on unstructured meshes was developed. The NBK model and the RTE solver were verified by solving two benchmark problems including the spectral radiance distribution emitted from one-dimensional slabs and the radiative heat transfer in a truncated conical enclosure. It was shown that the results are accurate and physically reliable by comparing with available data. To examine the applicability of the methods to realistic multi-dimensional problems in non-isothermal and non-homogeneous conditions, radiation in an axisymmetric combustion chamber was analyzed, and then the infrared signature emitted from an aircraft exhaust plume was predicted. For modeling the plume flow involving radiative cooling, a flow-radiation coupled procedure was devised in a loosely coupled manner by adopting a Navier-Stokes flow solver based on unstructured meshes. It was shown that the predicted radiative cooling for the combustion chamber is physically more accurate than other predictions, and is as accurate as that by the LBL calculations. It was found that the infrared signature of aircraft exhaust plume can also be obtained accurately, equivalent to the LBL calculations, by using the present narrow-band approach with a much improved numerical efficiency.

Fluid-structure interaction of a pulsatile flow with an aortic valve model: A combined experimental and numerical study.

PubMed

Sigüenza, Julien; Pott, Desiree; Mendez, Simon; Sonntag, Simon J; Kaufmann, Tim A S; Steinseifer, Ulrich; Nicoud, Franck

2018-04-01

The complex fluid-structure interaction problem associated with the flow of blood through a heart valve with flexible leaflets is investigated both experimentally and numerically. In the experimental test rig, a pulse duplicator generates a pulsatile flow through a biomimetic rigid aortic root where a model of aortic valve with polymer flexible leaflets is implanted. High-speed recordings of the leaflets motion and particle image velocimetry measurements were performed together to investigate the valve kinematics and the dynamics of the flow. Large eddy simulations of the same configuration, based on a variant of the immersed boundary method, are also presented. A massively parallel unstructured finite-volume flow solver is coupled with a finite-element solid mechanics solver to predict the fluid-structure interaction between the unsteady flow and the valve. Detailed analysis of the dynamics of opening and closure of the valve are conducted, showing a good quantitative agreement between the experiment and the simulation regarding the global behavior, in spite of some differences regarding the individual dynamics of the valve leaflets. A multicycle analysis (over more than 20 cycles) enables to characterize the generation of turbulence downstream of the valve, showing similar flow features between the experiment and the simulation. The flow transitions to turbulence after peak systole, when the flow starts to decelerate. Fluctuations are observed in the wake of the valve, with maximum amplitude observed at the commissure side of the aorta. Overall, a very promising experiment-vs-simulation comparison is shown, demonstrating the potential of the numerical method. Copyright © 2017 John Wiley & Sons, Ltd.

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

Numerical analysis of the three-dimensional swirling flow in centrifugal compressor volutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayder, E.; Van den Braembussche, R.

1994-07-01

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge-Kutta time-stepping scheme. Themore » artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.« less

Perturbation theory and numerical modelling of weakly and moderately nonlinear incompressible Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Herrmann, M.; Velikovich, A. L.; Abarzhi, S. I.

2014-10-01

A study of incompressible two-dimensional Richtmyer-Meshkov instability by means of high-order Eulerian perturbation theory and numerical simulations is reported. Nonlinear corrections to Richtmyer's impulsive formula for the bubble and spike growth rates have been calculated analytically for arbitrary Atwood number and an explicit formula has been obtained for it in the Boussinesq limit. Conditions for early-time acceleration and deceleration of the bubble and the spike have been derived. In our simulations we have solved 2D unsteady Navier-Stokes equations for immiscible incompressible fluids using the finite volume fractional step flow solver NGA developed by, coupled to the level set based interface solver LIT,. The impact of small amounts of viscosity and surface tension on the RMI flow dynamics is studied numerically. Simulation results are compared to the theory to demonstrate successful code verification and highlight the influence of the theory's ideal inviscid flow assumption. Theoretical time histories of the interface curvature at the bubble and spike tip and the profiles of vertical and horizontal velocities have been favorably compared to simulation results, which converge to the theoretical predictions as the Reynolds and Weber numbers are increased. Work supported by the US DOE/NNSA.

Discontinuous Galerkin (DG) Method for solving time dependent convection-diffusion type temperature equation : Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

NASA Astrophysics Data System (ADS)

He, Y.; Puckett, E. G.; Billen, M. I.; Kellogg, L. H.

2016-12-01

For a convection-dominated system, like convection in the Earth's mantle, accurate modeling of the temperature field in terms of the interaction between convective and diffusive processes is one of the most common numerical challenges. In the geodynamics community using Finite Element Method (FEM) with artificial entropy viscosity is a popular approach to resolve this difficulty, but introduce numerical diffusion. The extra artificial viscosity added into the temperature system will not only oversmooth the temperature field where the convective process dominates, but also change the physical properties by increasing the local material conductivity, which will eventually change the local conservation of energy. Accurate modeling of temperature is especially important in the mantle, where material properties are strongly dependent on temperature. In subduction zones, for example, the rheology of the cold sinking slab depends nonlinearly on the temperature, and physical processes such as slab detachment, rollback, and melting all are sensitively dependent on temperature and rheology. Therefore methods that overly smooth the temperature may inaccurately represent the physical processes governing subduction, lithospheric instabilities, plume generation and other aspects of mantle convection. Here we present a method for modeling the temperature field in mantle dynamics simulations using a new solver implemented in the ASPECT software. The new solver for the temperature equation uses a Discontinuous Galerkin (DG) approach, which combines features of both finite element and finite volume methods, and is particularly suitable for problems satisfying the conservation law, and the solution has a large variation locally. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a local discrete maximum principle in order to eliminate the overshoots and undershoots in the temperature locally. To demonstrate the capabilities of this new method we present benchmark results (e.g., falling sphere), and a simple subduction models with kinematic surface boundary condition. To evaluate the trade-offs in computational speed and solution accuracy we present results for the same benchmarks using the Finite Element entropy viscosity method available in ASPECT.

Application of Biot-Savart Solver to Predict Axis Switching Phenomena in Finite-Span Vortices Expelled from a Synthetic Jet

NASA Astrophysics Data System (ADS)

Straccia, Joseph; Farnsworth, John

2016-11-01

The Biot-Savart law is a simple yet powerful inviscid and incompressible relationship between the velocity induced at a point and the circulation, orientation and distance of separation of a vortex line. The authors have developed an algorithm for obtaining numerical solutions of the Biot-Savart relationship to predict the self-induced velocity on a vortex line of arbitrary shape. In this work the Biot-Savart solver was used to predict the self-induced propagation of non-circular, finite-span vortex rings expelled from synthetic jets with rectangular orifices of varying aspect ratios. The solver's prediction of the time varying shape of the vortex ring and frequency of axis switching was then compared with Particle Image Velocimetry (PIV) data from a synthetic jet expelled into a quiescent flow i.e. zero cross flow condition. Conclusions about the effectiveness and limitations of this simple, inviscid relationship are drawn from this experimental data. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1144083.

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

NASA Technical Reports Server (NTRS)

Datta, Anubhav; Johnson, Wayne R.

2009-01-01

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

NASA Astrophysics Data System (ADS)

Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk

2018-05-01

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

Study of dynamic fluid-structure coupling with application to human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Faber, Justin; Bodony, Daniel

2013-11-01

Two-dimensional direct numerical simulations of a compressible, viscous fluid interacting with a non-linear, viscoelastic solid are used to study the generation of the human voice. The vocal fold (VF) tissues are modeled using a finite-strain fractional derivative constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The viscoelastic solver is validated through in-house experiments using Agarose Gel, a human tissue simulant, undergoing static and harmonic deformation measured with load cell and optical diagnostics. The phonation simulations highlight the role tissue nonlinearity and viscosity play in the glottal jet dynamics and in the radiated sound. Supported by the National Science Foundation (CAREER award number 1150439).

An Approximate Axisymmetric Viscous Shock Layer Aeroheating Method for Three-Dimensional Bodies

NASA Technical Reports Server (NTRS)

Brykina, Irina G.; Scott, Carl D.

1998-01-01

A technique is implemented for computing hypersonic aeroheating, shear stress, and other flow properties on the windward side of a three-dimensional (3D) blunt body. The technique uses a 2D/axisymmetric flow solver modified by scale factors for a, corresponding equivalent axisymmetric body. Examples are given in which a 2D solver is used to calculate the flow at selected meridional planes on elliptic paraboloids in reentry flight. The report describes the equations and the codes used to convert the body surface parameters into input used to scale the 2D viscous shock layer equations in the axisymmetric viscous shock layer code. Very good agreement is obtained with solutions to finite rate chemistry 3D thin viscous shock layer equations for a finite rate catalytic body.

Array-based Hierarchical Mesh Generation in Parallel

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2015-11-03

In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Computer-Aided Transformation of PDE Models: Languages, Representations, and a Calculus of Operations

DTIC Science & Technology

2016-01-05

discretizations . We maintain that what is clear at the mathematical level should be equally clear in computation. In this small STIR project, we separate the...concerns of describing and discretizing such models by defining an input language representing PDE, including steady-state and tran- sient, linear and...solvers, such as [8, 9], focused on the solvers themselves and particular families of discretizations (e. g. finite elements), and now it is natural to

Finite difference elastic wave modeling with an irregular free surface using ADER scheme

NASA Astrophysics Data System (ADS)

Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.

2015-06-01

In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

Backward Raman Amplification in the Long-wavelength Infrared

DTIC Science & Technology

2016-12-29

mechanism for generating intense, broad bandwidth, long-wavelength infrared radiation. An electromagnetic finite-difference time-domain simulation...couples a finite-difference time-domain electromagnetic solver with a collisional, relativistic cold fluid plasma model [30]. The simulation domain... electromagnetic simulations coupled to a relativistic cold fluid plasma model with electron- ion collisions. Using a pump pulse that could be generated by a CO

Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence.

PubMed

Soltwisch, Victor; Hönicke, Philipp; Kayser, Yves; Eilbracht, Janis; Probst, Jürgen; Scholze, Frank; Beckhoff, Burkhard

2018-03-29

The geometry of a Si3N4 lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing-wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing-wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.

Particle transport in the human respiratory tract: formulation of a nodal inverse distance weighted Eulerian-Lagrangian transport and implementation of the Wind-Kessel algorithm for an oral delivery.

PubMed

Kannan, Ravishekar; Guo, Peng; Przekwas, Andrzej

2016-06-01

This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational finite volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's finite volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted Eulerian-Lagrangian formulation to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a finite number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Wakefield Simulation of CLIC PETS Structure Using Parallel 3D Finite Element Time-Domain Solver T3P

DOE Office of Scientific and Technical Information (OSTI.GOV)

Candel, A.; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic time-domain code T3P. Higher-order Finite Element methods on conformal unstructured meshes and massively parallel processing allow unprecedented simulation accuracy for wakefield computations and simulations of transient effects in realistic accelerator structures. Applications include simulation of wakefield damping in the Compact Linear Collider (CLIC) power extraction and transfer structure (PETS).

Development of a parallel FE simulator for modeling the whole trans-scale failure process of rock from meso- to engineering-scale

NASA Astrophysics Data System (ADS)

Li, Gen; Tang, Chun-An; Liang, Zheng-Zhao

2017-01-01

Multi-scale high-resolution modeling of rock failure process is a powerful means in modern rock mechanics studies to reveal the complex failure mechanism and to evaluate engineering risks. However, multi-scale continuous modeling of rock, from deformation, damage to failure, has raised high requirements on the design, implementation scheme and computation capacity of the numerical software system. This study is aimed at developing the parallel finite element procedure, a parallel rock failure process analysis (RFPA) simulator that is capable of modeling the whole trans-scale failure process of rock. Based on the statistical meso-damage mechanical method, the RFPA simulator is able to construct heterogeneous rock models with multiple mechanical properties, deal with and represent the trans-scale propagation of cracks, in which the stress and strain fields are solved for the damage evolution analysis of representative volume element by the parallel finite element method (FEM) solver. This paper describes the theoretical basis of the approach and provides the details of the parallel implementation on a Windows - Linux interactive platform. A numerical model is built to test the parallel performance of FEM solver. Numerical simulations are then carried out on a laboratory-scale uniaxial compression test, and field-scale net fracture spacing and engineering-scale rock slope examples, respectively. The simulation results indicate that relatively high speedup and computation efficiency can be achieved by the parallel FEM solver with a reasonable boot process. In laboratory-scale simulation, the well-known physical phenomena, such as the macroscopic fracture pattern and stress-strain responses, can be reproduced. In field-scale simulation, the formation process of net fracture spacing from initiation, propagation to saturation can be revealed completely. In engineering-scale simulation, the whole progressive failure process of the rock slope can be well modeled. It is shown that the parallel FE simulator developed in this study is an efficient tool for modeling the whole trans-scale failure process of rock from meso- to engineering-scale.

An Open Source Framework for Coupled Hydro-Hydrogeo-Chemical Systems in Catchment Research

NASA Astrophysics Data System (ADS)

Delfs, J.; Sachse, A.; Gayler, S.; Grathwohl, P.; He, W.; Jang, E.; Kalbacher, T.; Klein, C.; Kolditz, O.; Maier, U.; Priesack, E.; Rink, K.; Selle, B.; Shao, H.; Singh, A. K.; Streck, T.; Sun, Y.; Wang, W.; Walther, M.

2013-12-01

This poster presents an open-source framework designed to assist water scientists in the study of catchment hydraulic functions with associated chemical processes, e.g. contaminant degradation, plant nutrient turnover. The model successfully calculates the feedbacks between surface water, subsurface water and air in standard benchmarks. In specific model applications to heterogeneous catchments, subsurface water is driven by density variations and runs through double porous media. Software codes of water science are tightly coupled by iteration, namely the Storm Water Management Model (SWMM) for urban runoff, Expert-N for simulating water fluxes and nutrient turnover in agricultural and forested soils, and OpenGeoSys (OGS) for groundwater. The coupled model calculates flow of hydrostatic shallow water over the land surface with finite volume and difference methods. The flow equations for water in the porous subsurface are discretized in space with finite elements. Chemical components are transferred through 1D, 2D or 3D watershed representations with advection-dispersion solvers or, as an alternative, random walk particle tracking. A transport solver can be in sequence with a chemical solver, e.g. PHREEQ-C, BRNS, additionally. Besides coupled partial differential equations, the concept of hydrological response units is employed in simulations at regional scale with scarce data availability. In this case, a conceptual hydrological model, specifically the Jena Adaptable Modeling System (JAMS), passes groundwater recharge through a software interface into OGS, which solves the partial differential equations of groundwater flow. Most components of the modeling framework are open source and can be modified for individual purposes. Applications range from temperate climate regions in Germany (Ammer catchment and Hessian Ried) to arid regions in the Middle East (Oman and Dead See). Some of the presented examples originate from intensively monitored research sites of the WESS research centre and the monitoring initiative TERENO. Other examples originate from the IWAS project on integrated water resources management. The model applications are primarily concerned with groundwater resources, which are endangered by overexploitation, intrusion of saltwater, and nitrate loads.

