Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

A multigrid method for steady Euler equations on unstructured adaptive grids

NASA Technical Reports Server (NTRS)

Riemslagh, Kris; Dick, Erik

1993-01-01

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Finite volume solution of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Loyd, B.; Murman, E. M.

1986-01-01

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

Numerical simulation and experimental investigation about internal and external flows†

NASA Astrophysics Data System (ADS)

Wang, Tao; Yang, Guowei; Huang, Guojun; Zhou, Liandi

2006-06-01

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (Re=5.6×106) around axisymmetric body with duct. The governing equation is a RANS equation with standard k ɛ turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Simulating hydrodynamics and ice cover in Lake Erie using an unstructured grid model

NASA Astrophysics Data System (ADS)

Fujisaki-Manome, A.; Wang, J.

2016-02-01

An unstructured grid Finite-Volume Coastal Ocean Model (FVCOM) is applied to Lake Erie to simulate seasonal ice cover. The model is coupled with an unstructured-grid, finite-volume version of the Los Alamos Sea Ice Model (UG-CICE). We replaced the original 2-time-step Euler forward scheme in time integration by the central difference (i.e., leapfrog) scheme to assure a neutrally inertial stability. The modified version of FVCOM coupled with the ice model is applied to the shallow freshwater lake in this study using unstructured grids to represent the complicated coastline in the Laurentian Great Lakes and refining the spatial resolution locally. We conducted multi-year simulations in Lake Erie from 2002 to 2013. The results were compared with the observed ice extent, water surface temperature, ice thickness, currents, and water temperature profiles. Seasonal and interannual variation of ice extent and water temperature was captured reasonably, while the modeled thermocline was somewhat diffusive. The modeled ice thickness tends to be systematically thinner than the observed values. The modeled lake currents compared well with measurements obtained from an Acoustic Doppler Current Profiler located in the deep part of the lake, whereas the simulated currents deviated from measurements near the surface, possibly due to the model's inability to reproduce the sharp thermocline during the summer and the lack of detailed representation of offshore wind fields in the interpolated meteorological forcing.

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

Definition of NASTRAN sets by use of parametric geometry

NASA Technical Reports Server (NTRS)

Baughn, Terry V.; Tiv, Mehran

1989-01-01

Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

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 grid generation system for multi-disciplinary design optimization

NASA Technical Reports Server (NTRS)

Jones, William T.; Samareh-Abolhassani, Jamshid

1995-01-01

A general multi-block three-dimensional volume grid generator is presented which is suitable for Multi-Disciplinary Design Optimization. The code is timely, robust, highly automated, and written in ANSI 'C' for platform independence. Algebraic techniques are used to generate and/or modify block face and volume grids to reflect geometric changes resulting from design optimization. Volume grids are generated/modified in a batch environment and controlled via an ASCII user input deck. This allows the code to be incorporated directly into the design loop. Generated volume grids are presented for a High Speed Civil Transport (HSCT) Wing/Body geometry as well a complex HSCT configuration including horizontal and vertical tails, engine nacelles and pylons, and canard surfaces.

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.

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

NASA Technical Reports Server (NTRS)

Engwirda, Darren

2017-01-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

NASA Astrophysics Data System (ADS)

Engwirda, Darren

2017-06-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi-Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

NASA Technical Reports Server (NTRS)

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

2002-01-01

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

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.

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.

A multi-resolution approach to electromagnetic modelling

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-07-01

We present a multi-resolution approach for 3-D magnetotelluric forward modelling. Our approach is motivated by the fact that fine-grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. With a conventional structured finite difference grid, the fine discretization required to adequately represent rapid variations near the surface is continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modelling is especially important for solving regularized inversion problems. We implement a multi-resolution finite difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of subgrids, with each subgrid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modelling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modelling operators on interfaces between adjacent subgrids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models shows that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

A multi-resolution approach to electromagnetic modeling.

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-04-01

We present a multi-resolution approach for three-dimensional magnetotelluric forward modeling. Our approach is motivated by the fact that fine grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography, and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. This is especially true for forward modeling required in regularized inversion, where conductivity variations at depth are generally very smooth. With a conventional structured finite-difference grid the fine discretization required to adequately represent rapid variations near the surface are continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modeling is especially important for solving regularized inversion problems. We implement a multi-resolution finite-difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of sub-grids, with each sub-grid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modeling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modeling operators on interfaces between adjacent sub-grids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models show that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

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

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

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.

Three Dimensional Flow and Pressure Patterns in a Hydrostatic Journal Bearing

NASA Technical Reports Server (NTRS)

Braun, M. Jack; Dzodzo, Milorad B.

1996-01-01

The flow in a hydrostatic journal bearing (HJB) is described by a mathematical model that uses the three dimensional non-orthogonal form of the Navier-Stokes equations. Using the u, v, w, and p, as primary variables, a conservative formulation, finite volume multi-block method is applied through a collocated, body fitted grid. The HJB has four shallow pockets with a depth/length ratio of 0.067. This paper represents a natural extension to the two and three dimensional studies undertaken prior to this project.

Comparative Study of Advanced Turbulence Models for Turbomachinery

NASA Technical Reports Server (NTRS)

Hadid, Ali H.; Sindir, Munir M.

1996-01-01

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

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.

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

A novel simulation theory and model system for multi-field coupling pipe-flow system

NASA Astrophysics Data System (ADS)

Chen, Yang; Jiang, Fan; Cai, Guobiao; Xu, Xu

2017-09-01

Due to the lack of a theoretical basis for multi-field coupling in many system-level models, a novel set of system-level basic equations for flow/heat transfer/combustion coupling is put forward. Then a finite volume model of quasi-1D transient flow field for multi-species compressible variable-cross-section pipe flow is established by discretising the basic equations on spatially staggered grids. Combining with the 2D axisymmetric model for pipe-wall temperature field and specific chemical reaction mechanisms, a finite volume model system is established; a set of specific calculation methods suitable for multi-field coupling system-level research is structured for various parameters in this model; specific modularisation simulation models can be further derived in accordance with specific structures of various typical components in a liquid propulsion system. This novel system can also be used to derive two sub-systems: a flow/heat transfer two-field coupling pipe-flow model system without chemical reaction and species diffusion; and a chemical equilibrium thermodynamic calculation-based multi-field coupling system. The applicability and accuracy of two sub-systems have been verified through a series of dynamic modelling and simulations in earlier studies. The validity of this system is verified in an air-hydrogen combustion sample system. The basic equations and the model system provide a unified universal theory and numerical system for modelling and simulation and even virtual testing of various pipeline systems.

Sampling Scattered Data Onto Rectangular Grids for Volume Visualization

DTIC Science & Technology

1989-12-01

30 4.4 Building A Rectangular Grid ..... ................ 30 4.5 Sampling Methds ...... ...................... 34 4.6...dimensional data have been developed recently. In computational fluid flow analysis, methods for constructing three dimen- sional numerical grids are...structure of rectangular grids. Because finite element analysis is useful in fields other than fluid flow analysis and the numerical grid has promising

Grid orthogonality effects on predicted turbine midspan heat transfer and performance

NASA Technical Reports Server (NTRS)

Boyle, R. J.; Ameri, A. A.

1995-01-01

The effect of five different C type grid geometries on the predicted heat transfer and aerodynamic performance of a turbine stator is examined. Predictions were obtained using two flow analysis codes. One was a finite difference analysis, and the other was a finite volume analysis. Differences among the grids in terms of heat transfer and overall performance were small. The most significant difference among the five grids occurred in the prediction of pitchwise variation in total pressure. There was consistency between results obtained with each of the flow analysis codes when the same grid was used. A grid generating procedure in which the viscous grid is embedded within an inviscid type grid resulted in the best overall performance.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

An interactive multi-block grid generation system

NASA Technical Reports Server (NTRS)

Kao, T. J.; Su, T. Y.; Appleby, Ruth

1992-01-01

A grid generation procedure combining interactive and batch grid generation programs was put together to generate multi-block grids for complex aircraft configurations. The interactive section provides the tools for 3D geometry manipulation, surface grid extraction, boundary domain construction for 3D volume grid generation, and block-block relationships and boundary conditions for flow solvers. The procedure improves the flexibility and quality of grid generation to meet the design/analysis requirements.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Multigrid Methods for Aerodynamic Problems in Complex Geometries

NASA Technical Reports Server (NTRS)

Caughey, David A.

1995-01-01

Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

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.

Accurate solutions for transonic viscous flow over finite wings

NASA Technical Reports Server (NTRS)

Vatsa, V. N.

1986-01-01

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

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.

Substantiation of basic scheme of grain cleaning machine for preparation of agricultural crops seeds

NASA Astrophysics Data System (ADS)

Giyevskiy, A. M.; Orobinsky, V. I.; Tarasenko, A. P.; Chernyshov, A. V.; Kurilov, D. O.

2018-03-01

The article presents data on the feasibility of the concept of a high-efficiency seed cleaner with the consistent use of the air flow in aspiration and the multi-tier placement of the sorting grids in grating mills. As a result of modeling, the directions for further improvement of air-screen seed cleaning machines have been identified: an increase in the proportion of sorting grids in the mills up to 70 ... 80% and an increase in the speed of the air flow in the channel of the pre-filter cleaning up to 8.0 m / s. Experiments have established the competence of using mathematical modeling of airflow in the pneumatic system with the use of a finite-volume method for solving hydrodynamic equations for substantiating the basic parameters of the pneumatic system.

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.

Curvilinear grids for WENO methods in astrophysical simulations

NASA Astrophysics Data System (ADS)

Grimm-Strele, H.; Kupka, F.; Muthsam, H. J.

2014-03-01

We investigate the applicability of curvilinear grids in the context of astrophysical simulations and WENO schemes. With the non-smooth mapping functions from Calhoun et al. (2008), we can tackle many astrophysical problems which were out of scope with the standard grids in numerical astrophysics. We describe the difficulties occurring when implementing curvilinear coordinates into our WENO code, and how we overcome them. We illustrate the theoretical results with numerical data. The WENO finite difference scheme works only for high Mach number flows and smooth mapping functions, whereas the finite volume scheme gives accurate results even for low Mach number flows and on non-smooth grids.

The three-dimensional Multi-Block Advanced Grid Generation System (3DMAGGS)

NASA Technical Reports Server (NTRS)

Alter, Stephen J.; Weilmuenster, Kenneth J.

1993-01-01

As the size and complexity of three dimensional volume grids increases, there is a growing need for fast and efficient 3D volumetric elliptic grid solvers. Present day solvers are limited by computational speed and do not have all the capabilities such as interior volume grid clustering control, viscous grid clustering at the wall of a configuration, truncation error limiters, and convergence optimization residing in one code. A new volume grid generator, 3DMAGGS (Three-Dimensional Multi-Block Advanced Grid Generation System), which is based on the 3DGRAPE code, has evolved to meet these needs. This is a manual for the usage of 3DMAGGS and contains five sections, including the motivations and usage, a GRIDGEN interface, a grid quality analysis tool, a sample case for verifying correct operation of the code, and a comparison to both 3DGRAPE and GRIDGEN3D. Since it was derived from 3DGRAPE, this technical memorandum should be used in conjunction with the 3DGRAPE manual (NASA TM-102224).

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.

Surface Modeling and Grid Generation of Orbital Sciences X34 Vehicle. Phase 1

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

1997-01-01

The surface modeling and grid generation requirements, motivations, and methods used to develop Computational Fluid Dynamic volume grids for the X34-Phase 1 are presented. The requirements set forth by the Aerothermodynamics Branch at the NASA Langley Research Center serve as the basis for the final techniques used in the construction of all volume grids, including grids for parametric studies of the X34. The Integrated Computer Engineering and Manufacturing code for Computational Fluid Dynamics (ICEM/CFD), the Grid Generation code (GRIDGEN), the Three-Dimensional Multi-block Advanced Grid Generation System (3DMAGGS) code, and Volume Grid Manipulator (VGM) code are used to enable the necessary surface modeling, surface grid generation, volume grid generation, and grid alterations, respectively. All volume grids generated for the X34, as outlined in this paper, were used for CFD simulations within the Aerothermodynamics Branch.

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.

FV-MHMM: A Discussion on Weighting Schemes.

NASA Astrophysics Data System (ADS)

Franc, J.; Gerald, D.; Jeannin, L.; Egermann, P.; Masson, R.

2016-12-01

Upscaling or homogenization techniques consist in finding block-equivalentor equivalent upscaled properties on a coarse grid from heterogeneousproperties defined on an underlying fine grid. However, this couldbecome costly and resource consuming. Harder et al., 2013, have developeda Multiscale Hybrid-Mixed Method (MHMM) of upscaling to treat Darcytype equations on heterogeneous fields formulated using a finite elementmethod. Recently, Franc et al. 2016, has extended this method of upscalingto finite volume formulation (FV-MHMM). Although convergence refiningLagrange multipliers space has been observed, numerical artefactscan occur while trapping numerically the flow in regions of low permeability. This work will present the development of the method along with theresults obtained from its classical formulation. Then, two weightingschemes and their benefits on the FV-MHMM method will be presented insome simple random permeability cases. Next example will involve alarger heterogeneous 2D permeability field extracted from the 10thSPE test case. Eventually, multiphase flow will be addressed asan extension of this single phase flow method. An elliptic pressureequation solved on the coarse grid via FV-MHMM will be sequentiallycoupled with a hyperbolic saturation equation on the fine grid. Theimproved accuracy thanks to the weighting scheme will be measuredcompared to a finite volume fine grid solution. References: Harder, C., Paredes, D. and Valentin, F., A family of multiscalehybrid-mixed finite element methods for the Darcy equation with roughcoefficients, Journal of Computational Physics, 2013. Franc J., Debenest G., Jeannin L., Egermann P. and Masson R., FV-MHMMfor reservoir modelling ECMOR XV-15th European Conference on the Mathematicsof Oil Recovery, 2015.

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.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 1: Theory and validations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Iannelli, G. S.; Manhardt, Paul D.; Orzechowski, J. A.

1993-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 2: FEMNAS user guide

NASA Technical Reports Server (NTRS)

Manhardt, Paul D.; Orzechowski, J. A.; Baker, A. J.

1992-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

NASA Astrophysics Data System (ADS)

Pletzer, Alexander; Jamroz, Ben; Crockett, Robert; Sides, Scott

2014-03-01

Different strategies for coupling fine-coarse grid patches are explored in the context of the adaptive mesh refinement (AMR) method. We show that applying linear interpolation to fill in the fine grid ghost values can produce a finite volume stencil of comparable accuracy to quadratic interpolation provided the cell volumes are adjusted. The volume of fine cells expands whereas the volume of neighboring coarse cells contracts. The amount by which the cells contract/expand depends on whether the interface is a face, an edge, or a corner. It is shown that quadratic or better interpolation is required when the conductivity is spatially varying, anisotropic, the refinement ratio is other than two, or when the fine-coarse interface is concave.

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

NASA Technical Reports Server (NTRS)

Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.

1996-01-01

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Multi-scale Methods in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Polyzou, W. N.; Michlin, Tracie; Bulut, Fatih

2018-05-01

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.

The multidimensional Self-Adaptive Grid code, SAGE, version 2

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1995-01-01

This new report on Version 2 of the SAGE code includes all the information in the original publication plus all upgrades and changes to the SAGE code since that time. The two most significant upgrades are the inclusion of a finite-volume option and the ability to adapt and manipulate zonal-matching multiple-grid files. In addition, the original SAGE code has been upgraded to Version 1.1 and includes all options mentioned in this report, with the exception of the multiple grid option and its associated features. Since Version 2 is a larger and more complex code, it is suggested (but not required) that Version 1.1 be used for single-grid applications. This document contains all the information required to run both versions of SAGE. The formulation of the adaption method is described in the first section of this document. The second section is presented in the form of a user guide that explains the input and execution of the code. The third section provides many examples. Successful application of the SAGE code in both two and three dimensions for the solution of various flow problems has proven the code to be robust, portable, and simple to use. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for complex grid structures. Modifications to the method and the simple but extensive input options make this a flexible and user-friendly code. The SAGE code can accommodate two-dimensional and three-dimensional, finite-difference and finite-volume, single grid, and zonal-matching multiple grid flow problems.

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.

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.

Calculations of Flowfield About Indented Nosetips,

DTIC Science & Technology

1982-08-23

agreement is good. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOE(ft,. Date E -t. , - NSWC TR 82-286 FOREWORD A finite difference computer program has been...Specific heat at constant pressure and volume respectively e Total energy per unit volume E ,F,H,R,S,T Functions of U AHT, HT Error in total enthalpy and...total enthalpy respectively ijGrid index in E and n directions respectively SI Identity matrix J,K Maximum grid point in E and n directions respectively

Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.; ,; ,; ,; ,; ,

2000-01-01

Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems, task 1: Ducted propfan analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1990-01-01

The time-dependent three-dimensional Euler equations of gas dynamics were solved numerically to study the steady compressible transonic flow about ducted propfan propulsion systems. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. An implicit residual smoothing operator was used to aid convergence. Two calculation grids were employed in this study. The first grid utilized an H-type mesh network with a branch cut opening to represent the axisymmetric cowl. The second grid utilized a multiple-block mesh system with a C-type grid about the cowl. The individual blocks were numerically coupled in the Euler solver. Grid systems were generated by a combined algebraic/elliptic algortihm developed specifically for ducted propfans. Numerical calculations were initially performed for unducted propfans to verify the accuracy of the three-dimensional Euler formulation. The Euler analyses were then applied for the calculation of ducted propfan flows, and predicted results were compared with experimental data for two cases. The three-dimensional Euler analyses displayed exceptional accuracy, although certain parameters were observed to be very sensitive to geometric deflections. Both solution schemes were found to be very robust and demonstrated nearly equal efficiency and accuracy, although it was observed that the multi-block C-grid formulation provided somewhat better resolution of the cowl leading edge region.