NASA Workshop on Computational Structural Mechanics 1987, part 1

NASA Technical Reports Server (NTRS)

Sykes, Nancy P. (Editor)

1989-01-01

Topics in Computational Structural Mechanics (CSM) are reviewed. CSM parallel structural methods, a transputer finite element solver, architectures for multiprocessor computers, and parallel eigenvalue extraction are among the topics discussed.

Application of a Third Order Upwind Scheme to Viscous Flow over Clean and Iced Wings

NASA Technical Reports Server (NTRS)

Bangalore, A.; Phaengsook, N.; Sankar, L. N.

1994-01-01

A 3-D compressible Navier-Stokes solver has been developed and applied to 3-D viscous flow over clean and iced wings. This method uses a third order accurate finite volume scheme with flux difference splitting to model the inviscid fluxes, and second order accurate symmetric differences to model the viscous terms. The effects of turbulence are modeled using a Kappa-epsilon model. In the vicinity of the sold walls the kappa and epsilon values are modeled using Gorski's algebraic model. Sampling results are presented for surface pressure distributions, for untapered swept clean and iced wings made of NACA 0012 airfoil sections. The leading edge of these sections is modified using a simulated ice shape. Comparisons with experimental data are given.

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1992-01-01

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samaddar, Debasmita; Coster, D. P.; Bonnin, X.

We show that numerical modelling of edge plasma physics may be successfully parallelized in time. The parareal algorithm has been employed for this purpose and the SOLPS code package coupling the B2.5 finite-volume fluid plasma solver with the kinetic Monte-Carlo neutral code Eirene has been used as a test bed. The complex dynamics of the plasma and neutrals in the scrape-off layer (SOL) region makes this a unique application. It is demonstrated that a significant computational gain (more than an order of magnitude) may be obtained with this technique. The use of the IPS framework for event-based parareal implementation optimizesmore » resource utilization and has been shown to significantly contribute to the computational gain.« less

Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1989-01-01

An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

DOE PAGES

Samaddar, Debasmita; Coster, D. P.; Bonnin, X.; ...

2017-07-31

We show that numerical modelling of edge plasma physics may be successfully parallelized in time. The parareal algorithm has been employed for this purpose and the SOLPS code package coupling the B2.5 finite-volume fluid plasma solver with the kinetic Monte-Carlo neutral code Eirene has been used as a test bed. The complex dynamics of the plasma and neutrals in the scrape-off layer (SOL) region makes this a unique application. It is demonstrated that a significant computational gain (more than an order of magnitude) may be obtained with this technique. The use of the IPS framework for event-based parareal implementation optimizesmore » resource utilization and has been shown to significantly contribute to the computational gain.« less

Improved 3-D turbomachinery CFD algorithm

NASA Technical Reports Server (NTRS)

Janus, J. Mark; Whitfield, David L.

1988-01-01

The building blocks of a computer algorithm developed for the time-accurate flow analysis of rotating machines are described. The flow model is a finite volume method utilizing a high resolution approximate Riemann solver for interface flux definitions. This block LU implicit numerical scheme possesses apparent unconditional stability. Multi-block composite gridding is used to orderly partition the field into a specified arrangement. Block interfaces, including dynamic interfaces, are treated such as to mimic interior block communication. Special attention is given to the reduction of in-core memory requirements by placing the burden on secondary storage media. Broad applicability is implied, although the results presented are restricted to that of an even blade count configuration. Several other configurations are presently under investigation, the results of which will appear in subsequent publications.

Comments regarding two upwind methods for solving two-dimensional external flows using unstructured grids

NASA Technical Reports Server (NTRS)

Kleb, W. L.

1994-01-01

Steady flow over the leading portion of a multicomponent airfoil section is studied using computational fluid dynamics (CFD) employing an unstructured grid. To simplify the problem, only the inviscid terms are retained from the Reynolds-averaged Navier-Stokes equations - leaving the Euler equations. The algorithm is derived using the finite-volume approach, incorporating explicit time-marching of the unsteady Euler equations to a time-asymptotic, steady-state solution. The inviscid fluxes are obtained through either of two approximate Riemann solvers: Roe's flux difference splitting or van Leer's flux vector splitting. Results are presented which contrast the solutions given by the two flux functions as a function of Mach number and grid resolution. Additional information is presented concerning code verification techniques, flow recirculation regions, convergence histories, and computational resources.

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Recent advances in the modeling of plasmas with the Particle-In-Cell methods

NASA Astrophysics Data System (ADS)

Vay, Jean-Luc; Lehe, Remi; Vincenti, Henri; Godfrey, Brendan; Lee, Patrick; Haber, Irv

2015-11-01

The Particle-In-Cell (PIC) approach is the method of choice for self-consistent simulations of plasmas from first principles. The fundamentals of the PIC method were established decades ago but improvements or variations are continuously being proposed. We report on several recent advances in PIC related algorithms, including: (a) detailed analysis of the numerical Cherenkov instability and its remediation, (b) analytic pseudo-spectral electromagnetic solvers in Cartesian and cylindrical (with azimuthal modes decomposition) geometries, (c) arbitrary-order finite-difference and generalized pseudo-spectral Maxwell solvers, (d) novel analysis of Maxwell's solvers' stencil variation and truncation, in application to domain decomposition strategies and implementation of Perfectly Matched Layers in high-order and pseudo-spectral solvers. Work supported by US-DOE Contracts DE-AC02-05CH11231 and the US-DOE SciDAC program ComPASS. Used resources of NERSC, supported by US-DOE Contract DE-AC02-05CH11231.

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

StagBL : A Scalable, Portable, High-Performance Discretization and Solver Layer for Geodynamic Simulation

NASA Astrophysics Data System (ADS)

Sanan, P.; Tackley, P. J.; Gerya, T.; Kaus, B. J. P.; May, D.

2017-12-01

StagBL is an open-source parallel solver and discretization library for geodynamic simulation,encapsulating and optimizing operations essential to staggered-grid finite volume Stokes flow solvers.It provides a parallel staggered-grid abstraction with a high-level interface in C and Fortran.On top of this abstraction, tools are available to define boundary conditions and interact with particle systems.Tools and examples to efficiently solve Stokes systems defined on the grid are provided in small (direct solver), medium (simple preconditioners), and large (block factorization and multigrid) model regimes.By working directly with leading application codes (StagYY, I3ELVIS, and LaMEM) and providing an API and examples to integrate with others, StagBL aims to become a community tool supplying scalable, portable, reproducible performance toward novel science in regional- and planet-scale geodynamics and planetary science.By implementing kernels used by many research groups beneath a uniform abstraction layer, the library will enable optimization for modern hardware, thus reducing community barriers to large- or extreme-scale parallel simulation on modern architectures. In particular, the library will include CPU-, Manycore-, and GPU-optimized variants of matrix-free operators and multigrid components.The common layer provides a framework upon which to introduce innovative new tools.StagBL will leverage p4est to provide distributed adaptive meshes, and incorporate a multigrid convergence analysis tool.These options, in addition to a wealth of solver options provided by an interface to PETSc, will make the most modern solution techniques available from a common interface. StagBL in turn provides a PETSc interface, DMStag, to its central staggered grid abstraction.We present public version 0.5 of StagBL, including preliminary integration with application codes and demonstrations with its own demonstration application, StagBLDemo. Central to StagBL is the notion of an uninterrupted pipeline from toy/teaching codes to high-performance, extreme-scale solves. StagBLDemo replicates the functionality of an advanced MATLAB-style regional geodynamics code, thus providing users with a concrete procedure to exceed the performance and scalability limitations of smaller-scale tools.

Study of the adaptive refinement on an open source 2D shallow-water flow solver using quadtree grid for flash flood simulations.

NASA Astrophysics Data System (ADS)

Kirstetter, G.; Popinet, S.; Fullana, J. M.; Lagrée, P. Y.; Josserand, C.

2015-12-01

The full resolution of shallow-water equations for modeling flash floods may have a high computational cost, so that majority of flood simulation softwares used for flood forecasting uses a simplification of this model : 1D approximations, diffusive or kinematic wave approximations or exotic models using non-physical free parameters. These kind of approximations permit to save a lot of computational time by sacrificing in an unquantified way the precision of simulations. To reduce drastically the cost of such 2D simulations by quantifying the lost of precision, we propose a 2D shallow-water flow solver built with the open source code Basilisk1, which is using adaptive refinement on a quadtree grid. This solver uses a well-balanced central-upwind scheme, which is at second order in time and space, and treats the friction and rain terms implicitly in finite volume approach. We demonstrate the validity of our simulation on the case of the flood of Tewkesbury (UK) occurred in July 2007, as shown on Fig. 1. On this case, a systematic study of the impact of the chosen criterium for adaptive refinement is performed. The criterium which has the best computational time / precision ratio is proposed. Finally, we present the power law giving the computational time in respect to the maximum resolution and we show that this law for our 2D simulation is close to the one of 1D simulation, thanks to the fractal dimension of the topography. [1] http://basilisk.fr/

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

PubMed Central

Veijola, Timo; Råback, Peter

2007-01-01

We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

DTIC Science & Technology

2016-12-01

support both mode-based structural representations and time-dependent, nonlinear finite element structural dynamics. This interim report describes...Adaptation, & Sensitivity Toolkit • Elasticity, heat transfer, & compressible flow • Adjoint solver for sensitivity analysis • High-order finite elements ...PROGRAM ELEMENT NUMBER 62201F 6. AUTHOR(S) Richard D. Snyder 5d. PROJECT NUMBER 2401 5e. TASK NUMBER N/A 5f. WORK UNIT NUMBER Q1FS 7

Application of an Upwind High Resolution Finite-Differencing Scheme and Multigrid Method in Steady-State Incompressible Flow Simulations

NASA Technical Reports Server (NTRS)

Yang, Cheng I.; Guo, Yan-Hu; Liu, C.- H.

1996-01-01

The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.

Fuel Optimal, Finite Thrust Guidance Methods to Circumnavigate with Lighting Constraints

NASA Astrophysics Data System (ADS)

Prince, E. R.; Carr, R. W.; Cobb, R. G.

This paper details improvements made to the authors' most recent work to find fuel optimal, finite-thrust guidance to inject an inspector satellite into a prescribed natural motion circumnavigation (NMC) orbit about a resident space object (RSO) in geosynchronous orbit (GEO). Better initial guess methodologies are developed for the low-fidelity model nonlinear programming problem (NLP) solver to include using Clohessy- Wiltshire (CW) targeting, a modified particle swarm optimization (PSO), and MATLAB's genetic algorithm (GA). These initial guess solutions may then be fed into the NLP solver as an initial guess, where a different NLP solver, IPOPT, is used. Celestial lighting constraints are taken into account in addition to the sunlight constraint, ensuring that the resulting NMC also adheres to Moon and Earth lighting constraints. The guidance is initially calculated given a fixed final time, and then solutions are also calculated for fixed final times before and after the original fixed final time, allowing mission planners to choose the lowest-cost solution in the resulting range which satisfies all constraints. The developed algorithms provide computationally fast and highly reliable methods for determining fuel optimal guidance for NMC injections while also adhering to multiple lighting constraints.

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Jorgenson, Philip C. E.

2007-01-01

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Finite-volume WENO scheme for viscous compressible multicomponent flows

PubMed Central

Coralic, Vedran; Colonius, Tim

2014-01-01

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358

Finite-volume WENO scheme for viscous compressible multicomponent flows.

PubMed

Coralic, Vedran; Colonius, Tim

2014-10-01

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.

Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers

NASA Technical Reports Server (NTRS)

Yarrow, Maurice; Vastano, John A.; Lomax, Harvard

1992-01-01

Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

Application of Aeroelastic Solvers Based on Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Srivastava, Rakesh

2001-01-01

The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors and turbines.

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strongmore » laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to increase the local character in phase-space of the numerical scheme, by considering multiscale reconstruction with more compact support and by replacing the semi-Lagrangian method with more local - in space - numerical scheme as compact finite difference schemes, discontinuous-Galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques.« less

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

High-Performance Java Codes for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Riley, Christopher; Chatterjee, Siddhartha; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2001-01-01

The computational science community is reluctant to write large-scale computationally -intensive applications in Java due to concerns over Java's poor performance, despite the claimed software engineering advantages of its object-oriented features. Naive Java implementations of numerical algorithms can perform poorly compared to corresponding Fortran or C implementations. To achieve high performance, Java applications must be designed with good performance as a primary goal. This paper presents the object-oriented design and implementation of two real-world applications from the field of Computational Fluid Dynamics (CFD): a finite-volume fluid flow solver (LAURA, from NASA Langley Research Center), and an unstructured mesh adaptation algorithm (2D_TAG, from NASA Ames Research Center). This work builds on our previous experience with the design of high-performance numerical libraries in Java. We examine the performance of the applications using the currently available Java infrastructure and show that the Java version of the flow solver LAURA performs almost within a factor of 2 of the original procedural version. Our Java version of the mesh adaptation algorithm 2D_TAG performs within a factor of 1.5 of its original procedural version on certain platforms. Our results demonstrate that object-oriented software design principles are not necessarily inimical to high performance.

Two-dimensional computational modeling of high-speed transient flow in gun tunnel

NASA Astrophysics Data System (ADS)

Mohsen, A. M.; Yusoff, M. Z.; Hasini, H.; Al-Falahi, A.

2018-03-01

In this work, an axisymmetric numerical model was developed to investigate the transient flow inside a 7-meter-long free piston gun tunnel. The numerical solution of the gun tunnel was carried out using the commercial solver Fluent. The governing equations of mass, momentum, and energy were discretized using the finite volume method. The dynamic zone of the piston was modeled as a rigid body, and its motion was coupled with the hydrodynamic forces from the flow solution based on the six-degree-of-freedom solver. A comparison of the numerical data with the theoretical calculations and experimental measurements of a ground-based gun tunnel facility showed good agreement. The effects of parameters such as working gases and initial pressure ratio on the test conditions in the facility were examined. The pressure ratio ranged from 10 to 50, and gas combinations of air-air, helium-air, air-nitrogen, and air-CO2 were used. The results showed that steady nozzle reservoir conditions can be maintained for a longer duration when the initial conditions across the diaphragm are adjusted. It was also found that the gas combination of helium-air yielded the highest shock wave strength and speed, but a longer test time was achieved in the test section when using the CO2 test gas.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1994-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1993-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Analysis of Asymmetric Aircraft Aerodynamics Due to an Experimental Wing Glove

NASA Technical Reports Server (NTRS)

Hartshorn, Fletcher

2011-01-01

Aerodynamic computational fluid dynamics analysis of a wing glove attached to one wing of a business jet is presented and discussed. A wing glove placed on only one wing will produce asymmetric aerodynamic effects that will result in overall changes in the forces and moments acting on the aircraft. These changes, referred to as deltas, need to be determined and quantified to ensure that the wing glove does not have a significant effect on the aircraft flight characteristics. TRANAIR (Calmar Research Corporation, Cato, New York), a nonlinear full potential solver, and Star-CCM+ (CD-adapco, Melville, New York), a finite volume full Reynolds-averaged Navier-Stokes computational fluid dynamics solver, are used to analyze a full aircraft with and without the glove at a variety of flight conditions, aircraft configurations, and angles of attack and sideslip. Changes in the aircraft lift, drag, and side force along with roll, pitch, and yaw are presented. Span lift and moment distributions are also presented for a more detailed look at the effects of the glove on the aircraft. Aerodynamic flow phenomena due to the addition of the glove are discussed. Results show that the glove produces only small changes in the aerodynamic forces and moments acting on the aircraft, most of which are insignificant.

Improved Regional Seismic Event Locations Using 3-D Velocity Models

DTIC Science & Technology

1999-12-15

regional velocity model to estimate event hypocenters. Travel times for the regional phases are calculated using a sophisticated eikonal finite...can greatly improve estimates of event locations. Our algorithm calculates travel times using a finite difference approximation of the eikonal ...such as IASP91 or J-B. 3-D velocity models require more sophisticated travel time modeling routines; thus, we use a 3-D eikonal equation solver

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

A stochastic-dynamic model for global atmospheric mass field statistics

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.; Kalnay-Rivas, E.

1981-01-01

A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations.

Surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow

NASA Astrophysics Data System (ADS)

Yang, Xiaofeng; Gui, Yewei; Tang, Wei; Du, Yanxia; Liu, Lei; Xiao, Guangming; Wei, Dong

2018-06-01

This paper deals with the surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow. An interface condition with finite-rate thermochemistry was established to balance the three-dimensional Navier-Stokes solver and TPS thermal response solver, and a series of coupled simulations of chemical non-equilibrium aerothermodynamics and structure heat transfer with various surface catalycities were performed for hypersonic Mars entries. The analysis of surface thermochemistry reveals that the surface chemical reactions have great contribution to aerodynamic heating, and the temperature-dependence of finite-rate catalysis highly influences the evolution of the coupling aerodynamic heating in the coupling process. For fixed free stream parameters with proper catalytic excitation energy, a "leap" phenomenon of the TPS-coupled heat flux with the coupling time appears in the initial stage of the coupling process, due to the strong thermochemical effects on the TPS surface.

Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach

NASA Astrophysics Data System (ADS)

Cervone, A.; Manservisi, S.; Scardovelli, R.

2010-09-01

A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions

NASA Astrophysics Data System (ADS)

Exl, Lukas

2017-12-01

An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall computation error is driven by the convergence of the finite Fourier series of the density. For smooth and fast-decaying densities the proposed method will be spectrally accurate. The method scales with O(N log N) operations, where N is the total number of discretization points in the Cartesian grid. The majority of the computational costs come from fast Fourier transforms (FFT), which makes it ideal for GPU computation. Several numerical computations on CPU and GPU validate the method and show efficiency and convergence behavior. Tests are performed using the Vienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU and GPU is provided to the interested community.

Application specific serial arithmetic arrays

NASA Technical Reports Server (NTRS)

Winters, K.; Mathews, D.; Thompson, T.

1990-01-01

High performance systolic arrays of serial-parallel multiplier elements may be rapidly constructed for specific applications by applying hardware description language techniques to a library of full-custom CMOS building blocks. Single clock pre-charged circuits have been implemented for these arrays at clock rates in excess of 100 Mhz using economical 2-micron (minimum feature size) CMOS processes, which may be quickly configured for a variety of applications. A number of application-specific arrays are presented, including a 2-D convolver for image processing, an integer polynomial solver, and a finite-field polynomial solver.

Immersed boundary method for Boltzmann model kinetic equations

NASA Astrophysics Data System (ADS)

Pekardan, Cem; Chigullapalli, Sruti; Sun, Lin; Alexeenko, Alina

2012-11-01

Three different immersed boundary method formulations are presented for Boltzmann model kinetic equations such as Bhatnagar-Gross-Krook (BGK) and Ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model equations. 1D unsteady IBM solution for a moving piston is compared with the DSMC results and 2D quasi-steady microscale gas damping solutions are verified by a conformal finite volume method solver. Transient analysis for a sinusoidally moving beam is also carried out for the different pressure conditions (1 atm, 0.1 atm and 0.01 atm) corresponding to Kn=0.05,0.5 and 5. Interrelaxation method (Method 2) is shown to provide a faster convergence as compared to the traditional interpolation scheme used in continuum IBM formulations. Unsteady damping in rarefied regime is characterized by a significant phase-lag which is not captured by quasi-steady approximations.

Unsteady RANS/DES analysis of flow around helicopter rotor blades at forword flight conditions

NASA Astrophysics Data System (ADS)

Zhang, Zhenyu; Qian, Yaoru

2018-05-01

In this paper, the complex flows around forward-flying helicopter blades are numerically investigated. Both the Reynolds-averaged Navier-Stokes (RANS) and the Detached Eddy Simulation (DES) methods are used for the analysis of characteristics like local dynamic flow separation, effects of radial sweeping and reversed flow. The flow was solved by a highly efficient finite volume solver with multi-block structured grids. Focusing upon the complexity of the advance ratio effects, above properties are fully recognized. The current results showed significant agreements between both RANS and DES methods at phases with attached flow phases. Detailed information of separating flow near the withdrawal phases are given by DES results. The flow analysis of these blades under reversed flow reveals a significant interaction between the reversed flow and the span-wise sweeping.

External heat transfer predictions in a highly loaded transonic linear turbine guide vane cascade using an upwind biased Navier-Stokes solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gehrer, A.; Jericha, H.

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition formore » the {epsilon}-equation and problems in the stagnation point region.« less

PBEQ-Solver for online visualization of electrostatic potential of biomolecules.

PubMed

Jo, Sunhwan; Vargyas, Miklos; Vasko-Szedlar, Judit; Roux, Benoît; Im, Wonpil

2008-07-01

PBEQ-Solver provides a web-based graphical user interface to read biomolecular structures, solve the Poisson-Boltzmann (PB) equations and interactively visualize the electrostatic potential. PBEQ-Solver calculates (i) electrostatic potential and solvation free energy, (ii) protein-protein (DNA or RNA) electrostatic interaction energy and (iii) pKa of a selected titratable residue. All the calculations can be performed in both aqueous solvent and membrane environments (with a cylindrical pore in the case of membrane). PBEQ-Solver uses the PBEQ module in the biomolecular simulation program CHARMM to solve the finite-difference PB equation of molecules specified by users. Users can interactively inspect the calculated electrostatic potential on the solvent-accessible surface as well as iso-electrostatic potential contours using a novel online visualization tool based on MarvinSpace molecular visualization software, a Java applet integrated within CHARMM-GUI (http://www.charmm-gui.org). To reduce the computational time on the server, and to increase the efficiency in visualization, all the PB calculations are performed with coarse grid spacing (1.5 A before and 1 A after focusing). PBEQ-Solver suggests various physical parameters for PB calculations and users can modify them if necessary. PBEQ-Solver is available at http://www.charmm-gui.org/input/pbeqsolver.

Nonlinear Krylov and moving nodes in the method of lines

NASA Astrophysics Data System (ADS)

Miller, Keith

2005-11-01

We report on some successes and problem areas in the Method of Lines from our work with moving node finite element methods. First, we report on our "nonlinear Krylov accelerator" for the modified Newton's method on the nonlinear equations of our stiff ODE solver. Since 1990 it has been robust, simple, cheap, and automatic on all our moving node computations. We publicize further trials with it here because it should be of great general usefulness to all those solving evolutionary equations. Second, we discuss the need for reliable automatic choice of spatially variable time steps. Third, we discuss the need for robust and efficient iterative solvers for the difficult linearized equations (Jx=b) of our stiff ODE solver. Here, the 1997 thesis of Zulu Xaba has made significant progress.

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

IGA-ADS: Isogeometric analysis FEM using ADS solver

NASA Astrophysics Data System (ADS)

Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav

2017-08-01

In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

PubMed Central

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2016-01-01

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented. PMID:27087702

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

PubMed

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Local Discontinuous Galerkin (LDG) Method for Advection of Active Compositional Fields with Discontinuous Boundaries: Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT

NASA Astrophysics Data System (ADS)

He, Y.; Billen, M. I.; Puckett, E. G.

2015-12-01

Flow in the Earth's mantle is driven by thermo-chemical convection in which the properties and geochemical signatures of rocks vary depending on their origin and composition. For example, tectonic plates are composed of compositionally-distinct layers of crust, residual lithosphere and fertile mantle, while in the lower-most mantle there are large compositionally distinct "piles" with thinner lenses of different material. Therefore, tracking of active or passive fields with distinct compositional, geochemical or rheologic properties is important for incorporating physical realism into mantle convection simulations, and for investigating the long term mixing properties of the mantle. The difficulty in numerically advecting fields arises because they are non-diffusive and have sharp boundaries, and therefore require different methods than usually used for temperature. Previous methods for tracking fields include the marker-chain, tracer particle, and field-correction (e.g., the Lenardic Filter) methods: each of these has different advantages or disadvantages, trading off computational speed with accuracy in tracking feature boundaries. Here we present a method for modeling active fields in mantle dynamics simulations using a new solver implemented in the deal.II package that underlies the ASPECT software. The new solver for the advection-diffusion equation uses a Local Discontinuous Galerkin (LDG) algorithm, which combines features of both finite element and finite volume methods, and is particularly suitable for problems with a dominant first-order term and discontinuities. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a global maximum/minimum. One potential drawback for the LDG method is that the total number of degrees of freedom is larger than the finite element method. To demonstrate the capabilities of this new method we present results for two benchmarks used previously: a falling cube with distinct buoyancy and viscosity, and a Rayleigh-Taylor instability of a compositionally buoyant layer. To evaluate the trade-offs in computational speed and solution accuracy we present results for these same benchmarks using the two field tracking methods available in ASPECT: active tracer particles and the entropy viscosity method.

A stable partitioned FSI algorithm for incompressible flow and deforming beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, L., E-mail: lil19@rpi.edu; Henshaw, W.D., E-mail: henshw@rpi.edu; Banks, J.W., E-mail: banksj3@rpi.edu

2016-05-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame usingmore » two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature.« less

Numerical and experimental analysis of the sedimentation of spherical colloidal suspensions under centrifugal force

NASA Astrophysics Data System (ADS)

Antonopoulou, Evangelia; Rohmann-Shaw, Connor F.; Sykes, Thomas C.; Cayre, Olivier J.; Hunter, Timothy N.; Jimack, Peter K.

2018-03-01

Understanding the sedimentation behaviour of colloidal suspensions is crucial in determining their stability. Since sedimentation rates are often very slow, centrifugation is used to expedite sedimentation experiments. The effect of centrifugal acceleration on sedimentation behaviour is not fully understood. Furthermore, in sedimentation models, interparticle interactions are usually omitted by using the hard-sphere assumption. This work proposes a one-dimensional model for sedimentation using an effective maximum volume fraction, with an extension for sedimentation under centrifugal force. A numerical implementation of the model using an adaptive finite difference solver is described. Experiments with silica suspensions are carried out using an analytical centrifuge. The model is shown to be a good fit with experimental data for 480 nm spherical silica, with the effects of centrifugation at 705 rpm studied. A conversion of data to Earth gravity conditions is proposed, which is shown to recover Earth gravity sedimentation rates well. This work suggests that the effective maximum volume fraction accurately captures interparticle interactions and provides insights into the effect of centrifugation on sedimentation.

Shock interaction with deformable particles using a constrained interface reinitialization scheme

NASA Astrophysics Data System (ADS)

Sridharan, P.; Jackson, T. L.; Zhang, J.; Balachandar, S.; Thakur, S.

2016-02-01

In this paper, we present axisymmetric numerical simulations of shock propagation in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. We use the Mie-Gruneisen equation of state to describe both the medium and the particle. The numerical method is a finite-volume based solver on a Cartesian grid, that allows for multi-material interfaces and shocks, and uses a novel constrained reinitialization scheme to precisely preserve particle mass and volume. We compute the unsteady inviscid drag coefficient as a function of time, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. We also compute the mass-averaged particle pressure and show that the observed oscillations inside the particle are on the particle-acoustic time scale. Finally, we present simplified point-particle models that can be used for macroscale simulations. In the Appendix, we extend the isothermal or isentropic assumption concerning the point-force models to non-ideal equations of state, thus justifying their use for the current problem.

Modelling and simulation of wood chip combustion in a hot air generator system.

PubMed

Rajika, J K A T; Narayana, Mahinsasa

2016-01-01

This study focuses on modelling and simulation of horizontal moving bed/grate wood chip combustor. A standalone finite volume based 2-D steady state Euler-Euler Computational Fluid Dynamics (CFD) model was developed for packed bed combustion. Packed bed combustion of a medium scale biomass combustor, which was retrofitted from wood log to wood chip feeding for Tea drying in Sri Lanka, was evaluated by a CFD simulation study. The model was validated by the experimental results of an industrial biomass combustor for a hot air generation system in tea industry. Open-source CFD tool; OpenFOAM was used to generate CFD model source code for the packed bed combustion and simulated along with an available solver for free board region modelling in the CFD tool. Height of the packed bed is about 20 cm and biomass particles are assumed to be spherical shape with constant surface area to volume ratio. Temperature measurements of the combustor are well agreed with simulation results while gas phase compositions have discrepancies. Combustion efficiency of the validated hot air generator is around 52.2 %.

LLNL contributions to ANL Report ANL/NE-16/6 "Sharp User Manual"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solberg, J. M.

Diablo is a Multiphysics implicit finite element code with an emphasis on coupled structural/thermal analysis. In the SHARP framework, it is used as the structural solver, and may also be used as the mesh smoother.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2014-02-01

Three-dimensional fluid-structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

On some Aitken-like acceleration of the Schwarz method

NASA Astrophysics Data System (ADS)

Garbey, M.; Tromeur-Dervout, D.

2002-12-01

In this paper we present a family of domain decomposition based on Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. We first present the so-called Aitken-Schwarz procedure for linear differential operators. The solver can be a direct solver when applied to the Helmholtz problem with five-point finite difference scheme on regular grids. We then introduce the Steffensen-Schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems. We show that these solvers have reasonable numerical efficiency compared to classical fast solvers for the Poisson problem or multigrids for more general linear and nonlinear elliptic problems. However, the salient feature of our method is that our algorithm has high tolerance to slow network in the context of distributed parallel computing and is attractive, generally speaking, to use with computer architecture for which performance is limited by the memory bandwidth rather than the flop performance of the CPU. This is nowadays the case for most parallel. computer using the RISC processor architecture. We will illustrate this highly desirable property of our algorithm with large-scale computing experiments.

Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems

PubMed Central

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2013-01-01

Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration. PMID:24415796

Assessing uncertainty in the turbulent upper-ocean mixed layer using an unstructured finite-element solver

NASA Astrophysics Data System (ADS)

Pacheco, Luz; Smith, Katherine; Hamlington, Peter; Niemeyer, Kyle

2017-11-01

Vertical transport flux in the ocean upper mixed layer has recently been attributed to submesoscale currents, which occur at scales on the order of kilometers in the horizontal direction. These phenomena, which include fronts and mixed-layer instabilities, have been of particular interest due to the effect of turbulent mixing on nutrient transport, facilitating phytoplankton blooms. We study these phenomena using a non-hydrostatic, large eddy simulation for submesoscale currents in the ocean, developed using the extensible, open-source finite element platform FEniCs. Our model solves the standard Boussinesq Euler equations in variational form using the finite element method. FEniCs enables the use of parallel computing on modern systems for efficient computing time, and is suitable for unstructured grids where irregular topography can be considered in the future. The solver will be verified against the well-established NCAR-LES model and validated against observational data. For the verification with NCAR-LES, the velocity, pressure, and buoyancy fields are compared through a surface-wind-driven, open-ocean case. We use this model to study the impacts of uncertainties in the model parameters, such as near-surface buoyancy flux and secondary circulation, and discuss implications.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

Simulation of all-scale atmospheric dynamics on unstructured meshes

NASA Astrophysics Data System (ADS)

Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng

2016-10-01

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

A Validated Open-Source Multisolver Fourth-Generation Composite Femur Model.

PubMed

MacLeod, Alisdair R; Rose, Hannah; Gill, Harinderjit S

2016-12-01

Synthetic biomechanical test specimens are frequently used for preclinical evaluation of implant performance, often in combination with numerical modeling, such as finite-element (FE) analysis. Commercial and freely available FE packages are widely used with three FE packages in particular gaining popularity: abaqus (Dassault Systèmes, Johnston, RI), ansys (ANSYS, Inc., Canonsburg, PA), and febio (University of Utah, Salt Lake City, UT). To the best of our knowledge, no study has yet made a comparison of these three commonly used solvers. Additionally, despite the femur being the most extensively studied bone in the body, no freely available validated model exists. The primary aim of the study was primarily to conduct a comparison of mesh convergence and strain prediction between the three solvers (abaqus, ansys, and febio) and to provide validated open-source models of a fourth-generation composite femur for use with all the three FE packages. Second, we evaluated the geometric variability around the femoral neck region of the composite femurs. Experimental testing was conducted using fourth-generation Sawbones® composite femurs instrumented with strain gauges at four locations. A generic FE model and four specimen-specific FE models were created from CT scans. The study found that the three solvers produced excellent agreement, with strain predictions being within an average of 3.0% for all the solvers (r2 > 0.99) and 1.4% for the two commercial codes. The average of the root mean squared error against the experimental results was 134.5% (r2 = 0.29) for the generic model and 13.8% (r2 = 0.96) for the specimen-specific models. It was found that composite femurs had variations in cortical thickness around the neck of the femur of up to 48.4%. For the first time, an experimentally validated, finite-element model of the femur is presented for use in three solvers. This model is freely available online along with all the supporting validation data.

Examples of Linking Codes Within GeoFramework

NASA Astrophysics Data System (ADS)

Tan, E.; Choi, E.; Thoutireddy, P.; Aivazis, M.; Lavier, L.; Quenette, S.; Gurnis, M.

2003-12-01

Geological processes usually encompass a broad spectrum of length and time scales. Traditionally, a modeling code (solver) is written to solve a problem with specific length and time scales in mind. The utility of the solver beyond the designated purpose is usually limited. Furthermore, two distinct solvers, even if each can solve complementary parts of a new problem, are difficult to link together to solve the problem as a whole. For example, Lagrangian deformation model with visco-elastoplastic crust is used to study deformation near plate boundary. Ideally, the driving force of the deformation should be derived from underlying mantle convection, and it requires linking the Lagrangian deformation model with a Eulerian mantle convection model. As our understanding of geological processes evolves, the need of integrated modeling codes, which should reuse existing codes as much as possible, begins to surface. GeoFramework project addresses this need by developing a suite of reusable and re-combinable tools for the Earth science community. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (Lagrangian) and fluid (Eulerian) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. Under the framework, a solver is aware of the existence of other solvers and can interact with each other via exchanging information across adjacent boundary. A solver needs to conform a standard interface and provide its own implementation for exchanging boundary information. The framework also provides facilities to control the coordination between interacting solvers. We will show an example of linking two solvers within GeoFramework. CitcomS is a finite element code which solves for thermal convection within a 3D spherical shell. CitcomS can solve for problems either within a full spherical (global) domain or a restricted (regional) domain of a full sphere by using different meshers. We can embed a regional CitcomS solver within a global CitcomS solver. We not that linking instances of the same solver is conceptually equivalent to linking to different solvers. The global solver has a coarser grid and a longer stable time step than the regional solver. Therefore, a global-solver time step consists of several regional-solver time steps. The time-marching scheme is described below. First, the global solver is advanced one global-solver time step. Then, the regional solver is advanced for several regional-solver time steps until it catches up global solver. Within each regional-solver time step, the velocity field of the global solver is interpolated in time and then is imposed to the regional solver as boundary conditions. Finally, the temperature field of the regional solver is extrapolated in space and is fed back to the global. These two solvers are linked and synchronized by the time-marching scheme. An effort to embed a visco-elastoplastic representation of the crust within viscous mantle flow is underway.

Modeling of Complex Coupled Fluid-Structure Interaction Systems in Arbitrary Water Depth

DTIC Science & Technology

2008-01-01

model in a particle finite element method ( PFEM ) based framework for the ALE-RANS solver and submitted a journal paper recently [1]. In the paper, we...developing a fluid-flexible structure interaction model without free surface using ALE-RANS and k-ε turbulence closure model implemented by PFEM . In...the ALE_RANS and k-ε turbulence closure model based on the particle finite element Method ( PFEM ) and obtained some satisfying results [1-2]. The

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Implementing a Loosely Coupled Fluid Structure Interaction Finite Element Model in PHASTA

NASA Astrophysics Data System (ADS)

Pope, David

Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary Lagrangian-Eulerian modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary Lagrangian-Eulerian modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.

Hierarchically partitioned nonlinear equation solvers

NASA Technical Reports Server (NTRS)

Padovan, Joseph

1987-01-01

By partitioning solution space into a number of subspaces, a new multiply constrained partitioned Newton-Raphson nonlinear equation solver is developed. Specifically, for a given iteration, each of the various separate partitions are individually and simultaneously controlled. Due to the generality of the scheme, a hierarchy of partition levels can be employed. For finite-element-type applications, this includes the possibility of degree-of-freedom, nodal, elemental, geometric substructural, material and kinematically nonlinear group controls. It is noted that such partitioning can be continuously updated, depending on solution conditioning. In this context, convergence is ascertained at the individual partition level.

Researched applied to transonic compressors in numerical fluid mechanics of inviscid flow and viscous flow

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1985-01-01

A streamline Euler solver which combines high accuracy and good convergence rates with capabilities for inverse or direct mode solution modes and an analysis technique for finite difference models of hyperbolic partial difference equations were developed.

Numerical Simulation of the Fluid-Structure Interaction of a Surface Effect Ship Bow Seal

NASA Astrophysics Data System (ADS)

Bloxom, Andrew L.

Numerical simulations of fluid-structure interaction (FSI) problems were performed in an effort to verify and validate a commercially available FSI tool. This tool uses an iterative partitioned coupling scheme between CD-adapco's STAR-CCM+ finite volume fluid solver and Simulia's Abaqus finite element structural solver to simulate the FSI response of a system. Preliminary verification and validation work (V&V) was carried out to understand the numerical behavior of the codes individually and together as a FSI tool. Verification and Validation work that was completed included code order verification of the respective fluid and structural solvers with Couette-Poiseuille flow and Euler-Bernoulli beam theory. These results confirmed the 2 nd order accuracy of the spatial discretizations used. Following that, a mixture of solution verifications and model calibrations was performed with the inclusion of the physics models implemented in the solution of the FSI problems. Solution verifications were completed for fluid and structural stand-alone models as well as for the coupled FSI solutions. These results re-confirmed the spatial order of accuracy but for more complex flows and physics models as well as the order of accuracy of the temporal discretizations. In lieu of a good material definition, model calibration is performed to reproduce the experimental results. This work used model calibration for both instances of hyperelastic materials which were presented in the literature as validation cases because these materials were defined as linear elastic. Calibrated, three dimensional models of the bow seal on the University of Michigan bow seal test platform showed the ability to reproduce the experimental results qualitatively through averaging of the forces and seal displacements. These simulations represent the only current 3D results for this case. One significant result of this study is the ability to visualize the flow around the seal and to directly measure the seal resistances at varying cushion pressures, seal immersions, forward speeds, and different seal materials. SES design analysis could greatly benefit from the inclusion of flexible seals in simulations, and this work is a positive step in that direction. In future work, the inclusion of more complex seal geometries and contact will further enhance the capability of this tool.

Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves

NASA Astrophysics Data System (ADS)

Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi-Qian

2012-12-01

This paper presents a novel numerical method for simulating the fluid-structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.

Influence of Eccentricity and Angular Velocity on Force Effects on Rotor of Magnetorheological Damper

NASA Astrophysics Data System (ADS)

Šedivý, Dominik; Ferfecki, Petr; Fialová, Simona

2018-06-01

This article presents the evaluation of force effects on squeeze film damper rotor. The rotor is placed eccentrically and its motion is translate-circular. The amplitude of rotor motion is smaller than its initial eccentricity. The force effects are calculated from pressure and viscous forces which were measured by using computational modeling. Damper was filled with magnetorheological fluid. Viscosity of this non-Newtonian fluid is given using Bingham rheology model. Yield stress is not constant and it is a function of magnetic induction which is described by many variables. The most important variables of magnetic induction are electric current and gap width between rotor and stator. The simulations were made in finite volume method based solver. The motion of the inner ring of squeeze film damper was carried out by dynamic mesh. Numerical solution was solved for five different initial eccentricities and angular velocities of rotor motion.

Aerodynamic Analysis of Morphing Blades

NASA Astrophysics Data System (ADS)

Harris, Caleb; Macphee, David; Carlisle, Madeline

2016-11-01

Interest in morphing blades has grown with applications for wind turbines and other aerodynamic blades. This passive control method has advantages over active control methods such as lower manufacturing and upkeep costs. This study has investigated the lift and drag forces on individual blades with experimental and computational analysis. The goal has been to show that these blades delay stall and provide larger lift-to-drag ratios at various angles of attack. Rigid and flexible airfoils were cast from polyurethane and silicone respectively, then lift and drag forces were collected from a load cell during 2-D testing in a wind tunnel. Experimental data was used to validate computational models in OpenFOAM. A finite volume fluid-structure-interaction solver was used to model the flexible blade in fluid flow. Preliminary results indicate delay in stall and larger lift-to-drag ratios by maintaining more optimal angles of attack when flexing. Funding from NSF REU site Grant EEC 1358991 is greatly appreciated.

An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.

Three Dimensional Solution of Pneumatic Active Control of Forebody Vortex Asymmetry

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; SharafEl-Din, Hazem H.; Liu, C. H.

1995-01-01

Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle range of 67.5 approaches minus 67.5 degrees is used for both normal and tangential ports of injection. The effective axial length of injection is varied from 0.03 to 0.05. The computational solver uses the implicit, upwind, flux difference splitting finite volume scheme, and the grid consists of 161 x 55 x 65 points in the wrap around, normal and axial directions, respectively. The results show that tangential injection is more effective than normal injection.

Navier-Stokes turbine heat transfer predictions using two-equation turbulence closures

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1992-01-01

Navier-Stokes calculations were carried out in order to predict the heat-transfer rates on turbine blades. The calculations were performed using TRAF2D which is a k-epsilon, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using Coakley's q-omega and Chien's k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a nonperiodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the SSME high-pressure fuel turbine. The comparison serves to highlight the weaknesses of the turbulence models for use in turbomachinery heat-transfer calculations.

Modeling Complex Biological Flows in Multi-Scale Systems using the APDEC Framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trebotich, D

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA-laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscousmore » flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.« less

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

NASA Technical Reports Server (NTRS)

Janus, J. Mark; Whitfield, David L.

1990-01-01

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Modeling complex biological flows in multi-scale systems using the APDEC framework

NASA Astrophysics Data System (ADS)

Trebotich, David

2006-09-01

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscous flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.

Assessment of the Unstructured Grid Software TetrUSS for Drag Prediction of the DLR-F4 Configuration

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar Z.; Frink, Neal T.

2002-01-01

An application of the NASA unstructured grid software system TetrUSS is presented for the prediction of aerodynamic drag on a transport configuration. The paper briefly describes the underlying methodology and summarizes the results obtained on the DLR-F4 transport configuration recently presented in the first AIAA computational fluid dynamics (CFD) Drag Prediction Workshop. TetrUSS is a suite of loosely coupled unstructured grid CFD codes developed at the NASA Langley Research Center. The meshing approach is based on the advancing-front and the advancing-layers procedures. The flow solver employs a cell-centered, finite volume scheme for solving the Reynolds Averaged Navier-Stokes equations on tetrahedral grids. For the present computations, flow in the viscous sublayer has been modeled with an analytical wall function. The emphasis of the paper is placed on the practicality of the methodology for accurately predicting aerodynamic drag data.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

rhoCentralRfFoam: An OpenFOAM solver for high speed chemically active flows - Simulation of planar detonations -

NASA Astrophysics Data System (ADS)

Gutiérrez Marcantoni, L. F.; Tamagno, J.; Elaskar, S.

2017-10-01

A new solver developed within the framework of OpenFOAM 2.3.0, called rhoCentralRfFoam which can be interpreted like an evolution of rhoCentralFoam, is presented. Its use, performing numerical simulations on initiation and propagation of planar detonation waves in combustible mixtures H2-Air and H2-O2-Ar, is described. Unsteady one dimensional (1D) Euler equations coupled with sources to take into account chemical activity, are numerically solved using the Kurganov, Noelle and Petrova second order scheme in a domain discretized with finite volumes. The computational code can work with any number of species and its corresponding reactions, but here it was tested with 13 chemically active species (one species inert), and 33 elementary reactions. A gaseous igniter which acts like a shock-tube driver, and powerful enough to generate a strong shock capable of triggering exothermic chemical reactions in fuel mixtures, is used to start planar detonations. The following main aspects of planar detonations are here, treated: induction time of combustible mixtures cited above and required mesh resolutions; convergence of overdriven detonations to Chapman-Jouguet states; detonation structure (ZND model); and the use of reflected shocks to determine induction times experimentally. The rhoCentralRfFoam code was verified comparing numerical results and it was validated, through analytical results and experimental data.

Solution of large nonlinear quasistatic structural mechanics problems on distributed-memory multiprocessor computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanford, M.