FVCOM one-way and two-way nesting using ESMF: Development and validation

NASA Astrophysics Data System (ADS)

Qi, Jianhua; Chen, Changsheng; Beardsley, Robert C.

2018-04-01

Built on the Earth System Modeling Framework (ESMF), the one-way and two-way nesting methods were implemented into the unstructured-grid Finite-Volume Community Ocean Model (FVCOM). These methods help utilize the unstructured-grid multi-domain nesting of FVCOM with an aim at resolving the multi-scale physical and ecosystem processes. A detail of procedures on implementing FVCOM into ESMF was described. The experiments were made to validate and evaluate the performance of the nested-grid FVCOM system. The first was made for a wave-current interaction case with a two-domain nesting with an emphasis on qualifying a critical need of nesting to resolve a high-resolution feature near the coast and harbor with little loss in computational efficiency. The second was conducted for the pseudo river plume cases to examine the differences in the model-simulated salinity between one-way and two-way nesting approaches and evaluate the performance of mass conservative two-way nesting method. The third was carried out for the river plume case in the realistic geometric domain in Mass Bay, supporting the importance for having the two-way nesting for coastal-estuarine integrated modeling. The nesting method described in this paper has been used in the Northeast Coastal Ocean Forecast System (NECOFS)-a global-regional-coastal nesting FVCOM system that has been placed into the end-to-end forecast and hindcast operations since 2007.

Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135

NASA Astrophysics Data System (ADS)

Toyokuni, G.; Takenaka, H.

2007-12-01

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.

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.

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

USGS Publications Warehouse

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2013-12-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed-sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2014-05-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Implicit gas-kinetic unified algorithm based on multi-block docking grid for multi-body reentry flows covering all flow regimes

NASA Astrophysics Data System (ADS)

Peng, Ao-Ping; Li, Zhi-Hui; Wu, Jun-Lin; Jiang, Xin-Yu

2016-12-01

Based on the previous researches of the Gas-Kinetic Unified Algorithm (GKUA) for flows from highly rarefied free-molecule transition to continuum, a new implicit scheme of cell-centered finite volume method is presented for directly solving the unified Boltzmann model equation covering various flow regimes. In view of the difficulty in generating the single-block grid system with high quality for complex irregular bodies, a multi-block docking grid generation method is designed on the basis of data transmission between blocks, and the data structure is constructed for processing arbitrary connection relations between blocks with high efficiency and reliability. As a result, the gas-kinetic unified algorithm with the implicit scheme and multi-block docking grid has been firstly established and used to solve the reentry flow problems around the multi-bodies covering all flow regimes with the whole range of Knudsen numbers from 10 to 3.7E-6. The implicit and explicit schemes are applied to computing and analyzing the supersonic flows in near-continuum and continuum regimes around a circular cylinder with careful comparison each other. It is shown that the present algorithm and modelling possess much higher computational efficiency and faster converging properties. The flow problems including two and three side-by-side cylinders are simulated from highly rarefied to near-continuum flow regimes, and the present computed results are found in good agreement with the related DSMC simulation and theoretical analysis solutions, which verify the good accuracy and reliability of the present method. It is observed that the spacing of the multi-body is smaller, the cylindrical throat obstruction is greater with the flow field of single-body asymmetrical more obviously and the normal force coefficient bigger. While in the near-continuum transitional flow regime of near-space flying surroundings, the spacing of the multi-body increases to six times of the diameter of the single-body, the interference effects of the multi-bodies tend to be negligible. The computing practice has confirmed that it is feasible for the present method to compute the aerodynamics and reveal flow mechanism around complex multi-body vehicles covering all flow regimes from the gas-kinetic point of view of solving the unified Boltzmann model velocity distribution function equation.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« less

A finite volume Fokker-Planck collision operator in constants-of-motion coordinates

NASA Astrophysics Data System (ADS)

Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.

2006-04-01

TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations

NASA Astrophysics Data System (ADS)

Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur

2017-11-01

Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, we present FPS coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh as well as in the computational domain. We present a comparison of the hybrid-grid FPS method and the lower-dimensional fracture model for several cases of isotropic and anisotropic fractured media which illustrate the benefits of the respective methods.

A 3-D enlarged cell technique (ECT) for elastic wave modelling of a curved free surface

NASA Astrophysics Data System (ADS)

Wei, Songlin; Zhou, Jianyang; Zhuang, Mingwei; Liu, Qing Huo

2016-09-01

The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.

A finite difference method for a coupled model of wave propagation in poroelastic materials.

PubMed

Zhang, Yang; Song, Limin; Deffenbaugh, Max; Toksöz, M Nafi

2010-05-01

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.; Lytle, John K.

1989-01-01

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.

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.

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).

Aerodynamic Characteristics of High Speed Trains under Cross Wind Conditions

NASA Astrophysics Data System (ADS)

Chen, W.; Wu, S. P.; Zhang, Y.

2011-09-01

Numerical simulation for the two models in cross-wind was carried out in this paper. The three-dimensional compressible Reynolds-averaged Navier-Stokes equations(RANS), combined with the standard k-ɛ turbulence model, were solved on multi-block hybrid grids by second order upwind finite volume technique. The impact of fairing on aerodynamic characteristics of the train models was analyzed. It is shown that, the flow separates on the fairing and a strong vortex is generated, the pressure on the upper middle car decreases dramatically, which leads to a large lift force. The fairing changes the basic patterns around the trains. In addition, formulas of the coefficient of aerodynamic force at small yaw angles up to 24° were expressed.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

NASA Technical Reports Server (NTRS)

Candler, Graham V.; Johnson, Heath B.; Nompelis, Ioannis; Subbareddy, Pramod K.; Drayna, Travis W.; Gidzak, Vladimyr; Barnhardt, Michael D.

2015-01-01

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Eiseman, Peter R.; Reno, Charles

1988-01-01

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Reno, Charles; Eiseman, Peter R.

1988-01-01

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1998-01-01

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

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.

PARADIGM USING JOINT DETERMINISTIC GRID MODELING AND SUB-GRID VARIABILITY STOCHASTIC DESCRIPTION AS A TEMPLATE FOR MODEL EVALUATION

EPA Science Inventory

The goal of achieving verisimilitude of air quality simulations to observations is problematic. Chemical transport models such as the Community Multi-Scale Air Quality (CMAQ) modeling system produce volume averages of pollutant concentration fields. When grid sizes are such tha...

GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows

NASA Technical Reports Server (NTRS)

2003-01-01

With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.

Efficient Development of High Fidelity Structured Volume Grids for Hypersonic Flow Simulations

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

2003-01-01

A new technique for the control of grid line spacing and intersection angles of a structured volume grid, using elliptic partial differential equations (PDEs) is presented. Existing structured grid generation algorithms make use of source term hybridization to provide control of grid lines, imposing orthogonality implicitly at the boundary and explicitly on the interior of the domain. A bridging function between the two types of grid line control is typically used to blend the different orthogonality formulations. It is shown that utilizing such a bridging function with source term hybridization can result in the excessive use of computational resources and diminishes robustness. A new approach, Anisotropic Lagrange Based Trans-Finite Interpolation (ALBTFI), is offered as a replacement to source term hybridization. The ALBTFI technique captures the essence of the desired grid controls while improving the convergence rate of the elliptic PDEs when compared with source term hybridization. Grid generation on a blunt cone and a Shuttle Orbiter is used to demonstrate and assess the ALBTFI technique, which is shown to be as much as 50% faster, more robust, and produces higher quality grids than source term hybridization.

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.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Turkel, Eli; Schaffer, Steve

1987-01-01

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing

NASA Astrophysics Data System (ADS)

Watanabe, T.; Nagata, K.

2016-08-01

We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting a value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES-LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.

Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing

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

Watanabe, T., E-mail: watanabe.tomoaki@c.nagoya-u.jp; Nagata, K.

We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting amore » value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES–LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.« less

Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2010-01-01

This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.

A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID

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

Feng, Xueshang; Zhang, Man; Zhou, Yufen, E-mail: fengx@spaceweather.ac.cn

In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space andmore » time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.« less

Simulations of Tornadoes, Tropical Cyclones, MJOs, and QBOs, using GFDL's multi-scale global climate modeling system

NASA Astrophysics Data System (ADS)

Lin, Shian-Jiann; Harris, Lucas; Chen, Jan-Huey; Zhao, Ming

2014-05-01

A multi-scale High-Resolution Atmosphere Model (HiRAM) is being developed at NOAA/Geophysical Fluid Dynamics Laboratory. The model's dynamical framework is the non-hydrostatic extension of the vertically Lagrangian finite-volume dynamical core (Lin 2004, Monthly Wea. Rev.) constructed on a stretchable (via Schmidt transformation) cubed-sphere grid. Physical parametrizations originally designed for IPCC-type climate predictions are in the process of being modified and made more "scale-aware", in an effort to make the model suitable for multi-scale weather-climate applications, with horizontal resolution ranging from 1 km (near the target high-resolution region) to as low as 400 km (near the antipodal point). One of the main goals of this development is to enable simulation of high impact weather phenomena (such as tornadoes, thunderstorms, category-5 hurricanes) within an IPCC-class climate modeling system previously thought impossible. We will present preliminary results, covering a very wide spectrum of temporal-spatial scales, ranging from simulation of tornado genesis (hours), Madden-Julian Oscillations (intra-seasonal), topical cyclones (seasonal), to Quasi Biennial Oscillations (intra-decadal), using the same global multi-scale modeling system.

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.

The NASA-Goddard Multi-Scale Modeling Framework - Land Information System: Global Land/atmosphere Interaction with Resolved Convection

NASA Technical Reports Server (NTRS)

Mohr, Karen Irene; Tao, Wei-Kuo; Chern, Jiun-Dar; Kumar, Sujay V.; Peters-Lidard, Christa D.

2013-01-01

The present generation of general circulation models (GCM) use parameterized cumulus schemes and run at hydrostatic grid resolutions. To improve the representation of cloud-scale moist processes and landeatmosphere interactions, a global, Multi-scale Modeling Framework (MMF) coupled to the Land Information System (LIS) has been developed at NASA-Goddard Space Flight Center. The MMFeLIS has three components, a finite-volume (fv) GCM (Goddard Earth Observing System Ver. 4, GEOS-4), a 2D cloud-resolving model (Goddard Cumulus Ensemble, GCE), and the LIS, representing the large-scale atmospheric circulation, cloud processes, and land surface processes, respectively. The non-hydrostatic GCE model replaces the single-column cumulus parameterization of fvGCM. The model grid is composed of an array of fvGCM gridcells each with a series of embedded GCE models. A horizontal coupling strategy, GCE4fvGCM4Coupler4LIS, offered significant computational efficiency, with the scalability and I/O capabilities of LIS permitting landeatmosphere interactions at cloud-scale. Global simulations of 2007e2008 and comparisons to observations and reanalysis products were conducted. Using two different versions of the same land surface model but the same initial conditions, divergence in regional, synoptic-scale surface pressure patterns emerged within two weeks. The sensitivity of largescale circulations to land surface model physics revealed significant functional value to using a scalable, multi-model land surface modeling system in global weather and climate prediction.

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

PubMed Central

Borazjani, Iman; Ge, Liang; Le, Trung; Sotiropoulos, Fotis

2013-01-01

We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position. PMID:23833331

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

NASA Astrophysics Data System (ADS)

Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

2017-11-01

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1992-01-01

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

CFD-ACE+: a CAD system for simulation and modeling of MEMS

NASA Astrophysics Data System (ADS)

Stout, Phillip J.; Yang, H. Q.; Dionne, Paul; Leonard, Andy; Tan, Zhiqiang; Przekwas, Andrzej J.; Krishnan, Anantha

1999-03-01

Computer aided design (CAD) systems are a key to designing and manufacturing MEMS with higher performance/reliability, reduced costs, shorter prototyping cycles and improved time- to-market. One such system is CFD-ACE+MEMS, a modeling and simulation environment for MEMS which includes grid generation, data visualization, graphical problem setup, and coupled fluidic, thermal, mechanical, electrostatic, and magnetic physical models. The fluid model is a 3D multi- block, structured/unstructured/hybrid, pressure-based, implicit Navier-Stokes code with capabilities for multi- component diffusion, multi-species transport, multi-step gas phase chemical reactions, surface reactions, and multi-media conjugate heat transfer. The thermal model solves the total enthalpy from of the energy equation. The energy equation includes unsteady, convective, conductive, species energy, viscous dissipation, work, and radiation terms. The electrostatic model solves Poisson's equation. Both the finite volume method and the boundary element method (BEM) are available for solving Poisson's equation. The BEM method is useful for unbounded problems. The magnetic model solves for the vector magnetic potential from Maxwell's equations including eddy currents but neglecting displacement currents. The mechanical model is a finite element stress/deformation solver which has been coupled to the flow, heat, electrostatic, and magnetic calculations to study flow, thermal electrostatically, and magnetically included deformations of structures. The mechanical or structural model can accommodate elastic and plastic materials, can handle large non-linear displacements, and can model isotropic and anisotropic materials. The thermal- mechanical coupling involves the solution of the steady state Navier equation with thermoelastic deformation. The electrostatic-mechanical coupling is a calculation of the pressure force due to surface charge on the mechanical structure. Results of CFD-ACE+MEMS modeling of MEMS such as cantilever beams, accelerometers, and comb drives are discussed.

A-Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Problems Coupled Through a Boundary with Non-Matching Grids

DTIC Science & Technology

2013-08-01

both MFE and GFV, are often similar in size. As a gross measure of the effect of geometric projection and of the use of quadrature, we also report the...interest MFE ∑(e,ψ) or GFV ∑(e,ψ). Tables 1 and 2 show this using coarse and fine forward solutions. Table 1. The forward problem with solution (4.1) is run...adjoint data components ψu and ψp are constant everywhere and ψξ = 0. adj. grid MFE ∑(e,ψ) ∑MFEi ratio GFV ∑(e,ψ) ∑GFV i ratio 20x20 : 32x32 1.96E−3

Constrained CVT meshes and a comparison of triangular mesh generators

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

Nguyen, Hoa; Burkardt, John; Gunzburger, Max

2009-01-01

Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. We focus on the uniform Delaunay triangulation of planar regions and, in particular, on how one selects the positions of the vertices of the triangulation. We discuss a recently developed method, based on the centroidal Voronoi tessellation (CVT) concept, for effecting such triangulations and present two algorithms, including one new one, for CVT-based grid generation. We also compare several methods, including CVT-based methods, for triangulatingmore » planar domains. To this end, we define several quantitative measures of the quality of uniform grids. We then generate triangulations of several planar regions, including some having complexities that are representative of what one may encounter in practice. We subject the resulting grids to visual and quantitative comparisons and conclude that all the methods considered produce high-quality uniform grids and that the CVT-based grids are at least as good as any of the others.« less

NASA Workshop on Computational Structural Mechanics 1987, part 3

NASA Technical Reports Server (NTRS)

Sykes, Nancy P. (Editor)

1989-01-01

Computational Structural Mechanics (CSM) topics are explored. Algorithms and software for nonlinear structural dynamics, concurrent algorithms for transient finite element analysis, computational methods and software systems for dynamics and control of large space structures, and the use of multi-grid for structural analysis are discussed.

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.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Simulations of Turbine Cooling Flows Using a Multiblock-Multigrid Scheme

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Ameri, Ali A.; Rigby, David L.

1996-01-01

Results from numerical simulations of air flow and heat transfer in a 'branched duct' geometry are presented. The geometry contains features, including pins and a partition, as are found in coolant passages of turbine blades. The simulations were performed using a multi-block structured grid system and a finite volume discretization of the governing equations (the compressible Navier-Stokes equations). The effects of turbulence on the mean flow and heat transfer were modeled using the Baldwin-Lomax turbulence model. The computed results are compared to experimental data. It was found that the extent of some regions of high heat transfer was somewhat under predicted. It is conjectured that the underlying reason is the local nature of the turbulence model which cannot account for upstream influence on the turbulence field. In general, however, the comparison with the experimental data is favorable.

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.

Transonic cascade flow calculations using non-periodic C-type grids

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1991-01-01

A new kind of C-type grid is proposed for turbomachinery flow calculations. This grid is nonperiodic on the wake and results in minimum skewness for cascades with high turning and large camber. Euler and Reynolds averaged Navier-Stokes equations are discretized on this type of grid using a finite volume approach. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. Jameson's explicit Runge-Kutta scheme is adopted for the integration in time, and computational efficiency is achieved through accelerating strategies such as multigriding and residual smoothing. A detailed numerical study was performed for a turbine rotor and for a vane. A grid dependence analysis is presented and the effect of artificial dissipation is also investigated. Comparison of calculations with experiments clearly demonstrates the advantage of the proposed grid.