1997-12-31

Most commercially-available quasistatic finite element programs assemble element stiffnesses into a global stiffness matrix, then use a direct linear equation solver to obtain nodal displacements. However, for large problems (greater than a few hundred thousand degrees of freedom), the memory size and computation time required for this approach becomes prohibitive. Moreover, direct solution does not lend itself to the parallel processing needed for today`s multiprocessor systems. This talk gives an overview of the iterative solution strategy of JAS3D, the nonlinear large-deformation quasistatic finite element program. Because its architecture is derived from an explicit transient-dynamics code, it does not ever assemblemore » a global stiffness matrix. The author describes the approach he used to implement the solver on multiprocessor computers, and shows examples of problems run on hundreds of processors and more than a million degrees of freedom. Finally, he describes some of the work he is presently doing to address the challenges of iterative convergence for ill-conditioned problems.« less

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1991-01-01

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Methods for compressible fluid simulation on GPUs using high-order finite differences

NASA Astrophysics Data System (ADS)

Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

2017-08-01

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Computational study of generic hypersonic vehicle flow fields

NASA Technical Reports Server (NTRS)

Narayan, Johnny R.

1994-01-01

The geometric data of the generic hypersonic vehicle configuration included body definitions and preliminary grids for the forebody (nose cone excluded), midsection (propulsion system excluded), and afterbody sections. This data was to be augmented by the nose section geometry (blunt conical section mated with the noncircular cross section of the forebody initial plane) along with a grid and a detailed supersonic combustion ramjet (scramjet) geometry (inlet and combustor) which should be merged with the nozzle portion of the afterbody geometry. The solutions were to be obtained by using a Navier-Stokes (NS) code such as TUFF for the nose portion, a parabolized Navier-Stokes (PNS) solver such as the UPS and STUFF codes for the forebody, a NS solver with finite rate hydrogen-air chemistry capability such as TUFF and SPARK for the scramjet and a suitable solver (NS or PNS) for the afterbody and external nozzle flows. The numerical simulation of the hypersonic propulsion system for the generic hypersonic vehicle is the major focus of this entire work. Supersonic combustion ramjet is such a propulsion system, hence the main thrust of the present task has been to establish a solution procedure for the scramjet flow. The scramjet flow is compressible, turbulent, and reacting. The fuel used is hydrogen and the combustion process proceeds at a finite rate. As a result, the solution procedure must be capable of addressing such flows.

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

NASA Astrophysics Data System (ADS)

Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

2018-01-01

An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Box truss analysis and technology development. Task 1: Mesh analysis and control

NASA Technical Reports Server (NTRS)

Bachtell, E. E.; Bettadapur, S. S.; Coyner, J. V.

1985-01-01

An analytical tool was developed to model, analyze and predict RF performance of box truss antennas with reflective mesh surfaces. The analysis system is unique in that it integrates custom written programs for cord tied mesh surfaces, thereby drastically reducing the cost of analysis. The analysis system is capable of determining the RF performance of antennas under any type of manufacturing or operating environment by integrating together the various disciplines of design, finite element analysis, surface best fit analysis and RF analysis. The Integrated Mesh Analysis System consists of six separate programs: The Mesh Tie System Model Generator, The Loadcase Generator, The Model Optimizer, The Model Solver, The Surface Topography Solver and The RF Performance Solver. Additionally, a study using the mesh analysis system was performed to determine the effect of on orbit calibration, i.e., surface adjustment, on a typical box truss antenna.

A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations

NASA Astrophysics Data System (ADS)

Qiang, Ji

2017-10-01

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of O(Nu(logNmode)) , where Nu is the total number of unknowns and Nmode is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

NASA Astrophysics Data System (ADS)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

NASA Technical Reports Server (NTRS)

Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.

2017-01-01

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chao; Pouransari, Hadi; Rajamanickam, Sivasankaran

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by everymore » processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.« less

Automated Finite Element Analysis of Elastically-Tailored Plates

NASA Technical Reports Server (NTRS)

Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer

2003-01-01

A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.

Making Sense of Math: How to Help Every Student become a Mathematical Thinker and Problem Solver (ASCD Arias)

ERIC Educational Resources Information Center

Seeley, Cathy L.

2016-01-01

In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…

Development of a finite volume two-dimensional model and its application in a bay with two inlets: Mobile Bay, Alabama

NASA Astrophysics Data System (ADS)

Lee, Jun; Lee, Jungwoo; Yun, Sang-Leen; Oh, Hye-Cheol

2017-08-01

The purpose of this study was to develop a two-dimensional shallow water flow model using the finite volume method on a combined unstructured triangular and quadrilateral grid system to simulate coastal, estuarine and river flows. The intercell numerical fluxes were calculated using the classical Osher-Solomon's approximate Riemann solver for the governing conservation laws to be able to handle wetting and drying processes and to capture a tidal bore like phenomenon. The developed model was validated with several benchmark test problems including the two-dimensional dam-break problem. The model results were well agreed with results of other models and experimental results in literature. The unstructured triangular and quadrilateral combined grid system was successfully implemented in the model, thus the developed model would be more flexible when applying in an estuarine system, which includes narrow channels. Then, the model was tested in Mobile Bay, Alabama, USA. The developed model reproduced water surface elevation well as having overall Predictive Skill of 0.98. We found that the primary inlet, Main Pass, only covered 35% of the fresh water exchange while it covered 89% of the total water exchange between the ocean and Mobile Bay. There were also discharge phase difference between MP and the secondary inlet, Pass aux Herons, and this phase difference in flows would act as a critical role in substances' exchange between the eastern Mississippi Sound and the northern Gulf of Mexico through Main Pass and Pass aux Herons in Mobile Bay.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

Advanced Fluid Reduced Order Models for Compressible Flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tezaur, Irina Kalashnikova; Fike, Jeffrey A.; Carlberg, Kevin Thomas

This report summarizes fiscal year (FY) 2017 progress towards developing and implementing within the SPARC in-house finite volume flow solver advanced fluid reduced order models (ROMs) for compressible captive-carriage flow problems of interest to Sandia National Laboratories for the design and qualification of nuclear weapons components. The proposed projection-based model order reduction (MOR) approach, known as the Proper Orthogonal Decomposition (POD)/Least- Squares Petrov-Galerkin (LSPG) method, can substantially reduce the CPU-time requirement for these simulations, thereby enabling advanced analyses such as uncertainty quantification and de- sign optimization. Following a description of the project objectives and FY17 targets, we overview briefly themore » POD/LSPG approach to model reduction implemented within SPARC . We then study the viability of these ROMs for long-time predictive simulations in the context of a two-dimensional viscous laminar cavity problem, and describe some FY17 enhancements to the proposed model reduction methodology that led to ROMs with improved predictive capabilities. Also described in this report are some FY17 efforts pursued in parallel to the primary objective of determining whether the ROMs in SPARC are viable for the targeted application. These include the implemen- tation and verification of some higher-order finite volume discretization methods within SPARC (towards using the code to study the viability of ROMs on three-dimensional cavity problems) and a novel structure-preserving constrained POD/LSPG formulation that can improve the accuracy of projection-based reduced order models. We conclude the report by summarizing the key takeaways from our FY17 findings, and providing some perspectives for future work.« less

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Gielda, T. P.; Soni, B. K.; Deese, J. E.; Agarwal, R. K.

1993-01-01

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

NASA Astrophysics Data System (ADS)

Pavish, D. L.; Gielda, T. P.; Soni, B. K.; Deese, J. E.; Agarwal, R. K.

1993-07-01

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

Radiation and scattering from printed antennas on cylindrically conformal platforms

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Bindiganavale, Sunil

1994-01-01

The goal was to develop suitable methods and software for the analysis of antennas on cylindrical coated and uncoated platforms. Specifically, the finite element boundary integral and finite element ABC methods were employed successfully and associated software were developed for the analysis and design of wraparound and discrete cavity-backed arrays situated on cylindrical platforms. This work led to the successful implementation of analysis software for such antennas. Developments which played a role in this respect are the efficient implementation of the 3D Green's function for a metallic cylinder, the incorporation of the fast Fourier transform in computing the matrix-vector products executed in the solver of the finite element-boundary integral system, and the development of a new absorbing boundary condition for terminating the finite element mesh on cylindrical surfaces.

Experimental and numerical study of drill bit drop tests on Kuru granite

NASA Astrophysics Data System (ADS)

Fourmeau, Marion; Kane, Alexandre; Hokka, Mikko

2017-01-01

This paper presents an experimental and numerical study of Kuru grey granite impacted with a seven-buttons drill bit mounted on an instrumented drop test machine. The force versus displacement curves during the impact, so-called bit-rock interaction (BRI) curves, were obtained using strain gauge measurements for two levels of impact energy. Moreover, the volume of removed rock after each drop test was evaluated by stereo-lithography (three-dimensional surface reconstruction). A modified version of the Holmquist-Johnson-Cook (MHJC) material model was calibrated using Kuru granite test results available from the literature. Numerical simulations of the single drop tests were carried out using the MHJC model available in the LS-DYNA explicit finite-element solver. The influence of the impact energy and additional confining pressure on the BRI curves and the volume of the removed rock is discussed. In addition, the influence of the rock surface shape before impact was evaluated using two different mesh geometries: a flat surface and a hyperbolic surface. The experimental and numerical results are compared and discussed in terms of drilling efficiency through the mechanical specific energy. This article is part of the themed issue 'Experimental testing and modelling of brittle materials at high strain rates'.

Finite element calculation of residual stress in dental restorative material

NASA Astrophysics Data System (ADS)

Grassia, Luigi; D'Amore, Alberto

2012-07-01

A finite element methodology for residual stresses calculation in dental restorative materials is proposed. The material under concern is a multifunctional methacrylate-based composite for dental restorations, activated by visible light. Reaction kinetics, curing shrinkage, and viscoelastic relaxation functions were required as input data on a structural finite element solver. Post cure effects were considered in order to quantify the residual stresses coming out from natural contraction with respect to those debited to the chemical shrinkage. The analysis showed for a given test case that residual stresses frozen in the dental restoration at uniform temperature of 37°C are of the same order of magnitude of the strength of the dental composite material per se.

A finite-difference time-domain electromagnetic solver in a generalized coordinate system

NASA Astrophysics Data System (ADS)

Hochberg, Timothy Allen

A new, finite-difference, time-domain method for the simulation of full-wave electromagnetic wave propogation in complex structures is developed. This method is simple and flexible; it allows for the simulation of transient wave propogation in a large class of practical structures. Boundary conditions are implemented for perfect and imperfect electrically conducting boundaries, perfect magnetically conducting boundaries, and absorbing boundaries. The method is validated with the aid of several different types of test cases. Two types of coaxial cables with helical breaks are simulated and the results are discussed.

Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

NASA Technical Reports Server (NTRS)

Housman, Jeffrey A.; Kiris, Cetin

2016-01-01

Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.

Finite element analysis of periodic transonic flow problems

NASA Technical Reports Server (NTRS)

Fix, G. J.

1978-01-01

Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.

Brownian dynamics without Green's functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Usabiaga, Florencio Balboa

2014-04-07

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. Thismore » is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.« less

On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions.

PubMed

Jallepalli, Ashok; Docampo-Sanchez, Julia; Ryan, Jennifer K; Haimes, Robert; Kirby, Robert M

2018-01-01

As the finite element method (FEM) and the finite volume method (FVM), both traditional and high-order variants, continue their proliferation into various applied engineering disciplines, it is important that the visualization techniques and corresponding data analysis tools that act on the results produced by these methods faithfully represent the underlying data. To state this in another way: the interpretation of data generated by simulation needs to be consistent with the numerical schemes that underpin the specific solver technology. As the verifiable visualization literature has demonstrated: visual artifacts produced by the introduction of either explicit or implicit data transformations, such as data resampling, can sometimes distort or even obfuscate key scientific features in the data. In this paper, we focus on the handling of elemental continuity, which is often only continuous or piecewise discontinuous, when visualizing primary or derived fields from FEM or FVM simulations. We demonstrate that traditional data handling and visualization of these fields introduce visual errors. In addition, we show how the use of the recently proposed line-SIAC filter provides a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous.

Heat transfer model and finite element formulation for simulation of selective laser melting

NASA Astrophysics Data System (ADS)

Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.

2017-10-01

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wan, Xiaoliang; Yu, Haijun

2017-02-01

This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence-free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne

2011-11-01

We present a coarse-grid projection (CGP) algorithm for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. Here, we investigate a particular CGP method for the vorticity-stream function formulation that uses the full weighting operation for mapping from fine to coarse grids, the third-order Runge-Kutta method for time stepping, and finite differences for the spatial discretization. After solving the Poisson equation on a coarsened grid, bilinear interpolation is used to obtain the fine data for consequent time stepping on the full grid. We compute several benchmark flows: the Taylor-Green vortex, a vortex pair merging, a double shear layer, decaying turbulence and the Taylor-Green vortex on a distorted grid. In all cases we use either FFT-based or V-cycle multigrid linear-cost Poisson solvers. Reducing the number of degrees of freedom of the Poisson solver by powers of two accelerates these computations while, for the first level of coarsening, retaining the same level of accuracy in the fine resolution vorticity field.

A Parallel Fast Sweeping Method for the Eikonal Equation

NASA Astrophysics Data System (ADS)

Baker, B.

2017-12-01

Recently, there has been an exciting emergence of probabilistic methods for travel time tomography. Unlike gradient-based optimization strategies, probabilistic tomographic methods are resistant to becoming trapped in a local minimum and provide a much better quantification of parameter resolution than, say, appealing to ray density or performing checkerboard reconstruction tests. The benefits associated with random sampling methods however are only realized by successive computation of predicted travel times in, potentially, strongly heterogeneous media. To this end this abstract is concerned with expediting the solution of the Eikonal equation. While many Eikonal solvers use a fast marching method, the proposed solver will use the iterative fast sweeping method because the eight fixed sweep orderings in each iteration are natural targets for parallelization. To reduce the number of iterations and grid points required the high-accuracy finite difference stencil of Nobel et al., 2014 is implemented. A directed acyclic graph (DAG) is created with a priori knowledge of the sweep ordering and finite different stencil. By performing a topological sort of the DAG sets of independent nodes are identified as candidates for concurrent updating. Additionally, the proposed solver will also address scalability during earthquake relocation, a necessary step in local and regional earthquake tomography and a barrier to extending probabilistic methods from active source to passive source applications, by introducing an asynchronous parallel forward solve phase for all receivers in the network. Synthetic examples using the SEG over-thrust model will be presented.

An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2018-03-01

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

A Method for Optimizing Non-Axisymmetric Liners for Multimodal Sound Sources

NASA Technical Reports Server (NTRS)

Watson, W. R.; Jones, M. G.; Parrott, T. L.; Sobieski, J.

2002-01-01

Central processor unit times and memory requirements for a commonly used solver are compared to that of a state-of-the-art, parallel, sparse solver. The sparse solver is then used in conjunction with three constrained optimization methodologies to assess the relative merits of non-axisymmetric versus axisymmetric liner concepts for improving liner acoustic suppression. This assessment is performed with a multimodal noise source (with equal mode amplitudes and phases) in a finite-length rectangular duct without flow. The sparse solver is found to reduce memory requirements by a factor of five and central processing time by a factor of eleven when compared with the commonly used solver. Results show that the optimum impedance of the uniform liner is dominated by the least attenuated mode, whose attenuation is maximized by the Cremer optimum impedance. An optimized, four-segmented liner with impedance segments in a checkerboard arrangement is found to be inferior to an optimized spanwise segmented liner. This optimized spanwise segmented liner is shown to attenuate substantially more sound than the optimized uniform liner and tends to be more effective at the higher frequencies. The most important result of this study is the discovery that when optimized, a spanwise segmented liner with two segments gives attenuations equal to or substantially greater than an optimized axially segmented liner with the same number of segments.

Numerical study of natural convection in a horizontal cylinder filled with water-based alumina nanofluid.

PubMed

Meng, Xiangyin; Li, Yan

2015-01-01

Natural heat convection of water-based alumina (Al2O3/water) nanofluids (with volume fraction 1% and 4%) in a horizontal cylinder is numerically investigated. The whole three-dimensional computational fluid dynamics (CFD) procedure is performed in a completely open-source way. Blender, enGrid, OpenFOAM and ParaView are employed for geometry creation, mesh generation, case simulation and post process, respectively. Original solver 'buoyantBoussinesqSimpleFoam' is selected for the present study, and a temperature-dependent solver 'buoyantBoussinesqSimpleTDFoam' is developed to ensure the simulation is more realistic. The two solvers are used for same cases and compared to corresponding experimental results. The flow regime in these cases is laminar (Reynolds number is 150) and the Rayleigh number range is 0.7 × 10(7) ~ 5 × 10(7). By comparison, the average natural Nusselt numbers of water and Al2O3/water nanofluids are found to increase with the Rayleigh number. At the same Rayleigh number, the Nusselt number is found to decrease with nanofluid volume fraction. The temperature-dependent solver is found better for water and 1% Al2O3/water nanofluid cases, while the original solver is better for 4% Al2O3/water nanofluid cases. Furthermore, due to strong three-dimensional flow features in the horizontal cylinder, three-dimensional CFD simulation is recommended instead of two-dimensional simplifications.

Hierarchial parallel computer architecture defined by computational multidisciplinary mechanics

NASA Technical Reports Server (NTRS)

Padovan, Joe; Gute, Doug; Johnson, Keith

1989-01-01

The goal is to develop an architecture for parallel processors enabling optimal handling of multi-disciplinary computation of fluid-solid simulations employing finite element and difference schemes. The goals, philosphical and modeling directions, static and dynamic poly trees, example problems, interpolative reduction, the impact on solvers are shown in viewgraph form.

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Final Report - Subcontract B623760

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bank, R.

2017-11-17

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent ofmore » the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.« less

An adjoint-based simultaneous estimation method of the asthenosphere's viscosity and afterslip using a fast and scalable finite-element adjoint solver

NASA Astrophysics Data System (ADS)

Agata, Ryoichiro; Ichimura, Tsuyoshi; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo

2018-04-01

The simultaneous estimation of the asthenosphere's viscosity and coseismic slip/afterslip is expected to improve largely the consistency of the estimation results to observation data of crustal deformation collected in widely spread observation points, compared to estimations of slips only. Such an estimate can be formulated as a non-linear inverse problem of material properties of viscosity and input force that is equivalent to fault slips based on large-scale finite-element (FE) modeling of crustal deformation, in which the degree of freedom is in the order of 109. We formulated and developed a computationally efficient adjoint-based estimation method for this inverse problem, together with a fast and scalable FE solver for the associated forward and adjoint problems. In a numerical experiment that imitates the 2011 Tohoku-Oki earthquake, the advantage of the proposed method is confirmed by comparing the estimated results with those obtained using simplified estimation methods. The computational cost required for the optimization shows that the proposed method enabled the targeted estimation to be completed with moderate amount of computational resources.

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Nark, Douglas M.; Nguyen, Duc T.; Tungkahotara, Siroj

2006-01-01

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

NASA Technical Reports Server (NTRS)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

Data Parallel Line Relaxation (DPLR) Code User Manual: Acadia - Version 4.01.1

NASA Technical Reports Server (NTRS)

Wright, Michael J.; White, Todd; Mangini, Nancy

2009-01-01

Data-Parallel Line Relaxation (DPLR) code is a computational fluid dynamic (CFD) solver that was developed at NASA Ames Research Center to help mission support teams generate high-value predictive solutions for hypersonic flow field problems. The DPLR Code Package is an MPI-based, parallel, full three-dimensional Navier-Stokes CFD solver with generalized models for finite-rate reaction kinetics, thermal and chemical non-equilibrium, accurate high-temperature transport coefficients, and ionized flow physics incorporated into the code. DPLR also includes a large selection of generalized realistic surface boundary conditions and links to enable loose coupling with external thermal protection system (TPS) material response and shock layer radiation codes.

Conjunction of 2D and 3D modified flow solvers for simulating spatio-temporal wind induced hydrodynamics in the Caspian Sea

NASA Astrophysics Data System (ADS)

Zounemat-Kermani, Mohammad; Sabbagh-Yazdi, Saeed-Reza

2010-06-01

The main objective of this study is the simulation of flow dynamics in the deep parts of the Caspian Sea, in which the southern and middle deep regions are surrounded by considerable areas of shallow zones. To simulate spatio-temporal wind induced hydrodynamics in deep waters, a conjunctive numerical model consisting of a 2D depth average model and a 3D pseudo compressible model is proposed. The 2D model is applied to determine time dependent free surface oscillations as well as the surface velocity patterns and is conjunct to the 3D flow solver for computing three-dimensional velocity and pressure fields which coverage to steady state for the top boundary condition. The modified 2D and 3D sets of equations are conjunct considering interface shear stresses. Both sets of 2D and 3D equations are solved on unstructured triangular and tetrahedral meshes using the Galerkin Finite Volume Method. The conjunctive model is utilized to investigate the deep currents affected by wind, Coriolis forces and the river inflow conditions of the Caspian Sea. In this study, the simulation of flow field due to major winds as well as transient winds in the Caspian Sea during a period of 6 hours in the winter season has been conducted and the numerical results for water surface level are then compared to the 2D numerical results.

The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Jr., Thomas E.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.

IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems

NASA Astrophysics Data System (ADS)

Hujeirat, A.

1998-07-01

The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and robustness of the code.

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

NASA Astrophysics Data System (ADS)

Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em

2015-09-01

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Yu-Hang, E-mail: yuhang_tang@brown.edu; Kudo, Shuhei, E-mail: shuhei-kudo@outlook.jp; Bian, Xin, E-mail: xin_bian@brown.edu

2015-09-15

Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create anmore » easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)« less

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

Compressor and Turbine Multidisciplinary Design for Highly Efficient Micro-gas Turbine

NASA Astrophysics Data System (ADS)

Barsi, Dario; Perrone, Andrea; Qu, Yonglei; Ratto, Luca; Ricci, Gianluca; Sergeev, Vitaliy; Zunino, Pietro

2018-06-01

Multidisciplinary design optimization (MDO) is widely employed to enhance turbomachinery components efficiency. The aim of this work is to describe a complete tool for the aero-mechanical design of a radial inflow turbine and a centrifugal compressor. The high rotational speed of such machines and the high exhaust gas temperature (only for the turbine) expose blades to really high stresses and therefore the aerodynamics design has to be coupled with the mechanical one through an integrated procedure. The described approach employs a fully 3D Reynolds Averaged Navier-Stokes (RANS) solver for the aerodynamics and an open source Finite Element Analysis (FEA) solver for the mechanical integrity assessment. Due to the high computational cost of both these two solvers, a meta model, such as an artificial neural network (ANN), is used to speed up the optimization design process. The interaction between two codes, the mesh generation and the post processing of the results are achieved via in-house developed scripting modules. The obtained results are widely presented and discussed.

Transient dynamic analysis of the Bao'An Stadium

NASA Astrophysics Data System (ADS)

Knight, David; Whitefield, Rowan; Nhieu, Eric; Tahmasebinia, Faham; Ansourian, Peter; Alonso-Marroquin, Fernando

2016-08-01

Bao'An Stadium is a unique structure that utilises 54m span cantilevers with tensioned members to support the roof. This report involves a simplified finite element model of Bao'An stadium using Strand7 to analyse the effects of deflections, buckling and earthquake loading. Modelling the cantilevers of the original structure with a double curvature was problematic due to unrealistic deflections and no total mass participation using the Spectral Response Solver. To rectify this, a simplified symmetrical stadium was created and the cable free length attribute was used to induce tension in the inner ring and bottom chord members to create upwards deflection. Further, in place of the Spectral Response Solver, the Transient Linear Dynamic Solver was inputted with an El-Centro earthquake. The stadium's response to a 0.20g earthquake and self-weight indicated the deflections satisfied AS1170.0, the loading in the columns was below the critical buckling load, and all structural members satisfied AS4100.

Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements

NASA Astrophysics Data System (ADS)

Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.

2000-11-01

In this paper we describe a fast parallel method for solving highly ill-conditioned saddle-point systems arising from mixed finite element simulations of stochastic partial differential equations (PDEs) modelling flow in heterogeneous media. Each realisation of these stochastic PDEs requires the solution of the linear first-order velocity-pressure system comprising Darcy's law coupled with an incompressibility constraint. The chief difficulty is that the permeability may be highly variable, especially when the statistical model has a large variance and a small correlation length. For reasonable accuracy, the discretisation has to be extremely fine. We solve these problems by first reducing the saddle-point formulation to a symmetric positive definite (SPD) problem using a suitable basis for the space of divergence-free velocities. The reduced problem is solved using parallel conjugate gradients preconditioned with an algebraically determined additive Schwarz domain decomposition preconditioner. The result is a solver which exhibits a good degree of robustness with respect to the mesh size as well as to the variance and to physically relevant values of the correlation length of the underlying permeability field. Numerical experiments exhibit almost optimal levels of parallel efficiency. The domain decomposition solver (DOUG, http://www.maths.bath.ac.uk/~parsoft) used here not only is applicable to this problem but can be used to solve general unstructured finite element systems on a wide range of parallel architectures.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

HONEI: A collection of libraries for numerical computations targeting multiple processor architectures

NASA Astrophysics Data System (ADS)

van Dyk, Danny; Geveler, Markus; Mallach, Sven; Ribbrock, Dirk; Göddeke, Dominik; Gutwenger, Carsten

2009-12-01

We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI's libraries, we achieve a two-fold speedup over straight forward C++ code using HONEI's SSE backend, and additional 3-4 and 4-16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development. Program summaryProgram title: HONEI Catalogue identifier: AEDW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv2 No. of lines in distributed program, including test data, etc.: 216 180 No. of bytes in distributed program, including test data, etc.: 1 270 140 Distribution format: tar.gz Programming language: C++ Computer: x86, x86_64, NVIDIA CUDA GPUs, Cell blades and PlayStation 3 Operating system: Linux RAM: at least 500 MB free Classification: 4.8, 4.3, 6.1 External routines: SSE: none; [1] for GPU, [2] for Cell backend Nature of problem: Computational science in general and numerical simulation in particular have reached a turning point. The revolution developers are facing is not primarily driven by a change in (problem-specific) methodology, but rather by the fundamental paradigm shift of the underlying hardware towards heterogeneity and parallelism. This is particularly relevant for data-intensive problems stemming from discretisations with local support, such as finite differences, volumes and elements. Solution method: To address these issues, we present a hardware aware collection of libraries combining the advantages of modern software techniques and hardware oriented programming. Applications built on top of these libraries can be configured trivially to execute on CPUs, GPUs or the Cell processor. In order to evaluate the performance and accuracy of our approach, we provide two domain specific applications; a multigrid solver for the Poisson problem and a fully explicit solver for 2D shallow water equations. Restrictions: HONEI is actively being developed, and its feature list is continuously expanded. Not all combinations of operations and architectures might be supported in earlier versions of the code. Obtaining snapshots from http://www.honei.org is recommended. Unusual features: The considered applications as well as all library operations can be run on NVIDIA GPUs and the Cell BE. Running time: Depending on the application, and the input sizes. The Poisson solver executes in few seconds, while the SWE solver requires up to 5 minutes for large spatial discretisations or small timesteps. References:http://www.nvidia.com/cuda. http://www.ibm.com/developerworks/power/cell.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

NASA Astrophysics Data System (ADS)

Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

2014-06-01

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context.

Numerical simulations of post-surgical flow and thrombosis in basilar artery aneurysms

NASA Astrophysics Data System (ADS)

Seshadhri, Santhosh; Lawton, Michael; Boussel, Loic; Saloner, David; Rayz, Vitaliy

2015-11-01

Surgical treatment of basilar artery aneurysms presents a major challenge since it is crucial to preserve the flow to the vital brainstem perforators branching of the basilar artery. In some cases, basilar aneurysms can be treated by clipping vessels in order to induce flow reduction and aneurysm thrombosis. Patient-specific CFD models can provide guidance to clinicians by simulating postoperative flows resulting from alternative surgeries. Several surgical options were evaluated for four basilar aneurysm patients. Patient-specific models were generated from preoperative MR angiography and MR velocimetry data and modified to simulate different procedures. The Navier-Stokes equations were solved with a finite-volume solver Fluent. Virtual contrast injections were simulated by solving the advection-diffusion equation in order to estimate the flow residence time and determine thrombus-prone regions. The results indicated on procedures that reduce intra-aneurysmal velocities and flow regions which are likely to become thrombosed. Thus CFD modeling can help improve the outcome of surgeries altering the flow in basilar aneurysms.

A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

NASA Astrophysics Data System (ADS)

Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

2014-11-01

We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

Overview of the relevant CFD work at Thiokol Corporation

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Loh, Hai-Tien

1992-01-01

An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.

Analysis of solid particles falling down and interacting in a channel with sedimentation using fictitious boundary method

NASA Astrophysics Data System (ADS)

Usman, K.; Walayat, K.; Mahmood, R.; Kousar, N.

2018-06-01

We have examined the behavior of solid particles in particulate flows. The interaction of particles with each other and with the fluid is analyzed. Solid particles can move freely through a fixed computational mesh using an Eulerian approach. Fictitious boundary method (FBM) is used for treating the interaction between particles and the fluid. Hydrodynamic forces acting on the particle's surface are calculated using an explicit volume integral approach. A collision model proposed by Glowinski, Singh, Joseph and coauthors is used to handle particle-wall and particle-particle interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW. Numerical experiments are performed considering two particles falling and colliding and sedimentation of many particles while interacting with each other. Results for these experiments are presented and compared with the reference values. Effects of the particle-particle interaction on the motion of the particles and on the physical behavior of the fluid-particle system has been analyzed.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

The Athena Astrophysical MHD Code in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Skinner, M. A.; Ostriker, E. C.

2011-10-01

We have developed a method for implementing cylindrical coordinates in the Athena MHD code (Skinner & Ostriker 2010). The extension has been designed to alter the existing Cartesian-coordinates code (Stone et al. 2008) as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport, a central feature of the Athena algorithm, while making use of previously implemented code modules such as the eigensystems and Riemann solvers. Angular-momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and constrained transport updates. Finally, we have developed a test suite of standard and novel problems in one-, two-, and three-dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the web.

Numerical investigation of flow parameters for solid rigid spheroidal particle in a pulsatile pipe flow

NASA Astrophysics Data System (ADS)

Varghese, Joffin; Jayakumar, J. S.