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.

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.

Dynamical Core in Atmospheric Model Does Matter in the Simulation of Arctic Climate

NASA Astrophysics Data System (ADS)

Jun, Sang-Yoon; Choi, Suk-Jin; Kim, Baek-Min

2018-03-01

Climate models using different dynamical cores can simulate significantly different winter Arctic climates even if equipped with virtually the same physics schemes. Current climate simulated by the global climate model using cubed-sphere grid with spectral element method (SE core) exhibited significantly warmer Arctic surface air temperature compared to that using latitude-longitude grid with finite volume method core. Compared to the finite volume method core, SE core simulated additional adiabatic warming in the Arctic lower atmosphere, and this was consistent with the eddy-forced secondary circulation. Downward longwave radiation further enhanced Arctic near-surface warming with a higher surface air temperature of about 1.9 K. Furthermore, in the atmospheric response to the reduced sea ice conditions with the same physical settings, only the SE core showed a robust cooling response over North America. We emphasize that special attention is needed in selecting the dynamical core of climate models in the simulation of the Arctic climate and associated teleconnection patterns.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part 1; Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2009-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

DOE PAGES

McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

2015-09-04

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

Accuracy Analysis for Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

A new computational analysis tool, downscaling test, is introduced and applied for studying the convergence rates of truncation and discretization errors of nite-volume discretization schemes on general irregular (e.g., unstructured) grids. The study shows that the design-order convergence of discretization errors can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all. The downscaling test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the downscaling test analysis. It is shown that the discretization accuracy of a common node-centered nite-volume scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for mixed grids. Alternative node-centered schemes are presented and demonstrated to provide second and third order accuracies on general mixed grids. The local accuracy deterioration at intersections of tangency and in flow/outflow boundaries is demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions is demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme.

Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid

NASA Astrophysics Data System (ADS)

Titarenko, Sofya; Hildyard, Mark

2017-07-01

In modern physics it has become common to find the solution of a problem by solving numerically a set of PDEs. Whether solving them on a finite difference grid or by a finite element approach, the main calculations are often applied to a stencil structure. In the last decade it has become usual to work with so called big data problems where calculations are very heavy and accelerators and modern architectures are widely used. Although CPU and GPU clusters are often used to solve such problems, parallelisation of any calculation ideally starts from a single processor optimisation. Unfortunately, it is impossible to vectorise a stencil structured loop with high level instructions. In this paper we suggest a new approach to rearranging the data structure which makes it possible to apply high level vectorisation instructions to a stencil loop and which results in significant acceleration. The suggested method allows further acceleration if shared memory APIs are used. We show the effectiveness of the method by applying it to an elastic wave propagation problem on a finite difference grid. We have chosen Intel architecture for the test problem and OpenMP (Open Multi-Processing) since they are extensively used in many applications.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2010-01-01

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.

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.

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

NASA Technical Reports Server (NTRS)

Gerritsen, Margot; Olsson, Pelle

1996-01-01

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Numerical computation of complex multi-body Navier-Stokes flows with applications for the integrated Space Shuttle launch vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1993-01-01

An enhanced grid system for the Space Shuttle Orbiter was built by integrating CAD definitions from several sources and then generating the surface and volume grids. The new grid system contains geometric components not modeled previously plus significant enhancements on geometry that has been modeled in the old grid system. The new orbiter grids were then integrated with new grids for the rest of the launch vehicle. Enhancements were made to the hyperbolic grid generator HYPGEN and new tools for grid projection, manipulation, and modification, Cartesian box grid and far field grid generation and post-processing of flow solver data were developed.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

High order multi-grid methods to solve the Poisson equation

NASA Technical Reports Server (NTRS)

Schaffer, S.

1981-01-01

High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.

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

Smart grid initialization reduces the computational complexity of multi-objective image registration based on a dual-dynamic transformation model to account for large anatomical differences

NASA Astrophysics Data System (ADS)

Bosman, Peter A. N.; Alderliesten, Tanja

2016-03-01

We recently demonstrated the strong potential of using dual-dynamic transformation models when tackling deformable image registration problems involving large anatomical differences. Dual-dynamic transformation models employ two moving grids instead of the common single moving grid for the target image (and single fixed grid for the source image). We previously employed powerful optimization algorithms to make use of the additional flexibility offered by a dual-dynamic transformation model with good results, directly obtaining insight into the trade-off between important registration objectives as a result of taking a multi-objective approach to optimization. However, optimization has so far been initialized using two regular grids, which still leaves a great potential of dual-dynamic transformation models untapped: a-priori grid alignment with image structures/areas that are expected to deform more. This allows (far) less grid points to be used, compared to using a sufficiently refined regular grid, leading to (far) more efficient optimization, or, equivalently, more accurate results using the same number of grid points. We study the implications of exploiting this potential by experimenting with two new smart grid initialization procedures: one manual expert-based and one automated image-feature-based. We consider a CT test case with large differences in bladder volume with and without a multi-resolution scheme and find a substantial benefit of using smart grid initialization.

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

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Ash, Robert L.

1992-01-01

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

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.

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.

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

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.

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.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2010-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Direct Density Functional Energy Minimization using an Tetrahedral Finite Element Grid

NASA Astrophysics Data System (ADS)

Vaught, A.; Schmidt, K. E.; Chizmeshya, A. V. G.

1998-03-01

We describe an O(N) (N proportional to volume) technique for solving electronic structure problems using the finite element method (FEM). A real--space tetrahedral grid is used as a basis to represent the electronic density, of a free or periodic system and Poisson's equation is solved as a boundary value problem. Nuclear cusps are treated using a local grid consisting of radial elements. These features facilitate the implementation of complicated energy functionals and permit a direct (constrained) energy minimization with respect to the density. We demonstrate the usefulness of the scheme by calculating the binding trends and polarizabilities of a number of atoms and molecules using a number of recently proposed non--local, orbital--free kinetic energy functionals^1,2. Scaling behavior, computational efficiency and the generalization to band--structure will also be discussed. indent 0 pt øbeylines øbeyspaces skip 0 pt ^1 P. Garcia-Gonzalez, J.E. Alvarellos and E. Chacon, Phys. Rev. B 54, 1897 (1996). ^2 A. J. Thakkar, Phys.Rev.B 46, 6920 (1992).

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

A parallel electrostatic Particle-in-Cell method on unstructured tetrahedral grids for large-scale bounded collisionless plasma simulations

NASA Astrophysics Data System (ADS)

Averkin, Sergey N.; Gatsonis, Nikolaos A.

2018-06-01

An unstructured electrostatic Particle-In-Cell (EUPIC) method is developed on arbitrary tetrahedral grids for simulation of plasmas bounded by arbitrary geometries. The electric potential in EUPIC is obtained on cell vertices from a finite volume Multi-Point Flux Approximation of Gauss' law using the indirect dual cell with Dirichlet, Neumann and external circuit boundary conditions. The resulting matrix equation for the nodal potential is solved with a restarted generalized minimal residual method (GMRES) and an ILU(0) preconditioner algorithm, parallelized using a combination of node coloring and level scheduling approaches. The electric field on vertices is obtained using the gradient theorem applied to the indirect dual cell. The algorithms for injection, particle loading, particle motion, and particle tracking are parallelized for unstructured tetrahedral grids. The algorithms for the potential solver, electric field evaluation, loading, scatter-gather algorithms are verified using analytic solutions for test cases subject to Laplace and Poisson equations. Grid sensitivity analysis examines the L2 and L∞ norms of the relative error in potential, field, and charge density as a function of edge-averaged and volume-averaged cell size. Analysis shows second order of convergence for the potential and first order of convergence for the electric field and charge density. Temporal sensitivity analysis is performed and the momentum and energy conservation properties of the particle integrators in EUPIC are examined. The effects of cell size and timestep on heating, slowing-down and the deflection times are quantified. The heating, slowing-down and the deflection times are found to be almost linearly dependent on number of particles per cell. EUPIC simulations of current collection by cylindrical Langmuir probes in collisionless plasmas show good comparison with previous experimentally validated numerical results. These simulations were also used in a parallelization efficiency investigation. Results show that the EUPIC has efficiency of more than 80% when the simulation is performed on a single CPU from a non-uniform memory access node and the efficiency is decreasing as the number of threads further increases. The EUPIC is applied to the simulation of the multi-species plasma flow over a geometrically complex CubeSat in Low Earth Orbit. The EUPIC potential and flowfield distribution around the CubeSat exhibit features that are consistent with previous simulations over simpler geometrical bodies.

On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models

NASA Astrophysics Data System (ADS)

Xu, S.; Wang, B.; Liu, J.

2015-10-01

In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz-Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal-longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land-sea distribution is present.

Generation of a composite grid for turbine flows and consideration of a numerical scheme

NASA Technical Reports Server (NTRS)

Choo, Y.; Yoon, S.; Reno, C.

1986-01-01

A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

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.

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

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.

Modular Multi-Sensor Display System Design Study. Volume 2. Detail Design and Application Analysis

DTIC Science & Technology

1974-08-01

control grid . 2. Horizontal AFC/Deflection Module - Generates horizontal sweep signals from input syncs to provide 525 to 1023 line television raster...separation, and gener- ate composite blanking for the CRT control grid . Signal Number of Lines Signal Type Characteristics Input Interface Composite...SEPERATOR DC RESTORA- TION l_i BLANKING VERT DRIVE ■♦ Bl" CRT " CATHODE * _fc> BRIGHTNESS ^ (FRONT PANEL) .CRT GRID ■♦• COMP SYNC Figure

Application of an unstructured grid flow solver to planes, trains and automobiles

NASA Technical Reports Server (NTRS)

Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram

1993-01-01

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

NASA Technical Reports Server (NTRS)

Tao, W.-K.; Chern, J.; Atlas, R.

2005-01-01

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Investigation of Navier-Stokes Code Verification and Design Optimization

NASA Technical Reports Server (NTRS)

Vaidyanathan, Rajkumar

2004-01-01

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Toward GEOS-6, A Global Cloud System Resolving Atmospheric Model

NASA Technical Reports Server (NTRS)

Putman, William M.

2010-01-01

NASA is committed to observing and understanding the weather and climate of our home planet through the use of multi-scale modeling systems and space-based observations. Global climate models have evolved to take advantage of the influx of multi- and many-core computing technologies and the availability of large clusters of multi-core microprocessors. GEOS-6 is a next-generation cloud system resolving atmospheric model that will place NASA at the forefront of scientific exploration of our atmosphere and climate. Model simulations with GEOS-6 will produce a realistic representation of our atmosphere on the scale of typical satellite observations, bringing a visual comprehension of model results to a new level among the climate enthusiasts. In preparation for GEOS-6, the agency's flagship Earth System Modeling Framework [JDl] has been enhanced to support cutting-edge high-resolution global climate and weather simulations. Improvements include a cubed-sphere grid that exposes parallelism; a non-hydrostatic finite volume dynamical core, and algorithm designed for co-processor technologies, among others. GEOS-6 represents a fundamental advancement in the capability of global Earth system models. The ability to directly compare global simulations at the resolution of spaceborne satellite images will lead to algorithm improvements and better utilization of space-based observations within the GOES data assimilation system

Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow. Degree awarded by Virginia Polytechnic Inst. and State Univ., 9 Nov. 2001

NASA Technical Reports Server (NTRS)

Wood, William A., III

2002-01-01

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

NASA Technical Reports Server (NTRS)

Lopez Ortega, Alejandro; Mikellides, Ioannis G.

2014-01-01

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

OpenMP performance for benchmark 2D shallow water equations using LBM

NASA Astrophysics Data System (ADS)

Sabri, Khairul; Rabbani, Hasbi; Gunawan, Putu Harry

2018-03-01

Shallow water equations or commonly referred as Saint-Venant equations are used to model fluid phenomena. These equations can be solved numerically using several methods, like Lattice Boltzmann method (LBM), SIMPLE-like Method, Finite Difference Method, Godunov-type Method, and Finite Volume Method. In this paper, the shallow water equation will be approximated using LBM or known as LABSWE and will be simulated in performance of parallel programming using OpenMP. To evaluate the performance between 2 and 4 threads parallel algorithm, ten various number of grids Lx and Ly are elaborated. The results show that using OpenMP platform, the computational time for solving LABSWE can be decreased. For instance using grid sizes 1000 × 500, the speedup of 2 and 4 threads is observed 93.54 s and 333.243 s respectively.

Computer-aided modeling and prediction of performance of the modified Lundell class of alternators in space station solar dynamic power systems

NASA Technical Reports Server (NTRS)

Demerdash, Nabeel A. O.; Wang, Ren-Hong

1988-01-01

The main purpose of this project is the development of computer-aided models for purposes of studying the effects of various design changes on the parameters and performance characteristics of the modified Lundell class of alternators (MLA) as components of a solar dynamic power system supplying electric energy needs in the forthcoming space station. Key to this modeling effort is the computation of magnetic field distribution in MLAs. Since the nature of the magnetic field is three-dimensional, the first step in the investigation was to apply the finite element method to discretize volume, using the tetrahedron as the basic 3-D element. Details of the stator 3-D finite element grid are given. A preliminary look at the early stage of a 3-D rotor grid is presented.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

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.

A comparison of two central difference schemes for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Maksymiuk, C. M.; Swanson, R. C.; Pulliam, T. H.

1990-01-01

Five viscous transonic airfoil cases were computed by two significantly different computational fluid dynamics codes: An explicit finite-volume algorithm with multigrid, and an implicit finite-difference approximate-factorization method with Eigenvector diagonalization. Both methods are described in detail, and their performance on the test cases is compared. The codes utilized the same grids, turbulence model, and computer to provide the truest test of the algorithms. The two approaches produce very similar results, which, for attached flows, also agree well with experimental results; however, the explicit code is considerably faster.

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

NASA Technical Reports Server (NTRS)

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

1991-01-01

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with 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. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

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].

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

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

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Schallhorn, Paul

1998-01-01

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

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

Integrated geometry and grid generation system for complex configurations

NASA Technical Reports Server (NTRS)

Akdag, Vedat; Wulf, Armin

1992-01-01

A grid generation system was developed that enables grid generation for complex configurations. The system called ICEM/CFD is described and its role in computational fluid dynamics (CFD) applications is presented. The capabilities of the system include full computer aided design (CAD), grid generation on the actual CAD geometry definition using robust surface projection algorithms, interfacing easily with known CAD packages through common file formats for geometry transfer, grid quality evaluation of the volume grid, coupling boundary condition set-up for block faces with grid topology generation, multi-block grid generation with or without point continuity and block to block interface requirement, and generating grid files directly compatible with known flow solvers. The interactive and integrated approach to the problem of computational grid generation not only substantially reduces manpower time but also increases the flexibility of later grid modifications and enhancements which is required in an environment where CFD is integrated into a product design cycle.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

ISCFD Nagoya 1989 - International Symposium on Computational Fluid Dynamics, 3rd, Nagoya, Japan, Aug. 28-31, 1989, Technical Papers

NASA Astrophysics Data System (ADS)

Recent advances in computational fluid dynamics are discussed in reviews and reports. Topics addressed include large-scale LESs for turbulent pipe and channel flows, numerical solutions of the Euler and Navier-Stokes equations on parallel computers, multigrid methods for steady high-Reynolds-number flow past sudden expansions, finite-volume methods on unstructured grids, supersonic wake flow on a blunt body, a grid-characteristic method for multidimensional gas dynamics, and CIC numerical simulation of a wave boundary layer. Consideration is given to vortex simulations of confined two-dimensional jets, supersonic viscous shear layers, spectral methods for compressible flows, shock-wave refraction at air/water interfaces, oscillatory flow in a two-dimensional collapsible channel, the growth of randomness in a spatially developing wake, and an efficient simplex algorithm for the finite-difference and dynamic linear-programming method in optimal potential control.

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.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

a Marker-Based Eulerian-Lagrangian Method for Multiphase Flow with Supersonic Combustion Applications

NASA Astrophysics Data System (ADS)

Fan, Xiaofeng; Wang, Jiangfeng

2016-06-01

The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.

RIACS

NASA Technical Reports Server (NTRS)

Oliger, Joseph

1997-01-01

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Application of advanced grid generation techniques for flow field computations about complex configurations

NASA Technical Reports Server (NTRS)

Kathong, Monchai; Tiwari, Surendra N.

1988-01-01

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan

1989-01-01

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

NASA Astrophysics Data System (ADS)

Huang, Wen-Feng; Ren, Yu-Xin; Jiang, Xiong

2018-02-01

This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202-228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver

NASA Astrophysics Data System (ADS)

Kestener, Pierre

2017-10-01

RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

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.