2017-09-01

Quantifying, forecasting and analysing the displacement rates of suspended particles are essential while discussing about blood flow analysis. Because blood is one of the major organs in the body, which enables transport phenomena, comprising of numerous blood cells. In order to model the blood flow, a flow domain was created and numerically simulated. Flow field velocity in the stream is solved utilizing Finite Volume Method utilizing FVM unstructured solver. In pulsatile flow, the effect of parameters such as average Reynolds number, tube radius, particle size and Womersley number are taken into account. In this study spheroidal particle trajectory in axial direction is simulated at different values of pulsating frequency including 1.2 Hz, 3.33 Hz and 4.00 Hz and various densities including 1005 kg/m3 and 1025 kg/m3 for the flow domain. The analysis accomplishes the interaction study of blood constituents for different flow situations which have applications in diagnosis and treatment of cardio vascular related diseases.

Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

NASA Astrophysics Data System (ADS)

Guédon, Gaël Raymond; Hyman, Jeffrey De'Haven; Inzoli, Fabio; Riva, Monica; Guadagnini, Alberto

2017-12-01

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.

Modeling Two-Phase Flow and Vapor Cycles Using the Generalized Fluid System Simulation Program

NASA Technical Reports Server (NTRS)

Smith, Amanda D.; Majumdar, Alok K.

2017-01-01

This work presents three new applications for the general purpose fluid network solver code GFSSP developed at NASA's Marshall Space Flight Center: (1) cooling tower, (2) vapor-compression refrigeration system, and (3) vapor-expansion power generation system. These systems are widely used across engineering disciplines in a variety of energy systems, and these models expand the capabilities and the use of GFSSP to include fluids and features that are not part of its present set of provided examples. GFSSP provides pressure, temperature, and species concentrations at designated locations, or nodes, within a fluid network based on a finite volume formulation of thermodynamics and conservation laws. This paper describes the theoretical basis for the construction of the models, their implementation in the current GFSSP modeling system, and a brief evaluation of the usefulness of the model results, as well as their applicability toward a broader spectrum of analytical problems in both university teaching and engineering research.

Shock wave-free interface interaction

NASA Astrophysics Data System (ADS)

Frolov, Roman; Minev, Peter; Krechetnikov, Rouslan

2016-11-01

The problem of shock wave-free interface interaction has been widely studied in the context of compressible two-fluid flows using analytical, experimental, and numerical techniques. While various physical effects and possible interaction patterns for various geometries have been identified in the literature, the effects of viscosity and surface tension are usually neglected in such models. In our study, we apply a novel numerical algorithm for simulation of viscous compressible two-fluid flows with surface tension to investigate the influence of these effects on the shock-interface interaction. The method combines together the ideas from Finite Volume adaptation of invariant domains preserving algorithm for systems of hyperbolic conservation laws by Guermond and Popov and ADI parallel solver for viscous incompressible NSEs by Guermond and Minev. This combination has been further extended to a two-fluid flow case, including surface tension effects. Here we report on a quantitative study of how surface tension and viscosity affect the structure of the shock wave-free interface interaction region.

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

Central upwind scheme for a compressible two-phase flow model.

PubMed

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Solid rocket booster internal flow analysis by highly accurate adaptive computational methods

NASA Technical Reports Server (NTRS)

Huang, C. Y.; Tworzydlo, W.; Oden, J. T.; Bass, J. M.; Cullen, C.; Vadaketh, S.

1991-01-01

The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described.

Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations

DTIC Science & Technology

1999-01-01

purpose of the second partitioning phase , on each SMP, is to minimize the communication within the SMP; even if a multi - threaded matrix vector product...8.7 Comparison of model with experimental data for send phase of matrix vector product on ne grid...140 8.4 Matrix vector product phase times : : : : : : : : : : : : : : : : : : : : : : : 145 9.1 Flat and

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

NASA Technical Reports Server (NTRS)

Kassab, A. J.; Kapat, J. S.

2001-01-01

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

High-Order Numerical Simulations of Wind Turbine Wakes

NASA Astrophysics Data System (ADS)

Kleusberg, E.; Mikkelsen, R. F.; Schlatter, P.; Ivanell, S.; Henningson, D. S.

2017-05-01

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite-volume solvers. We employ the higher-order spectral-element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral-element method enables an accurate representation of the vortical structures, with lower numerical dissipation than the more commonly used finite-volume codes. The wind-turbine blades are modeled as body forces using the actuator-line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates homogeneous isotropic turbulence of wind-tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology (NTNU Blind Tests), investigate parametric influences and compare computational aspects with existing numerical simulations. In general the results show good agreement between the experiments and the numerical simulations both for a single-turbine setup as well as a two-turbine setup where the turbines are offset in the spanwise direction. A shift in the wake center caused by the tower wake is detected similar to experiments. The additional velocity deficit caused by the tower agrees well with the experimental data. The wake is captured well by Nek5000 in comparison with experiments both for the single wind turbine and in the two-turbine setup. The blade loading however shows large discrepancies for the high-turbulence, two-turbine case. While the experiments predicted higher thrust for the downstream turbine than for the upstream turbine, the opposite case was observed in Nek5000.

A free software for pore-scale modelling: solving Stokes equation for velocity fields and permeability values in 3D pore geometries

NASA Astrophysics Data System (ADS)

Gerke, Kirill; Vasilyev, Roman; Khirevich, Siarhei; Karsanina, Marina; Collins, Daniel; Korost, Dmitry; Mallants, Dirk

2015-04-01

In this contribution we introduce a novel free software which solves the Stokes equation to obtain velocity fields for low Reynolds-number flows within externally generated 3D pore geometries. Provided with velocity fields, one can calculate permeability for known pressure gradient boundary conditions via Darcy's equation. Finite-difference schemes of 2nd and 4th order of accuracy are used together with an artificial compressibility method to iteratively converge to a steady-state solution of Stokes' equation. This numerical approach is much faster and less computationally demanding than the majority of open-source or commercial softwares employing other algorithms (finite elements/volumes, lattice Boltzmann, etc.) The software consists of two parts: 1) a pre and post-processing graphical interface, and 2) a solver. The latter is efficiently parallelized to use any number of available cores (the speedup on 16 threads was up to 10-12 depending on hardware). Due to parallelization and memory optimization our software can be used to obtain solutions for 300x300x300 voxels geometries on modern desktop PCs. The software was successfully verified by testing it against lattice Boltzmann simulations and analytical solutions. To illustrate the software's applicability for numerous problems in Earth Sciences, a number of case studies have been developed: 1) identifying the representative elementary volume for permeability determination within a sandstone sample, 2) derivation of permeability/hydraulic conductivity values for rock and soil samples and comparing those with experimentally obtained values, 3) revealing the influence of the amount of fine-textured material such as clay on filtration properties of sandy soil. This work was partially supported by RSF grant 14-17-00658 (pore-scale modelling) and RFBR grants 13-04-00409-a and 13-05-01176-a.

Level set methods for detonation shock dynamics using high-order finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dobrev, V. A.; Grogan, F. C.; Kolev, T. V.

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two-more » and three-dimensional benchmark problems as well as applications to DSD.« less

Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling

NASA Astrophysics Data System (ADS)

Yang, Huanhuan; Gunzburger, Max

2017-06-01

Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic optimization algorithm is posed based on the conditional value-at-risk measure so that an ideal acoustic liner impedance is determined that is robust in the presence of uncertainties. A parallel reduced-order modeling framework is developed that dramatically improves the computational efficiency of the stochastic optimization solver for a realistic nacelle geometry. The reduced stochastic optimization solver takes less than 500 seconds to execute. In addition, well-posedness and finite element error analyses of the state system and optimization problem are provided.

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Bin; Chen, Luoping; Hu, Xiaozhe

2016-03-05

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigatemore » the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.« less

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M.; Jonkman, J.

2015-01-01

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented asmore » validation.« less

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

NASA Technical Reports Server (NTRS)

Wang, X. Y.; Himansu, A.; Chang, S. C.; Jorgenson, P. C. E.; Reddy, D. R. (Technical Monitor)

2002-01-01

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

GPU accelerated FDTD solver and its application in MRI.

PubMed

Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S

2010-01-01

The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD solver and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

Explicit and implicit springback simulation in sheet metal forming using fully coupled ductile damage and distortional hardening model

NASA Astrophysics Data System (ADS)

Yetna n'jock, M.; Houssem, B.; Labergere, C.; Saanouni, K.; Zhenming, Y.

2018-05-01

The springback is an important phenomenon which accompanies the forming of metallic sheets especially for high strength materials. A quantitative prediction of springback becomes very important for newly developed material with high mechanical characteristics. In this work, a numerical methodology is developed to quantify this undesirable phenomenon. This methodoly is based on the use of both explicit and implicit finite element solvers of Abaqus®. The most important ingredient of this methodology consists on the use of highly predictive mechanical model. A thermodynamically-consistent, non-associative and fully anisotropic elastoplastic constitutive model strongly coupled with isotropic ductile damage and accounting for distortional hardening is then used. An algorithm for local integration of the complete set of the constitutive equations is developed. This algorithm considers the rotated frame formulation (RFF) to ensure the incremental objectivity of the model in the framework of finite strains. This algorithm is implemented in both explicit (Abaqus/Explicit®) and implicit (Abaqus/Standard®) solvers of Abaqus® through the users routine VUMAT and UMAT respectively. The implicit solver of Abaqus® has been used to study spingback as it is generally a quasi-static unloading. In order to compare the methods `efficiency, the explicit method (Dynamic Relaxation Method) proposed by Rayleigh has been also used for springback prediction. The results obtained within U draw/bending benchmark are studied, discussed and compared with experimental results as reference. Finally, the purpose of this work is to evaluate the reliability of different methods predict efficiently springback in sheet metal forming.

Fluid-structure coupling for wind turbine blade analysis using OpenFOAM

NASA Astrophysics Data System (ADS)

Dose, Bastian; Herraez, Ivan; Peinke, Joachim

2015-11-01

Modern wind turbine rotor blades are designed increasingly large and flexible. This structural flexibility represents a problem for the field of Computational Fluid Dynamics (CFD), which is used for accurate load calculations and detailed investigations of rotor aerodynamics. As the blade geometries within CFD simulations are considered stiff, the effect of blade deformation caused by aerodynamic loads cannot be captured by the common CFD approach. Coupling the flow solver with a structural solver can overcome this restriction and enables the investigation of flexible wind turbine blades. For this purpose, a new Finite Element (FE) solver was implemented into the open source CFD code OpenFOAM. Using a beam element formulation based on the Geometrically Exact Beam Theory (GEBT), the structural model can capture geometric non-linearities such as large deformations. Coupled with CFD solvers of the OpenFOAM package, the new framework represents a powerful tool for aerodynamic investigations. In this work, we investigated the aerodynamic performance of a state of the art wind turbine. For different wind speeds, aerodynamic key parameters are evaluated and compared for both, rigid and flexible blade geometries. The present work is funded within the framework of the joint project Smart Blades (0325601D) by the German Federal Ministry for Economic Affairs and Energy (BMWi) under decision of the German Federal Parliament.

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pelanti, Marica, E-mail: Marica.Pelanti@ens.f; Bouchut, Francois, E-mail: francois.bouchut@univ-mlv.f; Mangeney, Anne, E-mail: mangeney@ipgp.jussieu.f

2011-02-01

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resultingmore » relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.« less

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

DOE PAGES

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

2015-12-10

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Computational Electromagnetics

DTIC Science & Technology

2011-02-20

finite differences use the continuation method instead, and have been shown to lead to unconditionally stable numerics for a wide range of realistic PDE...best previous solvers were restricted to two-dimensional (range and height) refractive index variations. The numerical method we introduced...however, is such that even its solution on the basis of Rytov’s method gives rise to extremely high computational costs. We thus resort to

Verification of continuum drift kinetic equation solvers in NIMROD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Held, E. D.; Ji, J.-Y.; Kruger, S. E.

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speedmore » coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.« less

Experimental and numerical study of drill bit drop tests on Kuru granite.

PubMed

Fourmeau, Marion; Kane, Alexandre; Hokka, Mikko

2017-01-28

This paper presents an experimental and numerical study of Kuru grey granite impacted with a seven-buttons drill bit mounted on an instrumented drop test machine. The force versus displacement curves during the impact, so-called bit-rock interaction (BRI) curves, were obtained using strain gauge measurements for two levels of impact energy. Moreover, the volume of removed rock after each drop test was evaluated by stereo-lithography (three-dimensional surface reconstruction). A modified version of the Holmquist-Johnson-Cook (MHJC) material model was calibrated using Kuru granite test results available from the literature. Numerical simulations of the single drop tests were carried out using the MHJC model available in the LS-DYNA explicit finite-element solver. The influence of the impact energy and additional confining pressure on the BRI curves and the volume of the removed rock is discussed. In addition, the influence of the rock surface shape before impact was evaluated using two different mesh geometries: a flat surface and a hyperbolic surface. The experimental and numerical results are compared and discussed in terms of drilling efficiency through the mechanical specific energy.This article is part of the themed issue 'Experimental testing and modelling of brittle materials at high strain rates'. © 2016 The Author(s).

Experimental and numerical study of drill bit drop tests on Kuru granite

PubMed Central

Kane, Alexandre; Hokka, Mikko

2017-01-01

This paper presents an experimental and numerical study of Kuru grey granite impacted with a seven-buttons drill bit mounted on an instrumented drop test machine. The force versus displacement curves during the impact, so-called bit–rock interaction (BRI) curves, were obtained using strain gauge measurements for two levels of impact energy. Moreover, the volume of removed rock after each drop test was evaluated by stereo-lithography (three-dimensional surface reconstruction). A modified version of the Holmquist–Johnson–Cook (MHJC) material model was calibrated using Kuru granite test results available from the literature. Numerical simulations of the single drop tests were carried out using the MHJC model available in the LS-DYNA explicit finite-element solver. The influence of the impact energy and additional confining pressure on the BRI curves and the volume of the removed rock is discussed. In addition, the influence of the rock surface shape before impact was evaluated using two different mesh geometries: a flat surface and a hyperbolic surface. The experimental and numerical results are compared and discussed in terms of drilling efficiency through the mechanical specific energy. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’. PMID:27956511

Discontinuous Galerkin method with Gaussian artificial viscosity on graphical processing units for nonlinear acoustics

NASA Astrophysics Data System (ADS)

Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François

2015-10-01

Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).

Effect of different types of nanofluids on free convection heat transfer around spherical mini-reactor

NASA Astrophysics Data System (ADS)

Jayhooni, S. M. H.; Rahimpour, M. R.