Modeling North Atlantic Nor'easters With Modern Wave Forecast Models

NASA Astrophysics Data System (ADS)

Perrie, Will; Toulany, Bechara; Roland, Aron; Dutour-Sikiric, Mathieu; Chen, Changsheng; Beardsley, Robert C.; Qi, Jianhua; Hu, Yongcun; Casey, Michael P.; Shen, Hui

2018-01-01

Three state-of-the-art operational wave forecast model systems are implemented on fine-resolution grids for the Northwest Atlantic. These models are: (1) a composite model system consisting of SWAN implemented within WAVEWATCHIII® (the latter is hereafter, WW3) on a nested system of traditional structured grids, (2) an unstructured grid finite-volume wave model denoted "SWAVE," using SWAN physics, and (3) an unstructured grid finite element wind wave model denoted as "WWM" (for "wind wave model") which uses WW3 physics. Models are implemented on grid systems that include relatively large domains to capture the wave energy generated by the storms, as well as including fine-resolution nearshore regions of the southern Gulf of Maine with resolution on the scale of 25 m to simulate areas where inundation and coastal damage have occurred, due to the storms. Storm cases include three intense midlatitude cases: a spring Nor'easter storm in May 2005, the Patriot's Day storm in 2007, and the Boxing Day storm in 2010. Although these wave model systems have comparable overall properties in terms of their performance and skill, it is found that there are differences. Models that use more advanced physics, as presented in recent versions of WW3, tuned to regional characteristics, as in the Gulf of Maine and the Northwest Atlantic, can give enhanced results.

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

Schnack, D.D.; Lottati, I.; Mikic, Z.

The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

Electromagnetic plasma simulation in realistic geometries

NASA Astrophysics Data System (ADS)

Brandon, S.; Ambrosiano, J. J.; Nielsen, D.

1991-08-01

Particle-in-Cell (PIC) calculations have become an indispensable tool to model the nonlinear collective behavior of charged particle species in electromagnetic fields. Traditional finite difference codes, such as CONDOR (2-D) and ARGUS (3-D), are used extensively to design experiments and develop new concepts. A wide variety of physical processes can be modeled simply and efficiently by these codes. However, experiments have become more complex. Geometrical shapes and length scales are becoming increasingly more difficult to model. Spatial resolution requirements for the electromagnetic calculation force large grids and small time steps. Many hours of CRAY YMP time may be required to complete 2-D calculation -- many more for 3-D calculations. In principle, the number of mesh points and particles need only to be increased until all relevant physical processes are resolved. In practice, the size of a calculation is limited by the computer budget. As a result, experimental design is being limited by the ability to calculate, not by the experimenters ingenuity or understanding of the physical processes involved. Several approaches to meet these computational demands are being pursued. Traditional PIC codes continue to be the major design tools. These codes are being actively maintained, optimized, and extended to handle large and more complex problems. Two new formulations are being explored to relax the geometrical constraints of the finite difference codes. A modified finite volume test code, TALUS, uses a data structure compatible with that of standard finite difference meshes. This allows a basic conformal boundary/variable grid capability to be retrofitted to CONDOR. We are also pursuing an unstructured grid finite element code, MadMax. The unstructured mesh approach provides maximum flexibility in the geometrical model while also allowing local mesh refinement.

Introducing Enabling Computational Tools to the Climate Sciences: Multi-Resolution Climate Modeling with Adaptive Cubed-Sphere Grids

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

Jablonowski, Christiane

The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively withmore » advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.« less

A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Durlofsky, L. J.

2016-10-01

A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Multi-hadron spectroscopy in a large physical volume

NASA Astrophysics Data System (ADS)

Bulava, John; Hörz, Ben; Morningstar, Colin

2018-03-01

We demonstrate the effcacy of the stochastic LapH method to treat all-toall quark propagation on a Nf = 2 + 1 CLS ensemble with large linear spatial extent L = 5:5 fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.

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

A new class of finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2014-02-01

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods

NASA Astrophysics Data System (ADS)

Lemoine, Grady

Poroelasticity theory models the mechanics of porous, fluid-saturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also been applied to modeling living bone and other porous media. Poroelastic media often interact with fluids, such as in ocean bottom acoustics or propagation of waves from soft tissue into bone. This thesis describes the development and testing of high-resolution finite volume numerical methods, and simulation codes implementing these methods, for modeling systems of poroelastic media and fluids in two and three dimensions. These methods operate on both rectilinear grids and logically rectangular mapped grids. To allow the use of these methods, Biot's equations of poroelasticity are formulated as a first-order hyperbolic system with a source term; this source term is incorporated using operator splitting. Some modifications are required to the classical high-resolution finite volume method. Obtaining correct solutions at interfaces between poroelastic media and fluids requires a novel transverse propagation scheme and the removal of the classical second-order correction term at the interface, and in three dimensions a new wave limiting algorithm is also needed to correctly limit shear waves. The accuracy and convergence rates of the methods of this thesis are examined for a variety of analytical solutions, including simple plane waves, reflection and transmission of waves at an interface between different media, and scattering of acoustic waves by a poroelastic cylinder. Solutions are also computed for a variety of test problems from the computational poroelasticity literature, as well as some original test problems designed to mimic possible applications for the simulation code.

Toward Improving Predictability of Extreme Hydrometeorological Events: the Use of Multi-scale Climate Modeling in the Northern High Plains

NASA Astrophysics Data System (ADS)

Munoz-Arriola, F.; Torres-Alavez, J.; Mohamad Abadi, A.; Walko, R. L.

2014-12-01

Our goal is to investigate possible sources of predictability of hydrometeorological extreme events in the Northern High Plains. Hydrometeorological extreme events are considered the most costly natural phenomena. Water deficits and surpluses highlight how the water-climate interdependence becomes crucial in areas where single activities drive economies such as Agriculture in the NHP. Nonetheless we recognize the Water-Climate interdependence and the regulatory role that human activities play, we still grapple to identify what sources of predictability could be added to flood and drought forecasts. To identify the benefit of multi-scale climate modeling and the role of initial conditions on flood and drought predictability on the NHP, we use the Ocean Land Atmospheric Model (OLAM). OLAM is characterized by a dynamic core with a global geodesic grid with hexagonal (and variably refined) mesh cells and a finite volume discretization of the full compressible Navier Stokes equations, a cut-grid cell method for topography (that reduces error in computational gradient computation and anomalous vertical dispersion). Our hypothesis is that wet conditions will drive OLAM's simulations of precipitation to wetter conditions affecting both flood forecast and drought forecast. To test this hypothesis we simulate precipitation during identified historical flood events followed by drought events in the NHP (i.e. 2011-2012 years). We initialized OLAM with CFS-data 1-10 days previous to a flooding event (as initial conditions) to explore (1) short-term and high-resolution and (2) long-term and coarse-resolution simulations of flood and drought events, respectively. While floods are assessed during a maximum of 15-days refined-mesh simulations, drought is evaluated during the following 15 months. Simulated precipitation will be compared with the Sub-continental Observation Dataset, a gridded 1/16th degree resolution data obtained from climatological stations in Canada, US, and Mexico. This in-progress research will ultimately contribute to integrate OLAM and VIC models and improve predictability of extreme hydrometeorological events.

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

2006-01-01

The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Mathematical modeling of polymer flooding using the unstructured Voronoi grid

NASA Astrophysics Data System (ADS)

Kireev, T. F.; Bulgakova, G. T.; Khatmullin, I. F.

2017-12-01

Effective recovery of unconventional oil reserves necessitates development of enhanced oil recovery techniques such as polymer flooding. The study investigated the model of polymer flooding with effects of adsorption and water salinity. The model takes into account six components that include elements of the classic black oil model. These components are polymer, salt, water, dead oil, dry gas and dissolved gas. Solution of the problem is obtained by finite volume method on unstructured Voronoi grid using fully implicit scheme and the Newton’s method. To compare several different grid configurations numerical simulation of polymer flooding is performed. The oil rates obtained by a hexagonal locally refined Voronoi grid are shown to be more accurate than the oil rates obtained by a rectangular grid with the same number of cells. The latter effect is caused by high solution accuracy near the wells due to the local grid refinement. Minimization of the grid orientation effect caused by the hexagonal pattern is also demonstrated. However, in the inter-well regions with large Voronoi cells flood front tends to flatten and the water breakthrough moment is smoothed.

Efficient discretization in finite difference method

NASA Astrophysics Data System (ADS)

Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris

2015-04-01

Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.

Multidimensional directional flux weighted upwind scheme for multiphase flow modeling in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Jin, G.

2012-12-01

Multiphase flow modeling is an important numerical tool for a better understanding of transport processes in the fields including, but not limited to, petroleum reservoir engineering, remedy of ground water contamination, and risk evaluation of greenhouse gases such as CO2 injected into deep saline reservoirs. However, accurate numerical modeling for multiphase flow remains many challenges that arise from the inherent tight coupling and strong non-linear nature of the governing equations and the highly heterogeneous media. The existence of counter current flow which is caused by the effect of adverse relative mobility contrast and gravitational and capillary forces will introduce additional numerical instability. Recently multipoint flux approximation (MPFA) has become a subject of extensive research and has been demonstrated with great success in reducing considerable grid orientation effects compared to the conventional single point upstream (SPU) weighting scheme, especially in higher dimensions. However, the present available MPFA schemes are mathematically targeted to certain types of grids in two dimensions, a more general form of MPFA scheme is needed for both 2-D and 3-D problems. In this work a new upstream weighting scheme based on multipoint directional incoming fluxes is proposed which incorporates full permeability tensor to account for the heterogeneity of the porous media. First, the multiphase governing equations are decoupled into an elliptic pressure equation and a hyperbolic or parabolic saturation depends on whether the gravitational and capillary pressures are presented or not. Next, a dual secondary grid (called finite volume grid) is formulated from a primary grid (called finite element grid) to create interaction regions for each grid cell over the entire simulation domain. Such a discretization must ensure the conservation of mass and maintain the continuity of the Darcy velocity across the boundaries between neighboring interaction regions. The pressure field is then implicitly calculated from the pressure equation, which in turn results in the derived velocity field for directional flux calculation at each grid node. Directional flux at the center of each interaction surface is also calculated by interpolation from the element nodal fluxes using shape functions. The MPFA scheme is performed by a specific linear combination of all incoming fluxes into the upstream cell represented by either nodal fluxes or interpolated surface boundary fluxes to produce an upwind directional fluxed weighted relative mobility at the center of the interaction region boundary. Such an upwind weighted relative mobility is then used for calculating the saturations of each fluid phase explicitly. The proposed upwind weighting scheme has been implemented into a mixed finite element-finite volume (FE-FV) method, which allows for handling complex reservoir geometry with second-order accuracies in approximating primary variables. The numerical solver has been tested with several bench mark test problems. The application of the proposed scheme to migration path analysis of CO2 injected into deep saline reservoirs in 3-D has demonstrated its ability and robustness in handling multiphase flow with adverse mobility contrast in highly heterogeneous porous media.

Vessel Segmentation and Blood Flow Simulation Using Level-Sets and Embedded Boundary Methods

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

Deschamps, T; Schwartz, P; Trebotich, D

In this article we address the problem of blood flow simulation in realistic vascular objects. The anatomical surfaces are extracted by means of Level-Sets methods that accurately model the complex and varying surfaces of pathological objects such as aneurysms and stenoses. The surfaces obtained are defined at the sub-pixel level where they intersect the Cartesian grid of the image domain. It is therefore straightforward to construct embedded boundary representations of these objects on the same grid, for which recent work has enabled discretization of the Navier-Stokes equations for incompressible fluids. While most classical techniques require construction of a structured meshmore » that approximates the surface in order to extrapolate a 3D finite-element gridding of the whole volume, our method directly simulates the blood-flow inside the extracted surface without losing any complicated details and without building additional grids.« less

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.

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.

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.

New multigrid approach for three-dimensional unstructured, adaptive grids

NASA Technical Reports Server (NTRS)

Parthasarathy, Vijayan; Kallinderis, Y.

1994-01-01

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1989-01-01

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

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

Kudryashov, Nikolay A.; Shilnikov, Kirill E.

Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumormore » tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.« less

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

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

A numerical study of hypersonic stagnation heat transfer predictions at a coordinate singularity

NASA Technical Reports Server (NTRS)

Grasso, Francesco; Gnoffo, Peter A.

1990-01-01

The problem of grid induced errors associated with a coordinate singularity on heating predictions in the stagnation region of a three-dimensional body in hypersonic flow is examined. The test problem is for Mach 10 flow over an Aeroassist Flight Experiment configuration. This configuration is composed of an elliptic nose, a raked elliptic cone, and a circular shoulder. Irregularities in the heating predictions in the vicinity of the coordinate singularity, located at the axis of the elliptic nose near the stagnation point, are examined with respect to grid refinement and grid restructuring. The algorithm is derived using a finite-volume formulation. An upwind-biased total-variation diminishing scheme is employed for the inviscid flux contribution, and central differences are used for the viscous terms.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

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.

Gigaflop (billion floating point operations per second) performance for computational electromagnetics

NASA Technical Reports Server (NTRS)

Shankar, V.; Rowell, C.; Hall, W. F.; Mohammadian, A. H.; Schuh, M.; Taylor, K.

1992-01-01

Accurate and rapid evaluation of radar signature for alternative aircraft/store configurations would be of substantial benefit in the evolution of integrated designs that meet radar cross-section (RCS) requirements across the threat spectrum. Finite-volume time domain methods offer the possibility of modeling the whole aircraft, including penetrable regions and stores, at longer wavelengths on today's gigaflop supercomputers and at typical airborne radar wavelengths on the teraflop computers of tomorrow. A structured-grid finite-volume time domain computational fluid dynamics (CFD)-based RCS code has been developed at the Rockwell Science Center, and this code incorporates modeling techniques for general radar absorbing materials and structures. Using this work as a base, the goal of the CFD-based CEM effort is to define, implement and evaluate various code development issues suitable for rapid prototype signature prediction.

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

3D magnetospheric parallel hybrid multi-grid method applied to planet–plasma interactions

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

Leclercq, L., E-mail: ludivine.leclercq@latmos.ipsl.fr; Modolo, R., E-mail: ronan.modolo@latmos.ipsl.fr; Leblanc, F.

2016-03-15

We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet–plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order tomore » conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.« less

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.

A Robust Absorbing Boundary Condition for Compressible Flows

NASA Technical Reports Server (NTRS)

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

2005-01-01

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Direct Replacement of Arbitrary Grid-Overlapping by Non-Structured Grid

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing

1994-01-01

A new approach that uses nonstructured mesh to replace the arbitrarily overlapped structured regions of embedded grids is presented. The present methodology uses the Chimera composite overlapping mesh system so that the physical domain of the flowfield is subdivided into regions which can accommodate easily-generated grid for complex configuration. In addition, a Delaunay triangulation technique generates nonstructured triangular mesh which wraps over the interconnecting region of embedded grids. It is designed that the present approach, termed DRAGON grid, has three important advantages: eliminating some difficulties of the Chimera scheme, such as the orphan points and/or bad quality of interpolation stencils; making grid communication in a fully conservative way; and implementation into three dimensions is straightforward. A computer code based on a time accurate, finite volume, high resolution scheme for solving the compressible Navier-Stokes equations has been further developed to include both the Chimera overset grid and the nonstructured mesh schemes. For steady state problems, the local time stepping accelerates convergence based on a Courant - Friedrichs - Leury (CFL) number near the local stability limit. Numerical tests on representative steady and unsteady supersonic inviscid flows with strong shock waves are demonstrated.

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

NASA Technical Reports Server (NTRS)

Thomas, James

2008-01-01

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Loubère, Raphaël

2016-08-01

In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear hyperbolic PDE systems on unstructured triangular and tetrahedral meshes in two and three space dimensions. This novel a posteriori limiter, which has been recently proposed for the simple Cartesian grid case in [62], is able to resolve discontinuities at a sub-grid scale and is substantially extended here to general unstructured simplex meshes in 2D and 3D. It can be summarized as follows: At the beginning of each time step, an approximation of the local minimum and maximum of the discrete solution is computed for each cell, taking into account also the vertex neighbors of an element. Then, an unlimited discontinuous Galerkin scheme of approximation degree N is run for one time step to produce a so-called candidate solution. Subsequently, an a posteriori detection step checks the unlimited candidate solution at time t n + 1 for positivity, absence of floating point errors and whether the discrete solution has remained within or at least very close to the bounds given by the local minimum and maximum computed in the first step. Elements that do not satisfy all the previously mentioned detection criteria are flagged as troubled cells. For these troubled cells, the candidate solution is discarded as inappropriate and consequently needs to be recomputed. Within these troubled cells the old discrete solution at the previous time tn is scattered onto small sub-cells (Ns = 2 N + 1 sub-cells per element edge), in order to obtain a set of sub-cell averages at time tn. Then, a more robust second order TVD finite volume scheme is applied to update the sub-cell averages within the troubled DG cells from time tn to time t n + 1. The new sub-grid data at time t n + 1 are finally gathered back into a valid cell-centered DG polynomial of degree N by using a classical conservative and higher order accurate finite volume reconstruction technique. Consequently, if the number Ns is sufficiently large (Ns ≥ N + 1), the subscale resolution capability of the DG scheme is fully maintained, while preserving at the same time an essentially non-oscillatory behavior of the solution at discontinuities. Many standard DG limiters only adjust the discrete solution in troubled cells, based on the limiting of higher order moments or by applying a nonlinear WENO/HWENO reconstruction on the data at the new time t n + 1. Instead, our new DG limiter entirely recomputes the troubled cells by solving the governing PDE system again starting from valid data at the old time level tn, but using this time a more robust scheme on the sub-grid level. In other words, the piecewise polynomials produced by the new limiter are the result of a more robust solution of the PDE system itself, while most standard DG limiters are simply based on a mere nonlinear data post-processing of the discrete solution. Technically speaking, the new method corresponds to an element-wise checkpointing and restarting of the solver, using a lower order scheme on the sub-grid. As a result, the present DG limiter is even able to cure floating point errors like NaN values that have occurred after divisions by zero or after the computation of roots from negative numbers. This is a unique feature of our new algorithm among existing DG limiters. The new a posteriori sub-cell stabilization approach is developed within a high order accurate one-step ADER-DG framework on multidimensional unstructured meshes for hyperbolic systems of conservation laws as well as for hyperbolic PDE with non-conservative products. The method is applied to the Euler equations of compressible gas dynamics, to the ideal magneto-hydrodynamics equations (MHD) as well as to the seven-equation Baer-Nunziato model of compressible multi-phase flows. A large set of standard test problems is solved in order to assess the accuracy and robustness of the new limiter.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

European Science Notes Information Bulletin Reports on Current European/ Middle Eastern Science

DTIC Science & Technology

1991-06-01

particularly those that involve shock wave/boundary layer cell-centered, finite-volume, explicit, Runge-Kutta interactions , still prov;de considerble...aircraft configuration attributed to using an interactive vcual grid generation was provided by A. Bocci and A. Baxendale, the Aircraft system developed...the surface pressure the complex problem of wing/body/pylon/store distributions with and without the mass flow through the interaction . Reasonable

Multi-scale modeling of Puget Sound using an unstructured-grid coastal ocean model: from tide flats to estuaries and coastal waters

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

Yang, Zhaoqing; Khangaonkar, Tarang

2010-11-19

Water circulation in Puget Sound, a large complex estuary system in the Pacific Northwest coastal ocean of the United States, is governed by multiple spatially and temporally varying forcings from tides, atmosphere (wind, heating/cooling, precipitation/evaporation, pressure), and river inflows. In addition, the hydrodynamic response is affected strongly by geomorphic features, such as fjord-like bathymetry and complex shoreline features, resulting in many distinguishing characteristics in its main and sub-basins. To better understand the details of circulation features in Puget Sound and to assist with proposed nearshore restoration actions for improving water quality and the ecological health of Puget Sound, a high-resolutionmore » (around 50 m in estuaries and tide flats) hydrodynamic model for the entire Puget Sound was needed. Here, a threedimensional circulation model of Puget Sound using an unstructured-grid finite volume coastal ocean model is presented. The model was constructed with sufficient resolution in the nearshore region to address the complex coastline, multi-tidal channels, and tide flats. Model open boundaries were extended to the entrance of the Strait of Juan de Fuca and the northern end of the Strait of Georgia to account for the influences of ocean water intrusion from the Strait of Juan de Fuca and the Fraser River plume from the Strait of Georgia, respectively. Comparisons of model results, observed data, and associated error statistics for tidal elevation, velocity, temperature, and salinity indicate that the model is capable of simulating the general circulation patterns on the scale of a large estuarine system as well as detailed hydrodynamics in the nearshore tide flats. Tidal characteristics, temperature/salinity stratification, mean circulation, and river plumes in estuaries with tide flats are discussed.« less

Numerical simulation of self-sustained oscillation of a voice-producing element based on Navier-Stokes equations and the finite element method.

PubMed

de Vries, Martinus P; Hamburg, Marc C; Schutte, Harm K; Verkerke, Gijsbertus J; Veldman, Arthur E P

2003-04-01

Surgical removal of the larynx results in radically reduced production of voice and speech. To improve voice quality a voice-producing element (VPE) is developed, based on the lip principle, called after the lips of a musician while playing a brass instrument. To optimize the VPE, a numerical model is developed. In this model, the finite element method is used to describe the mechanical behavior of the VPE. The flow is described by two-dimensional incompressible Navier-Stokes equations. The interaction between VPE and airflow is modeled by placing the grid of the VPE model in the grid of the aerodynamical model, and requiring continuity of forces and velocities. By applying and increasing pressure to the numerical model, pulses comparable to glottal volume velocity waveforms are obtained. By variation of geometric parameters their influence can be determined. To validate this numerical model, an in vitro test with a prototype of the VPE is performed. Experimental and numerical results show an acceptable agreement.

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.

Three-dimensional unsteady Euler equations solutions on dynamic grids

NASA Technical Reports Server (NTRS)

Belk, D. M.; Janus, J. M.; Whitfield, D. L.

1985-01-01

A method is presented for solving the three-dimensional unsteady Euler equations on dynamic grids based on flux vector splitting. The equations are cast in curvilinear coordinates and a finite volume discretization is used for handling arbitrary geometries. The discretized equations are solved using an explicit upwind second-order predictor corrector scheme that is stable for a CFL of 2. Characteristic variable boundary conditions are developed and used for unsteady impermeable surfaces and for the far-field boundary. Dynamic-grid results are presented for an oscillating air-foil and for a store separating from a reflection plate. For the cases considered of stores separating from a reflection plate, the unsteady aerodynamic forces on the store are significantly different from forces obtained by steady-state aerodynamics with the body inclination angle changed to account for plunge velocity.

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

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.

Asynchronous discrete event schemes for PDEs

NASA Astrophysics Data System (ADS)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Decomposition of the Seismic Source Using Numerical Simulations and Observations of Nuclear Explosions

DTIC Science & Technology

2017-05-31

SUBJECT TERMS nonlinear finite element calculations, nuclear explosion monitoring, topography 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18...3D North Korea calculations........ Figure 6. The CRAM 3D finite element outer grid (left) is rectangular......................... Figure 7. Stress...Figure 6. The CRAM 3D finite element outer grid (left) is rectangular. The inner grid (center) is shaped to match the shape of the explosion shock wave

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Physics design of the injector source for ITER neutral beam injector (invited).

PubMed

Antoni, V; Agostinetti, P; Aprile, D; Cavenago, M; Chitarin, G; Fonnesu, N; Marconato, N; Pilan, N; Sartori, E; Serianni, G; Veltri, P

2014-02-01

Two Neutral Beam Injectors (NBI) are foreseen to provide a substantial fraction of the heating power necessary to ignite thermonuclear fusion reactions in ITER. The development of the NBI system at unprecedented parameters (40 A of negative ion current accelerated up to 1 MV) requires the realization of a full scale prototype, to be tested and optimized at the Test Facility under construction in Padova (Italy). The beam source is the key component of the system and the design of the multi-grid accelerator is the goal of a multi-national collaborative effort. In particular, beam steering is a challenging aspect, being a tradeoff between requirements of the optics and real grids with finite thickness and thermo-mechanical constraints due to the cooling needs and the presence of permanent magnets. In the paper, a review of the accelerator physics and an overview of the whole R&D physics program aimed to the development of the injector source are presented.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

NASA Astrophysics Data System (ADS)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

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.

A Calculation Method for Convective Heat and Mass Transfer in Multiply-Slotted Film-Cooling Applications.

DTIC Science & Technology

1980-01-01

Transport of Heat ..... .......... 8 3. THE SOLUTION PROCEDURE ..... .. ................. 8 3.1 The Finite-Difference Grid Network ... .......... 8 3.2...The Finite-Difference Grid Network. Figure 4: The Iterative Solution Procedure used at each Streamwise Station. Figure 5: Velocity Profiles in the...the finite-difference grid in the y-direction. I is the mixing length. L is the distance in the x-direction from the injection slot entrance to the

GRIDGEN Version 1.0: a computer program for generating unstructured finite-volume grids

USGS Publications Warehouse

Lien, Jyh-Ming; Liu, Gaisheng; Langevin, Christian D.

2015-01-01

GRIDGEN is a computer program for creating layered quadtree grids for use with numerical models, such as the MODFLOW–USG program for simulation of groundwater flow. The program begins by reading a three-dimensional base grid, which can have variable row and column widths and spatially variable cell top and bottom elevations. From this base grid, GRIDGEN will continuously divide into four any cell intersecting user-provided refinement features (points, lines, and polygons) until the desired level of refinement is reached. GRIDGEN will then smooth, or balance, the grid so that no two adjacent cells, including overlying and underlying cells, differ by more than a user-specified level tolerance. Once these gridding processes are completed, GRIDGEN saves a tree structure file so that the layered quadtree grid can be quickly reconstructed as needed. Once a tree structure file has been created, GRIDGEN can then be used to (1) export the layered quadtree grid as a shapefile, (2) export grid connectivity and cell information as ASCII text files for use with MODFLOW–USG or other numerical models, and (3) intersect the grid with shapefiles of points, lines, or polygons, and save intersection output as ASCII text files and shapefiles. The GRIDGEN program is demonstrated by creating a layered quadtree grid for the Biscayne aquifer in Miami-Dade County, Florida, using hydrologic features to control where refinement is added.

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

2003-01-01

The use of multi-dimensional finite volume numerical techniques with finite thickness models for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the one-dimensional semi -infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody were investigated. An array of streamwise orientated heating striations were generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients due to the striation patterns two-dimensional heat transfer techniques were necessary to obtain accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates because it did not account for lateral heat conduction in the model.

Computational physical oceanography -- A comprehensive approach based on generalized CFD/grid techniques for planetary scale simulations of oceanic flows. Final report, September 1, 1995--August 31, 1996

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

Beddhu, M.; Jiang, M.Y.; Whitfield, D.L.

The original intention for this work was to impart the technology that was developed in the field of computational aeronautics to the field of computational physical oceanography. This technology transfer involved grid generation techniques and solution procedures to solve the governing equations over the grids thus generated. Specifically, boundary fitting non-orthogonal grids would be generated over a sphere taking into account the topography of the ocean floor and the topography of the continents. The solution methodology to be employed involved the application of an upwind, finite volume discretization procedure that uses higher order numerical fluxes at the cell faces tomore » discretize the governing equations and an implicit Newton relaxation technique to solve the discretized equations. This report summarizes the efforts put forth during the past three years to achieve these goals and indicates the future direction of this work as it is still an ongoing effort.« less

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 2: Unsteady Ducted Propfan Analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1991-01-01

The primary objective was the development of a time dependent 3-D Euler/Navier-Stokes aerodynamic analysis to predict unsteady compressible transonic flows about ducted and unducted propfan propulsion systems at angle of attack. The resulting computer codes are referred to as Advanced Ducted Propfan Analysis Codes (ADPAC). A computer program user's manual is presented for the ADPAC. Aerodynamic calculations were based on a four stage Runge-Kutta time marching finite volume solution technique with added numerical dissipation. A time accurate implicit residual smoothing operator was used for unsteady flow predictions. For unducted propfans, a single H-type grid was used to discretize each blade passage of the complete propeller. For ducted propfans, a coupled system of five grid blocks utilizing an embedded C grid about the cowl leading edge was used to discretize each blade passage. Grid systems were generated by a combined algebraic/elliptic algorithm developed specifically for ducted propfans. Numerical calculations were compared with experimental data for both ducted and unducted flows.

Multiscale Methods for Accurate, Efficient, and Scale-Aware Models of the Earth System

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

Goldhaber, Steve; Holland, Marika

The major goal of this project was to contribute improvements to the infrastructure of an Earth System Model in order to support research in the Multiscale Methods for Accurate, Efficient, and Scale-Aware models of the Earth System project. In support of this, the NCAR team accomplished two main tasks: improving input/output performance of the model and improving atmospheric model simulation quality. Improvement of the performance and scalability of data input and diagnostic output within the model required a new infrastructure which can efficiently handle the unstructured grids common in multiscale simulations. This allows for a more computationally efficient model, enablingmore » more years of Earth System simulation. The quality of the model simulations was improved by reducing grid-point noise in the spectral element version of the Community Atmosphere Model (CAM-SE). This was achieved by running the physics of the model using grid-cell data on a finite-volume grid.« less

Stability Analysis of Algebraic Reconstruction for Immersed Boundary Methods with Application in Flow and Transport in Porous Media

NASA Astrophysics Data System (ADS)

Yousefzadeh, M.; Battiato, I.

2017-12-01

Flow and reactive transport problems in porous media often involve complex geometries with stationary or evolving boundaries due to absorption and dissolution processes. Grid based methods (e.g. finite volume, finite element, etc.) are a vital tool for studying these problems. Yet, implementing these methods requires one to answer a very first question of what type of grid is to be used. Among different possible answers, Cartesian grids are one of the most attractive options as they possess simple discretization stencil and are usually straightforward to generate at roughly no computational cost. The Immersed Boundary Method, a Cartesian based methodology, maintains most of the useful features of the structured grids while exhibiting a high-level resilience in dealing with complex geometries. These features make it increasingly more attractive to model transport in evolving porous media as the cost of grid generation reduces greatly. Yet, stability issues and severe time-step restriction due to explicit-time implementation combined with limited studies on the implementation of Neumann (constant flux) and linear and non-linear Robin (e.g. reaction) boundary conditions (BCs) have significantly limited the applicability of IBMs to transport in porous media. We have developed an implicit IBM capable of handling all types of BCs and addressed some numerical issues, including unconditional stability criteria, compactness and reduction of spurious oscillations near the immersed boundary. We tested the method for several transport and flow scenarios, including dissolution processes in porous media, and demonstrate its capabilities. Successful validation against both experimental and numerical data has been carried out.

Development and application of a volume penalization immersed boundary method for the computation of blood flow and shear stresses in cerebral vessels and aneurysms.

PubMed

Mikhal, Julia; Geurts, Bernard J

2013-12-01

A volume-penalizing immersed boundary method is presented for the simulation of laminar incompressible flow inside geometrically complex blood vessels in the human brain. We concentrate on cerebral aneurysms and compute flow in curved brain vessels with and without spherical aneurysm cavities attached. We approximate blood as an incompressible Newtonian fluid and simulate the flow with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. A key element of the immersed boundary method is the so-called masking function. This is a binary function with which we identify at any location in the domain whether it is 'solid' or 'fluid', allowing to represent objects immersed in a Cartesian grid. We compare three definitions of the masking function for geometries that are non-aligned with the grid. In each case a 'staircase' representation is used in which a grid cell is either 'solid' or 'fluid'. Reliable findings are obtained with our immersed boundary method, even at fairly coarse meshes with about 16 grid cells across a velocity profile. The validation of the immersed boundary method is provided on the basis of classical Poiseuille flow in a cylindrical pipe. We obtain first order convergence for the velocity and the shear stress, reflecting the fact that in our approach the solid-fluid interface is localized with an accuracy on the order of a grid cell. Simulations for curved vessels and aneurysms are done for different flow regimes, characterized by different values of the Reynolds number (Re). The validation is performed for laminar flow at Re = 250, while the flow in more complex geometries is studied at Re = 100 and Re = 250, as suggested by physiological conditions pertaining to flow of blood in the circle of Willis.

A WENO-Limited, ADER-DT, Finite-Volume Scheme for Efficient, Robust, and Communication-Avoiding Multi-Dimensional Transport

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

Norman, Matthew R

2014-01-01

The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free, WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates a range of choices for the user when approaching their specific application while maintaining good parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping, strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronizationmore » and data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively and qualitatively what a user should expect when employing this method in their application.« less

Optical properties of ordered vertical arrays of multi-walled carbon nanotubes from FDTD simulations.

PubMed

Bao, Hua; Ruan, Xiulin; Fisher, Timothy S

2010-03-15

A finite-difference time-domain (FDTD) method is used to model thermal radiative properties of vertical arrays of multi-walled carbon nanotubes (MWCNT). Individual CNTs are treated as solid circular cylinders with an effective dielectric tensor. Consistent with experiments, the results confirm that CNT arrays are highly absorptive. Compared with the commonly used Maxwell-Garnett theory, the FDTD calculations generally predict larger reflectance and absorbance, and smaller transmittance, which are attributed to the diffraction and scattering within the cylinder array structure. The effects of volume fraction, tube length, tube distance, and incident angle on radiative properties are investigated systematically. Low volume fraction and long tubes are more favorable to achieve low reflectance and high absorbance. For a fixed volume fraction and finite tube length, larger periodicity results in larger reflectance and absorbance. The angular dependence studies reveal an optimum incident angle at which the reflectance can be minimized. The results also suggest that an even darker material could be achieved by using CNTs with good alignment on the top surface.

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

Quirk, James J.

1994-01-01

Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

Further Improvement in 3DGRAPE

NASA Technical Reports Server (NTRS)

Alter, Stephen

2004-01-01

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

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.

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.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

NASA Technical Reports Server (NTRS)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Optimal variable-grid finite-difference modeling for porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-12-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs.

Finite Element Methods and Multiphase Continuum Theory for Modeling 3D Air-Water-Sediment Interactions

NASA Astrophysics Data System (ADS)

Kees, C. E.; Miller, C. T.; Dimakopoulos, A.; Farthing, M.

2016-12-01

The last decade has seen an expansion in the development and application of 3D free surface flow models in the context of environmental simulation. These models are based primarily on the combination of effective algorithms, namely level set and volume-of-fluid methods, with high-performance, parallel computing. These models are still computationally expensive and suitable primarily when high-fidelity modeling near structures is required. While most research on algorithms and implementations has been conducted in the context of finite volume methods, recent work has extended a class of level set schemes to finite element methods on unstructured methods. This work considers models of three-phase flow in domains containing air, water, and granular phases. These multi-phase continuum mechanical formulations show great promise for applications such as analysis of coastal and riverine structures. This work will consider formulations proposed in the literature over the last decade as well as new formulations derived using the thermodynamically constrained averaging theory, an approach to deriving and closing macroscale continuum models for multi-phase and multi-component processes. The target applications require the ability to simulate wave breaking and structure over-topping, particularly fully three-dimensional, non-hydrostatic flows that drive these phenomena. A conservative level set scheme suitable for higher-order finite element methods is used to describe the air/water phase interaction. The interaction of these air/water flows with granular materials, such as sand and rubble, must also be modeled. The range of granular media dynamics targeted including flow and wave transmision through the solid media as well as erosion and deposition of granular media and moving bed dynamics. For the granular phase we consider volume- and time-averaged continuum mechanical formulations that are discretized with the finite element method and coupled to the underlying air/water flow via operator splitting (fractional step) schemes. Particular attention will be given to verification and validation of the numerical model and important qualitative features of the numerical methods including phase conservation, wave energy dissipation, and computational efficiency in regimes of interest.

Numerical study of 3D flow structure near a cylinder piercing turbulent free-convection boundary layer on a vertical plate

NASA Astrophysics Data System (ADS)

Levchenya, A. M.; Smirnov, E. M.; Zhukovskaya, V. D.

2018-05-01

The present contribution covers RANS-based simulation of 3D flow near a cylinder introduced into turbulent vertical-plate free-convection boundary layer. Numerical solutions were obtained with a finite-volume Navier-Stokes code of second-order accuracy using refined grids. Peculiarities of the flow disturbed by the obstacle are analyzed. Cylinder-diameter effect on the horseshoe vortex size and its position is evaluated.

Numerical Prediction of Periodic Vortex Shedding in Subsonic and Transonic Turbine Cascade Flows

NASA Astrophysics Data System (ADS)

Mensink, C.

1996-05-01

Periodic vortex shedding at the trailing edge of a turbine cascade has been investigated numerically for a subsonic and a transonic cascade flow. The numerical investigation was carried out by a finite volume multiblock code, solving the 2D compressible Reynolds-averaged Navier-Stokes equations on a set of non-overlapping grid blocks that are connected in a conservative way. Comparisons are made with experimental results previously obtained by Sieverding and Heinemann.

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.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Boundary condition identification for a grid model by experimental and numerical dynamic analysis

NASA Astrophysics Data System (ADS)

Mao, Qiang; Devitis, John; Mazzotti, Matteo; Bartoli, Ivan; Moon, Franklin; Sjoblom, Kurt; Aktan, Emin

2015-04-01

There is a growing need to characterize unknown foundations and assess substructures in existing bridges. It is becoming an important issue for the serviceability and safety of bridges as well as for the possibility of partial reuse of existing infrastructures. Within this broader contest, this paper investigates the possibility of identifying, locating and quantifying changes of boundary conditions, by leveraging a simply supported grid structure with a composite deck. Multi-reference impact tests are operated for the grid model and modification of one supporting bearing is done by replacing a steel cylindrical roller with a roller of compliant material. Impact based modal analysis provide global modal parameters such as damped natural frequencies, mode shapes and flexibility matrix that are used as indicators of boundary condition changes. An updating process combining a hybrid optimization algorithm and the finite element software suit ABAQUS is presented in this paper. The updated ABAQUS model of the grid that simulates the supporting bearing with springs is used to detect and quantify the change of the boundary conditions.

Numerical grid generation in computational field simulations. Volume 1

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

Soni, B.K.; Thompson, J.F.; Haeuser, J.

1996-12-31

To enhance the CFS technology to its next level of applicability (i.e., to create acceptance of CFS in an integrated product and process development involving multidisciplinary optimization) the basic requirements are: rapid turn-around time, reliable and accurate simulation, affordability and appropriate linkage to other engineering disciplines. In response to this demand, there has been a considerable growth in the grid generation related research activities involving automization, parallel processing, linkage with the CAD-CAM systems, CFS with dynamic motion and moving boundaries, strategies and algorithms associated with multi-block structured, unstructured, hybrid, hexahedral, and Cartesian grids, along with its applicability to various disciplinesmore » including biomedical, semiconductor, geophysical, ocean modeling, and multidisciplinary optimization.« less

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

USGS Publications Warehouse

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

Finite Element Barotropic Model for the Indian and Western Pacific OceanBasin: Tidal Model Data Comparisons and Sensitivities

DTIC Science & Technology

2018-01-11

From - To) 01/11/2018 Final Technical Report June 01 2016 - Dec 30 2017 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Finite - Element Barotropic Model...grid finite - element barotropic fully hydrodynamic model in order to understand the shallow-water dynamics of the Indian Ocean and Western Pacific Ocean...dissipative dissipative processes are explored. 15. SUBJECTTERMS finite - element , unstructured grid, barotropic tides, bathymetry, internal tide

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Linear scaling computation of the Fock matrix. VI. Data parallel computation of the exchange-correlation matrix

NASA Astrophysics Data System (ADS)

Gan, Chee Kwan; Challacombe, Matt

2003-05-01

Recently, early onset linear scaling computation of the exchange-correlation matrix has been achieved using hierarchical cubature [J. Chem. Phys. 113, 10037 (2000)]. Hierarchical cubature differs from other methods in that the integration grid is adaptive and purely Cartesian, which allows for a straightforward domain decomposition in parallel computations; the volume enclosing the entire grid may be simply divided into a number of nonoverlapping boxes. In our data parallel approach, each box requires only a fraction of the total density to perform the necessary numerical integrations due to the finite extent of Gaussian-orbital basis sets. This inherent data locality may be exploited to reduce communications between processors as well as to avoid memory and copy overheads associated with data replication. Although the hierarchical cubature grid is Cartesian, naive boxing leads to irregular work loads due to strong spatial variations of the grid and the electron density. In this paper we describe equal time partitioning, which employs time measurement of the smallest sub-volumes (corresponding to the primitive cubature rule) to load balance grid-work for the next self-consistent-field iteration. After start-up from a heuristic center of mass partitioning, equal time partitioning exploits smooth variation of the density and grid between iterations to achieve load balance. With the 3-21G basis set and a medium quality grid, equal time partitioning applied to taxol (62 heavy atoms) attained a speedup of 61 out of 64 processors, while for a 110 molecule water cluster at standard density it achieved a speedup of 113 out of 128. The efficiency of equal time partitioning applied to hierarchical cubature improves as the grid work per processor increases. With a fine grid and the 6-311G(df,p) basis set, calculations on the 26 atom molecule α-pinene achieved a parallel efficiency better than 99% with 64 processors. For more coarse grained calculations, superlinear speedups are found to result from reduced computational complexity associated with data parallelism.

Energy stable and high-order-accurate finite difference methods on staggered grids

NASA Astrophysics Data System (ADS)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Mod-2 wind turbine system concept and preliminary design report. Volume 1: Executive summary

NASA Technical Reports Server (NTRS)

1979-01-01

The configuration development of the MOD-2 wind turbine system is presented. The MOD-2 is design optimized for commercial production rates which, in multi-unit installations, will be integrated into a utility power grid and achieve a cost of electricity at less than 4 cents per kilowatt hour.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1974-01-01

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Multi-off-grid methods in multi-step integration of ordinary differential equations

NASA Technical Reports Server (NTRS)

Beaudet, P. R.

1974-01-01

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Real time estimation of generation, extinction and flow of muscle fibre action potentials in high density surface EMG.

PubMed

Mesin, Luca

2015-02-01

Developing a real time method to estimate generation, extinction and propagation of muscle fibre action potentials from bi-dimensional and high density surface electromyogram (EMG). A multi-frame generalization of an optical flow technique including a source term is considered. A model describing generation, extinction and propagation of action potentials is fit to epochs of surface EMG. The algorithm is tested on simulations of high density surface EMG (inter-electrode distance equal to 5mm) from finite length fibres generated using a multi-layer volume conductor model. The flow and source term estimated from interference EMG reflect the anatomy of the muscle, i.e. the direction of the fibres (2° of average estimation error) and the positions of innervation zone and tendons under the electrode grid (mean errors of about 1 and 2mm, respectively). The global conduction velocity of the action potentials from motor units under the detection system is also obtained from the estimated flow. The processing time is about 1 ms per channel for an epoch of EMG of duration 150 ms. A new real time image processing algorithm is proposed to investigate muscle anatomy and activity. Potential applications are proposed in prosthesis control, automatic detection of optimal channels for EMG index extraction and biofeedback. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Multi-scale Modeling System: Developments, Applications and Critical Issues

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Chern, Jiundar; Atlas, Robert; Randall, David; Lin, Xin; Khairoutdinov, Marat; Li, Jui-Lin; Waliser, Duane E.; Hou, Arthur; Peters-Lidard, Christa;

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.

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm.

PubMed

Vogel, Curtis R; Yang, Qiang

2006-08-21

We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1990-01-01

A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1989-01-01

A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

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.

Segmentation of Unstructured Datasets

NASA Technical Reports Server (NTRS)

Bhat, Smitha

1996-01-01

Datasets generated by computer simulations and experiments in Computational Fluid Dynamics tend to be extremely large and complex. It is difficult to visualize these datasets using standard techniques like Volume Rendering and Ray Casting. Object Segmentation provides a technique to extract and quantify regions of interest within these massive datasets. This thesis explores basic algorithms to extract coherent amorphous regions from two-dimensional and three-dimensional scalar unstructured grids. The techniques are applied to datasets from Computational Fluid Dynamics and from Finite Element Analysis.

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

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Finite-Difference Algorithm for Simulating 3D Electromagnetic Wavefields in Conductive Media

NASA Astrophysics Data System (ADS)

Aldridge, D. F.; Bartel, L. C.; Knox, H. A.

2013-12-01

Electromagnetic (EM) wavefields are routinely used in geophysical exploration for detection and characterization of subsurface geological formations of economic interest. Recorded EM signals depend strongly on the current conductivity of geologic media. Hence, they are particularly useful for inferring fluid content of saturated porous bodies. In order to enhance understanding of field-recorded data, we are developing a numerical algorithm for simulating three-dimensional (3D) EM wave propagation and diffusion in heterogeneous conductive materials. Maxwell's equations are combined with isotropic constitutive relations to obtain a set of six, coupled, first-order partial differential equations governing the electric and magnetic vectors. An advantage of this system is that it does not contain spatial derivatives of the three medium parameters electric permittivity, magnetic permeability, and current conductivity. Numerical solution methodology consists of explicit, time-domain finite-differencing on a 3D staggered rectangular grid. Temporal and spatial FD operators have order 2 and N, where N is user-selectable. We use an artificially-large electric permittivity to maximize the FD timestep, and thus reduce execution time. For the low frequencies typically used in geophysical exploration, accuracy is not unduly compromised. Grid boundary reflections are mitigated via convolutional perfectly matched layers (C-PMLs) imposed at the six grid flanks. A shared-memory-parallel code implementation via OpenMP directives enables rapid algorithm execution on a multi-thread computational platform. Good agreement is obtained in comparisons of numerically-generated data with reference solutions. EM wavefields are sourced via point current density and magnetic dipole vectors. Spatially-extended inductive sources (current carrying wire loops) are under development. We are particularly interested in accurate representation of high-conductivity sub-grid-scale features that are common in industrial environments (borehole casing, pipes, railroad tracks). Present efforts are oriented toward calculating the EM responses of these objects via a First Born Approximation approach. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations

NASA Astrophysics Data System (ADS)

Kim, Sungtae; Lee, Soogab; Kim, Kyu Hong

2008-04-01

A new numerical method toward accurate and efficient aeroacoustic computations of multi-dimensional compressible flows has been developed. The core idea of the developed scheme is to unite the advantages of the wavenumber-extended optimized scheme and M-AUSMPW+/MLP schemes by predicting a physical distribution of flow variables more accurately in multi-space dimensions. The wavenumber-extended optimization procedure for the finite volume approach based on the conservative requirement is newly proposed for accuracy enhancement, which is required to capture the acoustic portion of the solution in the smooth region. Furthermore, the new distinguishing mechanism which is based on the Gibbs phenomenon in discontinuity, between continuous and discontinuous regions is introduced to eliminate the excessive numerical dissipation in the continuous region by the restricted application of MLP according to the decision of the distinguishing function. To investigate the effectiveness of the developed method, a sequence of benchmark simulations such as spherical wave propagation, nonlinear wave propagation, shock tube problem and vortex preservation test problem are executed. Also, throughout more realistic shock-vortex interaction and muzzle blast flow problems, the utility of the new method for aeroacoustic applications is verified by comparing with the previous numerical or experimental results.

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

NASA Technical Reports Server (NTRS)

Siclari, Michael J.

1999-01-01

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Numerical study of supersonic combustors by multi-block grids with mismatched interfaces

NASA Technical Reports Server (NTRS)

Moon, Young J.

1990-01-01

A three dimensional, finite rate chemistry, Navier-Stokes code was extended to a multi-block code with mismatched interface for practical calculations of supersonic combustors. To ensure global conservation, a conservative algorithm was used for the treatment of mismatched interfaces. The extended code was checked against one test case, i.e., a generic supersonic combustor with transverse fuel injection, examining solution accuracy, convergence, and local mass flux error. After testing, the code was used to simulate the chemically reacting flow fields in a scramjet combustor with parallel fuel injectors (unswept and swept ramps). Computational results were compared with experimental shadowgraph and pressure measurements. Fuel-air mixing characteristics of the unswept and swept ramps were compared and investigated.

Finite element analysis of transonic flows in cascades: Importance of computational grids in improving accuracy and convergence

NASA Technical Reports Server (NTRS)

Ecer, A.; Akay, H. U.

1981-01-01

The finite element method is applied for the solution of transonic potential flows through a cascade of airfoils. Convergence characteristics of the solution scheme are discussed. Accuracy of the numerical solutions is investigated for various flow regions in the transonic flow configuration. The design of an efficient finite element computational grid is discussed for improving accuracy and convergence.

Sources of spurious force oscillations from an immersed boundary method for moving-body problems

NASA Astrophysics Data System (ADS)

Lee, Jongho; Kim, Jungwoo; Choi, Haecheon; Yang, Kyung-Soo

2011-04-01

When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132-150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.

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.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

The GeoClaw software for depth-averaged flows with adaptive refinement

USGS Publications Warehouse

Berger, M.J.; George, D.L.; LeVeque, R.J.; Mandli, Kyle T.

2011-01-01

Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses high-resolution shock-capturing finite volume methods on logically rectangular grids, including latitude-longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of large-scale geophysical problems. Examples are given illustrating its use for modeling tsunamis and dam-break flooding problems. Documentation and download information is available at www.clawpack.org/geoclaw. ?? 2011.

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

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

Sousa, E.M., E-mail: sousae@uw.edu; Shumlak, U., E-mail: shumlak@uw.edu

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutralmore » physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.« less

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

Finite difference time domain grid generation from AMC helicopter models

NASA Technical Reports Server (NTRS)

Cravey, Robin L.

1992-01-01

A simple technique is presented which forms a cubic grid model of a helicopter from an Aircraft Modeling Code (AMC) input file. The AMC input file defines the helicopter fuselage as a series of polygonal cross sections. The cubic grid model is used as an input to a Finite Difference Time Domain (FDTD) code to obtain predictions of antenna performance on a generic helicopter model. The predictions compare reasonably well with measured data.

Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows.

DTIC Science & Technology

1986-09-01

respectively. Here h is a parameter which is usually related to the size of the grid associated with the finite element partitioning of Q. Then one... grid and of not at least performing serious mesh refinement studies. It also points out the usefulness of rigorous results concerning the stability...overconstrained the .1% approximate velocity field. However, by employing different grids for the ’z pressure and velocity fields, the linear-constant

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.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

Fast High Resolution Volume Carving for 3D Plant Shoot Reconstruction

PubMed Central

Scharr, Hanno; Briese, Christoph; Embgenbroich, Patrick; Fischbach, Andreas; Fiorani, Fabio; Müller-Linow, Mark

2017-01-01

Volume carving is a well established method for visual hull reconstruction and has been successfully applied in plant phenotyping, especially for 3d reconstruction of small plants and seeds. When imaging larger plants at still relatively high spatial resolution (≤1 mm), well known implementations become slow or have prohibitively large memory needs. Here we present and evaluate a computationally efficient algorithm for volume carving, allowing e.g., 3D reconstruction of plant shoots. It combines a well-known multi-grid representation called “Octree” with an efficient image region integration scheme called “Integral image.” Speedup with respect to less efficient octree implementations is about 2 orders of magnitude, due to the introduced refinement strategy “Mark and refine.” Speedup is about a factor 1.6 compared to a highly optimized GPU implementation using equidistant voxel grids, even without using any parallelization. We demonstrate the application of this method for trait derivation of banana and maize plants. PMID:29033961

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Seismic wavefield simulation in 2D elastic and viscoelastic tilted transversely isotropic media: comparisons between four different kinds of finite-difference grid schemes

NASA Astrophysics Data System (ADS)

Li, Zhong-sheng; Bai, Chao-ying; Sun, Yao-chong

2013-08-01

In this paper, we use the staggered grid, the auxiliary grid, the rotated staggered grid and the non-staggered grid finite-difference methods to simulate the wavefield propagation in 2D elastic tilted transversely isotropic (TTI) and viscoelastic TTI media, respectively. Under the stability conditions, we choose different spatial and temporal intervals to get wavefront snapshots and synthetic seismograms to compare the four algorithms in terms of computational accuracy, CPU time, phase shift, frequency dispersion and amplitude preservation. The numerical results show that: (1) the rotated staggered grid scheme has the least memory cost and the fastest running speed; (2) the non-staggered grid scheme has the highest computational accuracy and least phase shift; (3) the staggered grid has less frequency dispersion even when the spatial interval becomes larger.

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Low-Dissipation Advection Schemes Designed for Large Eddy Simulations of Hypersonic Propulsion Systems

NASA Technical Reports Server (NTRS)

White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.

2012-01-01

The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Assessment of sub-grid scale dispersion closure with regularized deconvolution method in a particle-laden turbulent jet

NASA Astrophysics Data System (ADS)

Wang, Qing; Zhao, Xinyu; Ihme, Matthias

2017-11-01

Particle-laden turbulent flows are important in numerous industrial applications, such as spray combustion engines, solar energy collectors etc. It is of interests to study this type of flows numerically, especially using large-eddy simulations (LES). However, capturing the turbulence-particle interaction in LES remains challenging due to the insufficient representation of the effect of sub-grid scale (SGS) dispersion. In the present work, a closure technique for the SGS dispersion using regularized deconvolution method (RDM) is assessed. RDM was proposed as the closure for the SGS dispersion in a counterflow spray that is studied numerically using finite difference method on a structured mesh. A presumed form of LES filter is used in the simulations. In the present study, this technique has been extended to finite volume method with an unstructured mesh, where no presumption on the filter form is required. The method is applied to a series of particle-laden turbulent jets. Parametric analyses of the model performance are conducted for flows with different Stokes numbers and Reynolds numbers. The results from LES will be compared against experiments and direct numerical simulations (DNS).

CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model.

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

Dennis, John; Edwards, Jim; Evans, Kate J

2012-01-01

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR's High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubed-sphere grid. The main motivation for including a spectral element dynamical core is to improve the scalability of CAM by allowing quasi-uniform grids for the sphere that do not require polar filters. In addition, the approach provides other state-of-the-art capabilities such as improved conservation properties. Spectral elements are used for the horizontal discretization, while most othermore » aspects of the dynamical core are a hybrid of well tested techniques from CAM's finite volume and global spectral dynamical core options. Here we first give a overview of the spectral element dynamical core as used in CAM. We then give scalability and performance results from CAM running with three different dynamical core options within the Community Earth System Model, using a pre-industrial time-slice configuration. We focus on high resolution simulations of 1/4 degree, 1/8 degree, and T340 spectral truncation.« less

Application of adaptive gridding to magnetohydrodynamic flows

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

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

Multiple-animal MR imaging using a 3T clinical scanner and multi-channel coil for volumetric analysis in a mouse tumor model.

PubMed

Mitsuda, Minoru; Yamaguchi, Masayuki; Furuta, Toshihiro; Nabetani, Akira; Hirayama, Akira; Nozaki, Atsushi; Niitsu, Mamoru; Fujii, Hirofumi

2011-01-01

Multiple small-animal magnetic resonance (MR) imaging to measure tumor volume may increase the throughput of preclinical cancer research assessing tumor response to novel therapies. We used a clinical scanner and multi-channel coil to evaluate the usefulness of this imaging to assess experimental tumor volume in mice. We performed a phantom study to assess 2-dimensional (2D) geometric distortion using 9-cm spherical and 32-cell (8×4 one-cm(2) grids) phantoms using a 3-tesla clinical MR scanner and dedicated multi-channel coil composed of 16 5-cm circular coils. Employing the multi-channel coil, we simultaneously scanned 6 or 8 mice bearing sarcoma 180 tumors. We estimated tumor volume from the sum of the product of tumor area and slice thickness on 2D spin-echo images (repetition time/echo time, 3500/16 ms; in-plane resolution, 0.195×0.195×1 mm(3)). After MR acquisition, we excised and weighed tumors, calculated reference tumor volumes from actual tumor weight assuming a density of 1.05 g/cm(3), and assessed the correlation between the estimated and reference volumes using Pearson's test. Two-dimensional geometric distortion was acceptable below 5% in the 9-cm spherical phantom and in every cell in the 32-cell phantom. We scanned up to 8 mice simultaneously using the multi-channel coil and found 11 tumors larger than 0.1 g in 12 mice. Tumor volumes were 1.04±0.73 estimated by MR imaging and 1.04±0.80 cm(3) by reference volume (average±standard deviation) and highly correlated (correlation coefficient, 0.995; P<0.01, Pearson's test). Use of multiple small-animal MR imaging employing a clinical scanner and multi-channel coil enabled accurate assessment of experimental tumor volume in a large number of mice and may facilitate high throughput monitoring of tumor response to therapy in preclinical research.

Optimization of multi-objective micro-grid based on improved particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Zhang, Jian; Gan, Yang

2018-04-01

The paper presents a multi-objective optimal configuration model for independent micro-grid with the aim of economy and environmental protection. The Pareto solution set can be obtained by solving the multi-objective optimization configuration model of micro-grid with the improved particle swarm algorithm. The feasibility of the improved particle swarm optimization algorithm for multi-objective model is verified, which provides an important reference for multi-objective optimization of independent micro-grid.

Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

NASA Astrophysics Data System (ADS)

Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

2018-01-01

This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

CAPRI (Computational Analysis PRogramming Interface): A Solid Modeling Based Infra-Structure for Engineering Analysis and Design Simulations

NASA Technical Reports Server (NTRS)

Haimes, Robert; Follen, Gregory J.

1998-01-01

CAPRI is a CAD-vendor neutral application programming interface designed for the construction of analysis and design systems. By allowing access to the geometry from within all modules (grid generators, solvers and post-processors) such tasks as meshing on the actual surfaces, node enrichment by solvers and defining which mesh faces are boundaries (for the solver and visualization system) become simpler. The overall reliance on file 'standards' is minimized. This 'Geometry Centric' approach makes multi-physics (multi-disciplinary) analysis codes much easier to build. By using the shared (coupled) surface as the foundation, CAPRI provides a single call to interpolate grid-node based data from the surface discretization in one volume to another. Finally, design systems are possible where the results can be brought back into the CAD system (and therefore manufactured) because all geometry construction and modification are performed using the CAD system's geometry kernel.

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone.

PubMed

Vafaeian, B; El-Rich, M; El-Bialy, T; Adeeb, S

2014-08-01

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone. Copyright © 2014 Elsevier B.V. All rights reserved.

A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids

PubMed Central

Boschitsch, Alexander H.; Fenley, Marcia O.

2011-01-01

An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent – analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities – obtained with both linear and nonlinear Poisson-Boltzmann equation – for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers. PMID:21984876

Improved Finite-Volume Method for Radiative Hydrodynamics

NASA Technical Reports Server (NTRS)

Wray, Alan

2012-01-01

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy for such simulations on structured and unstructured grids compared to more conventional approaches. Results will be shown for shock radiation during hypersonic reentry. Issues of parallelization within a radiation sweep will also be discussed.

Prediction and control of slender-wing rock

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Salman, Ahmed A.

1992-01-01

The unsteady Euler equations and the Euler equations of rigid-body dynamics, both written in the moving frame of reference, are sequentially solved to simulate the limit-cycle rock motion of slender delta wings. The governing equations of the fluid flow and the dynamics of the present multidisciplinary problem are solved using an implicit, approximately-factored, central-difference-like, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. For the control of wing-rock motion, leading-edge flaps are forced to oscillate anti-symmetrically at prescribed frequency and amplitude, which are tuned in order to suppress the rock motion. Since the computational grid deforms due to the leading-edge flaps motion, the grid is dynamically deformed using the Navier-displacement equations. Computational applications cover locally-conical and three-dimensional solutions for the wing-rock simulation and its control.

A three-dimensional electrostatic particle-in-cell methodology on unstructured Delaunay-Voronoi grids

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

Gatsonis, Nikolaos A.; Spirkin, Anton

2009-06-01

The mathematical formulation and computational implementation of a three-dimensional particle-in-cell methodology on unstructured Delaunay-Voronoi tetrahedral grids is presented. The method allows simulation of plasmas in complex domains and incorporates the duality of the Delaunay-Voronoi in all aspects of the particle-in-cell cycle. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints. Electric potential and fields are derived from a finite-volume formulation of Gauss' law using the Voronoi-Delaunay dual. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured Delaunay grids. Error andmore » sensitivity analysis examines the effects of particles/cell, grid scaling, and timestep on the numerical heating, the slowing-down time, and the deflection times. The problem of current collection by cylindrical Langmuir probes in collisionless plasmas is used for validation. Numerical results compare favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. The versatility of the methodology is demonstrated with the simulation of a complex plasma microsensor, a directional micro-retarding potential analyzer that includes a low transparency micro-grid.« less

DNA-Cryptography-Based Obfuscated Systolic Finite Field Multiplier for Secure Cryptosystem in Smart Grid

NASA Astrophysics Data System (ADS)

Chen, Shaobo; Chen, Pingxiuqi; Shao, Qiliang; Basha Shaik, Nazeem; Xie, Jiafeng

2017-05-01

The elliptic curve cryptography (ECC) provides much stronger security per bits compared to the traditional cryptosystem, and hence it is an ideal role in secure communication in smart grid. On the other side, secure implementation of finite field multiplication over GF(2 m ) is considered as the bottle neck of ECC. In this paper, we present a novel obfuscation strategy for secure implementation of systolic field multiplier for ECC in smart grid. First, for the first time, we propose a novel obfuscation technique to derive a novel obfuscated systolic finite field multiplier for ECC implementation. Then, we employ the DNA cryptography coding strategy to obfuscate the field multiplier further. Finally, we obtain the area-time-power complexity of the proposed field multiplier to confirm the efficiency of the proposed design. The proposed design is highly obfuscated with low overhead, suitable for secure cryptosystem in smart grid.

Numerical simulation of aerothermal loads in hypersonic engine inlets due to shock impingement

NASA Technical Reports Server (NTRS)

Ramakrishnan, R.

1992-01-01

The effect of shock impingement on an axial corner simulating the inlet of a hypersonic vehicle engine is modeled using a finite-difference procedure. A three-dimensional dynamic grid adaptation procedure is utilized to move the grids to regions with strong flow gradients. The adaptation procedure uses a grid relocation stencil that is valid at both the interior and boundary points of the finite-difference grid. A linear combination of spatial derivatives of specific flow variables, calculated with finite-element interpolation functions, are used as adaptation measures. This computational procedure is used to study laminar and turbulent Mach 6 flows in the axial corner. The description of flow physics and qualitative measures of heat transfer distributions on cowl and strut surfaces obtained from the analysis are compared with experimental observations. Conclusions are drawn regarding the capability of the numerical scheme for enhanced modeling of high-speed compressible flows.

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.

SutraPlot, a graphical post-processor for SUTRA, a model for ground-water flow with solute or energy transport

USGS Publications Warehouse

Souza, W.R.

1999-01-01

This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1

Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation

PubMed Central

Kerckhoffs, Roy C. P.; Neal, Maxwell L.; Gu, Quan; Bassingthwaighte, James B.; Omens, Jeff H.; McCulloch, Andrew D.

2010-01-01

In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system. PMID:17111210

Computer simulations of phase field drops on super-hydrophobic surfaces

NASA Astrophysics Data System (ADS)

Fedeli, Livio

2017-09-01

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Treatment of internal sources in the finite-volume ELLAM

USGS Publications Warehouse

Healy, R.W.; ,; ,; ,; ,; ,

2000-01-01

The finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) is a mass-conservative approach for solving the advection-dispersion equation. The method has been shown to be accurate and efficient for solving advection-dominated problems of solute transport in ground water in 1, 2, and 3 dimensions. Previous implementations of FVELLAM have had difficulty in representing internal sources because the standard assumption of lowest order Raviart-Thomas velocity field does not hold for source cells. Therefore, tracking of particles within source cells is problematic. A new approach has been developed to account for internal sources in FVELLAM. It is assumed that the source is uniformly distributed across a grid cell and that instantaneous mixing takes place within the cell, such that concentration is uniform across the cell at any time. Sub-time steps are used in the time-integration scheme to track mass outflow from the edges of the source cell. This avoids the need for tracking within the source cell. We describe the new method and compare results for a test problem with a wide range of cell Peclet numbers.

Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test

NASA Astrophysics Data System (ADS)

Ivankovic, A.; Muzaferija, S.; Demirdzic, I.

1997-07-01

Rapid Crack Propagation (RCP) along pressurised plastic pipes is by far the most dangerous pipe failure mode. Despite the economic benefits offered by increasing pipe size and operating pressure, both strategies increase the risk and the potential consequences of RCP. It is therefore extremely important to account for RCP in establishing the safe operational conditions. Combined experimental-numerical study is the only reliable approach of addressing the problem, and extensive research is undertaken by various fracture groups (e.g. Southwest Research Institute - USA, Imperial College - UK). This paper presents numerical results from finite volume modelling of full-scale test on medium density polyethylene gas pressurised pipes. The crack speed and pressure profile are prescribed in the analysis. Both steady-state and transient RCPs are considered, and the comparison between the two shown. The steady-state results are efficiently achieved employing a full multigrid acceleration technique, where sets of progressively finer grids are used in V-cycles. Also, the effect of inelastic behaviour of polyethylene on RCP results is demonstrated.

Development of a Hydrodynamic Model of Puget Sound and Northwest Straits

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

Yang, Zhaoqing; Khangaonkar, Tarang P.

2007-12-10

The hydrodynamic model used in this study is the Finite Volume Coastal Ocean Model (FVCOM) developed by the University of Massachusetts at Dartmouth. The unstructured grid and finite volume framework, as well as the capability of wetting/drying simulation and baroclinic simulation, makes FVCOM a good fit to the modeling needs for nearshore restoration in Puget Sound. The model domain covers the entire Puget Sound, Strait of Juan de Fuca, San Juan Passages, and Georgia Strait at the United States-Canada Border. The model is driven by tide, freshwater discharge, and surface wind. Preliminary model validation was conducted for tides at variousmore » locations in the straits and Puget Sound using National Oceanic and Atmospheric Administration (NOAA) tide data. The hydrodynamic model was successfully linked to the NOAA oil spill model General NOAA Operational Modeling Environment model (GNOME) to predict particle trajectories at various locations in Puget Sound. Model results demonstrated that the Puget Sound GNOME model is a useful tool to obtain first-hand information for emergency response such as oil spill and fish migration pathways.« less

Resonance Extraction from the Finite Volume

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

Doring, Michael; Molina Peralta, Raquel

2016-06-01

The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T- or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are dis-more » cussed, like the scalar meson f0(980) and the excited baryons N(1535)1/2^- and Lambda(1405)1/2^-.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong, E-mail: yidong.xia@inl.gov; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the Hydra-TH code. -- Highlights: •We performed a comprehensive study to verify and validate the turbulence models in Hydra-TH. •Hydra-TH delivers 2nd-order grid convergence for the incompressible Navier–Stokes equations. •Hydra-TH can accurately simulate the laminar boundary layers. •Hydra-TH can accurately simulate the turbulent boundary layers with RANS turbulence models. •Hydra-TH delivers high-fidelity LES capability for simulating turbulent flows in confined space.« less

Structure of the Nucleon and its Excitations

NASA Astrophysics Data System (ADS)

Kamleh, Waseem; Leinweber, Derek; Liu, Zhan-wei; Stokes, Finn; Thomas, Anthony; Thomas, Samuel; Wu, Jia-jun

2018-03-01

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

NASA Technical Reports Server (NTRS)

Madsen, Niel K.

1992-01-01

Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Model of interaction in Smart Grid on the basis of multi-agent system

NASA Astrophysics Data System (ADS)

Engel, E. A.; Kovalev, I. V.; Engel, N. E.

2016-11-01

This paper presents model of interaction in Smart Grid on the basis of multi-agent system. The use of travelling waves in the multi-agent system describes the behavior of the Smart Grid from the local point, which is being the complement of the conventional approach. The simulation results show that the absorption of the wave in the distributed multi-agent systems is effectively simulated the interaction in Smart Grid.

A Virtual World of Visualization

NASA Technical Reports Server (NTRS)

1998-01-01

In 1990, Sterling Software, Inc., developed the Flow Analysis Software Toolkit (FAST) for NASA Ames on contract. FAST is a workstation based modular analysis and visualization tool. It is used to visualize and animate grids and grid oriented data, typically generated by finite difference, finite element and other analytical methods. FAST is now available through COSMIC, NASA's software storehouse.

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.

PBSM3D: A finite volume, scalar-transport blowing snow model for use with variable resolution meshes

NASA Astrophysics Data System (ADS)

Marsh, C.; Wayand, N. E.; Pomeroy, J. W.; Wheater, H. S.; Spiteri, R. J.

2017-12-01

Blowing snow redistribution results in heterogeneous snowcovers that are ubiquitous in cold, windswept environments. Capturing this spatial and temporal variability is important for melt and runoff simulations. Point scale blowing snow transport models are difficult to apply in fully distributed hydrological models due to landscape heterogeneity and complex wind fields. Many existing distributed snow transport models have empirical wind flow and/or simplified wind direction algorithms that perform poorly in calculating snow redistribution where there are divergent wind flows, sharp topography, and over large spatial extents. Herein, a steady-state scalar transport model is discretized using the finite volume method (FVM), using parameterizations from the Prairie Blowing Snow Model (PBSM). PBSM has been applied in hydrological response units and grids to prairie, arctic, glacier, and alpine terrain and shows a good capability to represent snow redistribution over complex terrain. The FVM discretization takes advantage of the variable resolution mesh in the Canadian Hydrological Model (CHM) to ensure efficient calculations over small and large spatial extents. Variable resolution unstructured meshes preserve surface heterogeneity but result in fewer computational elements versus high-resolution structured (raster) grids. Snowpack, soil moisture, and streamflow observations were used to evaluate CHM-modelled outputs in a sub-arctic and an alpine basin. Newly developed remotely sensed snowcover indices allowed for validation over large basins. CHM simulations of snow hydrology were improved by inclusion of the blowing snow model. The results demonstrate the key role of snow transport processes in creating pre-melt snowcover heterogeneity and therefore governing post-melt soil moisture and runoff generation dynamics.

Arc Length Based Grid Distribution For Surface and Volume Grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1996-01-01

Techniques are presented for distributing grid points on parametric surfaces and in volumes according to a specified distribution of arc length. Interpolation techniques are introduced which permit a given distribution of grid points on the edges of a three-dimensional grid block to be propagated through the surface and volume grids. Examples demonstrate how these methods can be used to improve the quality of grids generated by transfinite interpolation.

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

An Embedded 3D Fracture Modeling Approach for Simulating Fracture-Dominated Fluid Flow and Heat Transfer in Geothermal Reservoirs

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

Johnston, Henry; Wang, Cong; Winterfeld, Philip

An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added tomore » the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.« less

Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

NASA Astrophysics Data System (ADS)

Simpson, J. J.; Taflove, A.

2005-12-01

We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time- Domain Method, 3rd. ed. Norwood, MA: Artech House, 2005. [2] M. Hayakawa, K. Ohta, A. P. Nickolaenko, and Y. Ando, "Anomalous effect in Schumann resonance phenomena observed in Japan, possibly associated with the Chi-Chi earthquake in Taiwan," Ann. Geophysicae, in press. [3] J. J. Simpson and A. Taflove, "3-D FDTD modeling of ULF/ELF propagation within the global Earth-ionosphere cavity using an optimized geodesic grid," Proc. IEEE AP-S International Symposium, Washington, D.C., July 2005.

Integrated Multi-Scale Data Analytics and Machine Learning for the Distribution Grid and Building-to-Grid Interface

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

Stewart, Emma M.; Hendrix, Val; Chertkov, Michael

This white paper introduces the application of advanced data analytics to the modernized grid. In particular, we consider the field of machine learning and where it is both useful, and not useful, for the particular field of the distribution grid and buildings interface. While analytics, in general, is a growing field of interest, and often seen as the golden goose in the burgeoning distribution grid industry, its application is often limited by communications infrastructure, or lack of a focused technical application. Overall, the linkage of analytics to purposeful application in the grid space has been limited. In this paper wemore » consider the field of machine learning as a subset of analytical techniques, and discuss its ability and limitations to enable the future distribution grid and the building-to-grid interface. To that end, we also consider the potential for mixing distributed and centralized analytics and the pros and cons of these approaches. Machine learning is a subfield of computer science that studies and constructs algorithms that can learn from data and make predictions and improve forecasts. Incorporation of machine learning in grid monitoring and analysis tools may have the potential to solve data and operational challenges that result from increasing penetration of distributed and behind-the-meter energy resources. There is an exponentially expanding volume of measured data being generated on the distribution grid, which, with appropriate application of analytics, may be transformed into intelligible, actionable information that can be provided to the right actors – such as grid and building operators, at the appropriate time to enhance grid or building resilience, efficiency, and operations against various metrics or goals – such as total carbon reduction or other economic benefit to customers. While some basic analysis into these data streams can provide a wealth of information, computational and human boundaries on performing the analysis are becoming significant, with more data and multi-objective concerns. Efficient applications of analysis and the machine learning field are being considered in the loop.« less

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.

Generalizing the TRAPRG and TRAPAX finite elements

NASA Technical Reports Server (NTRS)

Hurwitz, M. M.

1983-01-01

The NASTRAN TRAPRG and TRAPAX finite elements are very restrictive as to shape and grid point numbering. The elements must be trapezoidal with two sides parallel to the radial axis. In addition, the ordering of the grid points on the element connection card must follow strict rules. The paper describes the generalization of these elements so that these restrictions no longer apply.

Program Calculates Forces in Bolted Structural Joints

NASA Technical Reports Server (NTRS)

Buder, Daniel A.

2005-01-01

FORTRAN 77 computer program calculates forces in bolts in the joints of structures. This program is used in conjunction with the NASTRAN finite-element structural-analysis program. A mathematical model of a structure is first created by approximating its load-bearing members with representative finite elements, then NASTRAN calculates the forces and moments that each finite element contributes to grid points located throughout the structure. The user selects the finite elements that correspond to structural members that contribute loads to the joints of interest, and identifies the grid point nearest to each such joint. This program reads the pertinent NASTRAN output, combines the forces and moments from the contributing elements to determine the resultant force and moment acting at each proximate grid point, then transforms the forces and moments from these grid points to the centroids of the affected joints. Then the program uses these joint loads to obtain the axial and shear forces in the individual bolts. The program identifies which bolts bear the greatest axial and/or shear loads. The program also performs a fail-safe analysis in which the foregoing calculations are repeated for a sequence of cases in which each fastener, in turn, is assumed not to transmit an axial force.

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.

PubMed

Sasaki, Akira; Kojo, Masashi; Hirose, Kikuji; Goto, Hidekazu

2011-11-02

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

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.

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M. S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M.-S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results are shown a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Simple Analytic Model for Nanowire Array Polarizers

NASA Astrophysics Data System (ADS)

Pelletier, Vincent; Asakawa, Koji; Wu, Mingshaw; Register, Richard; Chaikin, Paul

2006-03-01

Cylinder-forming diblock copolymers can be used to pattern nanowire arrays on a transparent substrate to be used as a polarizer, as described by Koji Asakawa in a complementary talk at this meeting. With a 33nm period, these wire arrays can polarize UV radiation, which is of great interest in lithography, astronomy and other areas. One can gain an analytical understanding of such an array made of non-perfectly conducting material of finite thickness using a model with an appropriately averaged complex dielectric function in an infinite wavelength approximation. This analysis predicts that the grid can go from an E-polarizer to an H-polarizer as the wavelength decreases below a cross-over wavelength, and experimental data confirm this cross-over. The overall response of the polarizing grid depends primarily on the plasma frequency of the metal used and the volume fraction of the nanowires, as well as the grid thickness. A numerical approach is also used to confirm the analytical model and assess departure from infinite wavelength effects. For our array dimensions, the polarization is only slightly different from this approximation for wavelengths down to 150nm.

Brief analysis of Jiangsu grid security and stability based on multi-infeed DC index in power system

NASA Astrophysics Data System (ADS)

Zhang, Wenjia; Wang, Quanquan; Ge, Yi; Huang, Junhui; Chen, Zhengfang

2018-02-01

The impact of Multi-infeed HVDC has gradually increased to security and stability operating in Jiangsu power grid. In this paper, an appraisal method of Multi-infeed HVDC power grid security and stability is raised with Multi-Infeed Effective Short Circuit Ratio, Multi-Infeed Interaction Factor and Commutation Failure Immunity Index. These indices are adopted in security and stability simulating calculation of Jiangsu Multi-infeed HVDC system. The simulation results indicate that Jiangsu power grid is operating with a strong DC system. It has high level of power grid security and stability, and meet the safety running requirements. Jinpin-Suzhou DC system is located in the receiving end with huge capacity, which is easily leading to commutation failure of the transmission line. In order to resolve this problem, dynamic reactive power compensation can be applied in power grid near Jinpin-Suzhou DC system. Simulation result shows this method is feasible to commutation failure.

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.

Computations of spray, fuel-air mixing, and combustion in a lean-premixed-prevaporized combustor

NASA Technical Reports Server (NTRS)

Dasgupta, A.; Li, Z.; Shih, T. I.-P.; Kundu, K.; Deur, J. M.

1993-01-01

A code was developed for computing the multidimensional flow, spray, combustion, and pollutant formation inside gas turbine combustors. The code developed is based on a Lagrangian-Eulerian formulation and utilizes an implicit finite-volume method. The focus of this paper is on the spray part of the code (both formulation and algorithm), and a number of issues related to the computation of sprays and fuel-air mixing in a lean-premixed-prevaporized combustor. The issues addressed include: (1) how grid spacings affect the diffusion of evaporated fuel, and (2) how spurious modes can arise through modelling of the spray in the Lagrangian computations. An upwind interpolation scheme is proposed to account for some effects of grid spacing on the artificial diffusion of the evaporated fuel. Also, some guidelines are presented to minimize errors associated with the spurious modes.

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

NASA Technical Reports Server (NTRS)

Frink, Neal T.

1996-01-01

A method Is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization Is accomplished by a cell-centered finite-volume formulation using an accurate lin- ear reconstruction scheme and upwind flux differencing. 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 sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy In predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

A machine learning approach for efficient uncertainty quantification using multiscale methods

NASA Astrophysics Data System (ADS)

Chan, Shing; Elsheikh, Ahmed H.

2018-02-01

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.

Numerical Simulations of Buoyancy Effects in low Density Gas Jets

NASA Technical Reports Server (NTRS)

Satti, R. P.; Pasumarthi, K. S.; Agrawal, A. K.

2004-01-01

This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

NASA Technical Reports Server (NTRS)

Frink, Neal T.

1996-01-01

A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. 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 sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

NASA Astrophysics Data System (ADS)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

SCISEAL: A CFD code for analysis of fluid dynamic forces in seals

NASA Technical Reports Server (NTRS)

Athavale, Mahesh; Przekwas, Andrzej

1994-01-01

A viewgraph presentation is made of the objectives, capabilities, and test results of the computer code SCISEAL. Currently, the seal code has: a finite volume, pressure-based integration scheme; colocated variables with strong conservation approach; high-order spatial differencing, up to third-order; up to second-order temporal differencing; a comprehensive set of boundary conditions; a variety of turbulence models and surface roughness treatment; moving grid formulation for arbitrary rotor whirl; rotor dynamic coefficients calculated by the circular whirl and numerical shaker methods; and small perturbation capabilities to handle centered and eccentric seals.

Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer

NASA Astrophysics Data System (ADS)

Yoon, Kyungho; Lee, Wonhye; Croce, Phillip; Cammalleri, Amanda; Yoo, Seung-Schik

2018-05-01

Transcranial focused ultrasound (tFUS) is emerging as a non-invasive brain stimulation modality. Complicated interactions between acoustic pressure waves and osseous tissue introduce many challenges in the accurate targeting of an acoustic focus through the cranium. Image-guidance accompanied by a numerical simulation is desired to predict the intracranial acoustic propagation through the skull; however, such simulations typically demand heavy computation, which warrants an expedited processing method to provide on-site feedback for the user in guiding the acoustic focus to a particular brain region. In this paper, we present a multi-resolution simulation method based on the finite-difference time-domain formulation to model the transcranial propagation of acoustic waves from a single-element transducer (250 kHz). The multi-resolution approach improved computational efficiency by providing the flexibility in adjusting the spatial resolution. The simulation was also accelerated by utilizing parallelized computation through the graphic processing unit. To evaluate the accuracy of the method, we measured the actual acoustic fields through ex vivo sheep skulls with different sonication incident angles. The measured acoustic fields were compared to the simulation results in terms of focal location, dimensions, and pressure levels. The computational efficiency of the presented method was also assessed by comparing simulation speeds at various combinations of resolution grid settings. The multi-resolution grids consisting of 0.5 and 1.0 mm resolutions gave acceptable accuracy (under 3 mm in terms of focal position and dimension, less than 5% difference in peak pressure ratio) with a speed compatible with semi real-time user feedback (within 30 s). The proposed multi-resolution approach may serve as a novel tool for simulation-based guidance for tFUS applications.

Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer.

PubMed

Yoon, Kyungho; Lee, Wonhye; Croce, Phillip; Cammalleri, Amanda; Yoo, Seung-Schik

2018-05-10

Transcranial focused ultrasound (tFUS) is emerging as a non-invasive brain stimulation modality. Complicated interactions between acoustic pressure waves and osseous tissue introduce many challenges in the accurate targeting of an acoustic focus through the cranium. Image-guidance accompanied by a numerical simulation is desired to predict the intracranial acoustic propagation through the skull; however, such simulations typically demand heavy computation, which warrants an expedited processing method to provide on-site feedback for the user in guiding the acoustic focus to a particular brain region. In this paper, we present a multi-resolution simulation method based on the finite-difference time-domain formulation to model the transcranial propagation of acoustic waves from a single-element transducer (250 kHz). The multi-resolution approach improved computational efficiency by providing the flexibility in adjusting the spatial resolution. The simulation was also accelerated by utilizing parallelized computation through the graphic processing unit. To evaluate the accuracy of the method, we measured the actual acoustic fields through ex vivo sheep skulls with different sonication incident angles. The measured acoustic fields were compared to the simulation results in terms of focal location, dimensions, and pressure levels. The computational efficiency of the presented method was also assessed by comparing simulation speeds at various combinations of resolution grid settings. The multi-resolution grids consisting of 0.5 and 1.0 mm resolutions gave acceptable accuracy (under 3 mm in terms of focal position and dimension, less than 5% difference in peak pressure ratio) with a speed compatible with semi real-time user feedback (within 30 s). The proposed multi-resolution approach may serve as a novel tool for simulation-based guidance for tFUS applications.

Self-consistent field theory simulations of polymers on arbitrary domains

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

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu; Laachi, Nabil; Delaney, Kris

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refinemore » the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.« less

Fluctuating hydrodynamics for multiscale modeling and simulation: energy and heat transfer in molecular fluids.

PubMed

Shang, Barry Z; Voulgarakis, Nikolaos K; Chu, Jhih-Wei

2012-07-28

This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Problems with heterogeneous and non-isotropic media or distorted grids

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

Hyman, J.; Shashkov, M.; Steinberg, S.

1996-08-01

This paper defines discretizations of the divergence and flux operators that produce symmetric, positive-definite, and accurate approximations to steady-state diffusion problems. Because discontinuous material properties and highly distorted grids are allowed, the flux operator, rather than the gradient, is used as a fundamental operator to be discretized. Resulting finite-difference scheme is similar to those obtained from the mixed finite-element method.

Composite sizing and ply orientation for stiffness requirements using a large finite element structural model

NASA Technical Reports Server (NTRS)

Radovcich, N. A.; Gentile, D. P.

1989-01-01

A NASTRAN bulk dataset preprocessor was developed to facilitate the integration of filamentary composite laminate properties into composite structural resizing for stiffness requirements. The NASCOMP system generates delta stiffness and delta mass matrices for input to the flutter derivative program. The flutter baseline analysis, derivative calculations, and stiffness and mass matrix updates are controlled by engineer defined processes under an operating system called CBUS. A multi-layered design variable grid system permits high fidelity resizing without excessive computer cost. The NASCOMP system uses ply layup drawings for basic input. The aeroelastic resizing for stiffness capability was used during an actual design exercise.

Capturing Multiscale Phenomena via Adaptive Mesh Refinement (AMR) in 2D and 3D Atmospheric Flows

NASA Astrophysics Data System (ADS)

Ferguson, J. O.; Jablonowski, C.; Johansen, H.; McCorquodale, P.; Ullrich, P. A.; Langhans, W.; Collins, W. D.

2017-12-01

Extreme atmospheric events such as tropical cyclones are inherently complex multiscale phenomena. Such phenomena are a challenge to simulate in conventional atmosphere models, which typically use rather coarse uniform-grid resolutions. To enable study of these systems, Adaptive Mesh Refinement (AMR) can provide sufficient local resolution by dynamically placing high-resolution grid patches selectively over user-defined features of interest, such as a developing cyclone, while limiting the total computational burden of requiring such high-resolution globally. This work explores the use of AMR with a high-order, non-hydrostatic, finite-volume dynamical core, which uses the Chombo AMR library to implement refinement in both space and time on a cubed-sphere grid. The characteristics of the AMR approach are demonstrated via a series of idealized 2D and 3D test cases designed to mimic atmospheric dynamics and multiscale flows. In particular, new