2013-06-01

In the present paper, free convection fluid flow and heat transfer of various water based nanofluids has been investigated numerically around a spherical mini-reactor. This numerical simulation is a finite-volume, steady, two dimensions, elliptic and multi-grid solver. The wall of the spherical mini-reactor are maintained at constant temperature TH and the temperature of nanofluid far from it is considered constant (TC). Computational fluid dynamics (CFD) is used for solving the relevant mathematical expressions for free convection heat transfer around it. The numerical simulation and available correlation are valid for based fluid. The effects of pertinent parameters, such as, Rayleigh number, and the volume fraction of the nanoparticles in the fluid flow and heat transfer around the spherical mini-reactor are investigated. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid is assumed to be less than 109 (Ra < 109). Besides, the percentages of the volumetric fraction of nanoparticle which is used for preparing the nanofluids, are between 0 and 4 (0 ⩽ φ ⩽ 4%). The obtained results show that the average Nusselt number for a range of the solid volume fraction of the nanofluid increases by increasing the Rayleigh number. Finally, the heat transfer has been enhanced not only by increasing the particle volume fraction but also by decreasing the size of particle diameter. Moreover, the Churchill's correlation is approximately appropriate for predicting the free convection heat transfer inside diverse kinds of nanofluids especially for high range of Rayleigh numbers.

Effect of Thermal cycles and Dimensions of the Geometry on Residual stress of the Alumina-Kovar Joint

NASA Astrophysics Data System (ADS)

Mishra, Srishti; Pal, Snehanshu; Karak, Swapan Kumar; Shah, Sejal; Venakata Nagaraju, M.; Chakraborty, Arun Kumar

2018-03-01

Finite element method is employed to determine the effect of variation of residual stress with dimension and the stress generated under its working condition along the Kovar. 3 different dimensions of Alumina-Kovar joint with height to diameter ratio of 3/10, using TiCuSil as a filler material. Transient Structural Analysis is carried out for three different dimensions (diameter × height) (i) 60mm × 20mm (Geometry 1) (ii) 90mm × 20mm (Geometry 2) (iii) 120mm × 20mm (Geometry 3). A comparative study has been carried out between the residual stresses developed in the brazed joint that have undergone 5 thermal cycles subsequent to brazing and that between the brazed joint. The heating and cooling rates from the brazed temperature is 10°C/up to room temperature. The brazing temperature and holding time considered for the analysis are 900°C and 10 minutes. Representative Volume Element (RVE) model is used for simulation. Sparse Matrix Direct Solver method is used to evaluate the results, using Augmented Lagrange method formulation in the contact region. All the simulations are performed in ANSYS Workbench 15.0, using solver target Mechanical APDL. From, the above simulations it is observed high concentration of residual stress is observed along the filler region i.e. in between Alumina and Kovar, as a result of difference in coefficient of thermal expansion between Alumina and Kovar. The residual stress decreases with increasing dimensions of the geometry and upon application of thermal cycles, subsequent to brazing.

Application of PDF methods to compressible turbulent flows

NASA Astrophysics Data System (ADS)

Delarue, B. J.; Pope, S. B.

1997-09-01

A particle method applying the probability density function (PDF) approach to turbulent compressible flows is presented. The method is applied to several turbulent flows, including the compressible mixing layer, and good agreement is obtained with experimental data. The PDF equation is solved using a Lagrangian/Monte Carlo method. To accurately account for the effects of compressibility on the flow, the velocity PDF formulation is extended to include thermodynamic variables such as the pressure and the internal energy. The mean pressure, the determination of which has been the object of active research over the last few years, is obtained directly from the particle properties. It is therefore not necessary to link the PDF solver with a finite-volume type solver. The stochastic differential equations (SDE) which model the evolution of particle properties are based on existing second-order closures for compressible turbulence, limited in application to low turbulent Mach number flows. Tests are conducted in decaying isotropic turbulence to compare the performances of the PDF method with the Reynolds-stress closures from which it is derived, and in homogeneous shear flows, at which stage comparison with direct numerical simulation (DNS) data is conducted. The model is then applied to the plane compressible mixing layer, reproducing the well-known decrease in the spreading rate with increasing compressibility. It must be emphasized that the goal of this paper is not as much to assess the performance of models of compressibility effects, as it is to present an innovative and consistent PDF formulation designed for turbulent inhomogeneous compressible flows, with the aim of extending it further to deal with supersonic reacting flows.

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makedonska, Nataliia; Painter, Scott L.; Bui, Quan M.

The discrete fracture network (DFN) model is a method to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. We present a new particle tracking capability, which is adapted to control volume (Voronoi polygons) flow solutions on unstructured grids (Delaunay triangulations) on three-dimensional DFNs. The locally mass-conserving finite-volume approach eliminates massmore » balance-related problems during particle tracking. The scalar fluxes calculated for each control volume face by the flow solver are used to reconstruct a Darcy velocity at each control volume centroid. The groundwater velocities can then be continuously interpolated to any point in the domain of interest. The control volumes at fracture intersections are split into four pieces, and the velocity is reconstructed independently on each piece, which results in multiple groundwater velocities at the intersection, one for each fracture on each side of the intersection line. This technique enables detailed particle transport representation through a complex DFN structure. Verified for small DFNs, the new simulation capability enables numerical experiments on advective transport in large DFNs to be performed. As a result, we demonstrate this particle transport approach on a DFN model using parameters similar to those of crystalline rock at a proposed geologic repository for spent nuclear fuel in Forsmark, Sweden.« less

Particle tracking approach for transport in three-dimensional discrete fracture networks: Particle tracking in 3-D DFNs

DOE PAGES

Makedonska, Nataliia; Painter, Scott L.; Bui, Quan M.; ...

2015-09-16

The discrete fracture network (DFN) model is a method to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. We present a new particle tracking capability, which is adapted to control volume (Voronoi polygons) flow solutions on unstructured grids (Delaunay triangulations) on three-dimensional DFNs. The locally mass-conserving finite-volume approach eliminates massmore » balance-related problems during particle tracking. The scalar fluxes calculated for each control volume face by the flow solver are used to reconstruct a Darcy velocity at each control volume centroid. The groundwater velocities can then be continuously interpolated to any point in the domain of interest. The control volumes at fracture intersections are split into four pieces, and the velocity is reconstructed independently on each piece, which results in multiple groundwater velocities at the intersection, one for each fracture on each side of the intersection line. This technique enables detailed particle transport representation through a complex DFN structure. Verified for small DFNs, the new simulation capability enables numerical experiments on advective transport in large DFNs to be performed. As a result, we demonstrate this particle transport approach on a DFN model using parameters similar to those of crystalline rock at a proposed geologic repository for spent nuclear fuel in Forsmark, Sweden.« less

Overcoming Challenges in Kinetic Modeling of Magnetized Plasmas and Vacuum Electronic Devices

NASA Astrophysics Data System (ADS)

Omelchenko, Yuri; Na, Dong-Yeop; Teixeira, Fernando

2017-10-01

We transform the state-of-the art of plasma modeling by taking advantage of novel computational techniques for fast and robust integration of multiscale hybrid (full particle ions, fluid electrons, no displacement current) and full-PIC models. These models are implemented in 3D HYPERS and axisymmetric full-PIC CONPIC codes. HYPERS is a massively parallel, asynchronous code. The HYPERS solver does not step fields and particles synchronously in time but instead executes local variable updates (events) at their self-adaptive rates while preserving fundamental conservation laws. The charge-conserving CONPIC code has a matrix-free explicit finite-element (FE) solver based on a sparse-approximate inverse (SPAI) algorithm. This explicit solver approximates the inverse FE system matrix (``mass'' matrix) using successive sparsity pattern orders of the original matrix. It does not reduce the set of Maxwell's equations to a vector-wave (curl-curl) equation of second order but instead utilizes the standard coupled first-order Maxwell's system. We discuss the ability of our codes to accurately and efficiently account for multiscale physical phenomena in 3D magnetized space and laboratory plasmas and axisymmetric vacuum electronic devices.

Linear solver performance in elastoplastic problem solution on GPU cluster

NASA Astrophysics Data System (ADS)

Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

2017-12-01

Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

Finite Larmor radius effects on the (m = 2, n = 1) cylindrical tearing mode

NASA Astrophysics Data System (ADS)

Chen, Y.; Chowdhury, J.; Parker, S. E.; Wan, W.

2015-04-01

New field solvers are developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate low-n modes. A novel discretization is developed for the ion polarization term in the gyrokinetic vorticity equation. An eigenmode analysis with finite Larmor radius effects is developed to study the linear resistive tearing mode. The mode growth rate is shown to scale with resistivity as γ ˜ η1/3, the same as the semi-collisional regime in previous kinetic treatments [Drake and Lee, Phys. Fluids 20, 1341 (1977)]. Tearing mode simulations with gyrokinetic ions are verified with the eigenmode calculation.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Design synthesis and optimization of permanent magnet synchronous machines based on computationally-efficient finite element analysis

NASA Astrophysics Data System (ADS)

Sizov, Gennadi Y.

In this dissertation, a model-based multi-objective optimal design of permanent magnet ac machines, supplied by sine-wave current regulated drives, is developed and implemented. The design procedure uses an efficient electromagnetic finite element-based solver to accurately model nonlinear material properties and complex geometric shapes associated with magnetic circuit design. Application of an electromagnetic finite element-based solver allows for accurate computation of intricate performance parameters and characteristics. The first contribution of this dissertation is the development of a rapid computational method that allows accurate and efficient exploration of large multi-dimensional design spaces in search of optimum design(s). The computationally efficient finite element-based approach developed in this work provides a framework of tools that allow rapid analysis of synchronous electric machines operating under steady-state conditions. In the developed modeling approach, major steady-state performance parameters such as, winding flux linkages and voltages, average, cogging and ripple torques, stator core flux densities, core losses, efficiencies and saturated machine winding inductances, are calculated with minimum computational effort. In addition, the method includes means for rapid estimation of distributed stator forces and three-dimensional effects of stator and/or rotor skew on the performance of the machine. The second contribution of this dissertation is the development of the design synthesis and optimization method based on a differential evolution algorithm. The approach relies on the developed finite element-based modeling method for electromagnetic analysis and is able to tackle large-scale multi-objective design problems using modest computational resources. Overall, computational time savings of up to two orders of magnitude are achievable, when compared to current and prevalent state-of-the-art methods. These computational savings allow one to expand the optimization problem to achieve more complex and comprehensive design objectives. The method is used in the design process of several interior permanent magnet industrial motors. The presented case studies demonstrate that the developed finite element-based approach practically eliminates the need for using less accurate analytical and lumped parameter equivalent circuit models for electric machine design optimization. The design process and experimental validation of the case-study machines are detailed in the dissertation.

Auto-adaptive finite element meshes

NASA Technical Reports Server (NTRS)

Richter, Roland; Leyland, Penelope

1995-01-01

Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

GPU-based RFA simulation for minimally invasive cancer treatment of liver tumours.

PubMed

Mariappan, Panchatcharam; Weir, Phil; Flanagan, Ronan; Voglreiter, Philip; Alhonnoro, Tuomas; Pollari, Mika; Moche, Michael; Busse, Harald; Futterer, Jurgen; Portugaller, Horst Rupert; Sequeiros, Roberto Blanco; Kolesnik, Marina

2017-01-01

Radiofrequency ablation (RFA) is one of the most popular and well-standardized minimally invasive cancer treatments (MICT) for liver tumours, employed where surgical resection has been contraindicated. Less-experienced interventional radiologists (IRs) require an appropriate planning tool for the treatment to help avoid incomplete treatment and so reduce the tumour recurrence risk. Although a few tools are available to predict the ablation lesion geometry, the process is computationally expensive. Also, in our implementation, a few patient-specific parameters are used to improve the accuracy of the lesion prediction. Advanced heterogeneous computing using personal computers, incorporating the graphics processing unit (GPU) and the central processing unit (CPU), is proposed to predict the ablation lesion geometry. The most recent GPU technology is used to accelerate the finite element approximation of Penne's bioheat equation and a three state cell model. Patient-specific input parameters are used in the bioheat model to improve accuracy of the predicted lesion. A fast GPU-based RFA solver is developed to predict the lesion by doing most of the computational tasks in the GPU, while reserving the CPU for concurrent tasks such as lesion extraction based on the heat deposition at each finite element node. The solver takes less than 3 min for a treatment duration of 26 min. When the model receives patient-specific input parameters, the deviation between real and predicted lesion is below 3 mm. A multi-centre retrospective study indicates that the fast RFA solver is capable of providing the IR with the predicted lesion in the short time period before the intervention begins when the patient has been clinically prepared for the treatment.

An immersed boundary method for fluid-structure interaction with compressible multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Li; Currao, Gaetano M. D.; Han, Feng; Neely, Andrew J.; Young, John; Tian, Fang-Bao

2017-10-01

This paper presents a two-dimensional immersed boundary method for fluid-structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid-structure interaction coupling. In the flow solver, the compressible multiphase Navier-Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge-Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

PUFoam : A novel open-source CFD solver for the simulation of polyurethane foams

NASA Astrophysics Data System (ADS)

Karimi, M.; Droghetti, H.; Marchisio, D. L.

2017-08-01

In this work a transient three-dimensional mathematical model is formulated and validated for the simulation of polyurethane (PU) foams. The model is based on computational fluid dynamics (CFD) and is coupled with a population balance equation (PBE) to describe the evolution of the gas bubbles/cells within the PU foam. The front face of the expanding foam is monitored on the basis of the volume-of-fluid (VOF) method using a compressible solver available in OpenFOAM version 3.0.1. The solver is additionally supplemented to include the PBE, solved with the quadrature method of moments (QMOM), the polymerization kinetics, an adequate rheological model and a simple model for the foam thermal conductivity. The new solver is labelled as PUFoam and is, for the first time in this work, validated for 12 different mixing-cup experiments. Comparison of the time evolution of the predicted and experimentally measured density and temperature of the PU foam shows the potentials and limitations of the approach.

A systematic approach to numerical dispersion in Maxwell solvers

NASA Astrophysics Data System (ADS)

Blinne, Alexander; Schinkel, David; Kuschel, Stephan; Elkina, Nina; Rykovanov, Sergey G.; Zepf, Matt

2018-03-01

The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which deviate from the correct values. The solution to Maxwell's equations in more than one dimension results in non-physical predictions such as numerical dispersion or numerical Cherenkov radiation emitted by a relativistic electron beam propagating in vacuum. Improved solvers, which keep the staggered Yee-type grid for electric and magnetic fields, generally modify the spatial derivative operator in the Maxwell-Faraday equation by increasing the computational stencil. These modified solvers can be characterized by different sets of coefficients, leading to different dispersion properties. In this work we introduce a norm function to rewrite the choice of coefficients into a minimization problem. We solve this problem numerically and show that the minimization procedure leads to phase and group velocities that are considerably closer to c as compared to schemes with manually set coefficients available in the literature. Depending on a specific problem at hand (e.g. electron beam propagation in plasma, high-order harmonic generation from plasma surfaces, etc.), the norm function can be chosen accordingly, for example, to minimize the numerical dispersion in a certain given propagation direction. Particle-in-cell simulations of an electron beam propagating in vacuum using our solver are provided.

Calculating qP-wave traveltimes in 2-D TTI media by high-order fast sweeping methods with a numerical quartic equation solver

NASA Astrophysics Data System (ADS)

Han, Song; Zhang, Wei; Zhang, Jie

2017-09-01

A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

Divergence-Free SPH for Incompressible and Viscous Fluids.

PubMed

Bender, Jan; Koschier, Dan

2017-03-01

In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials.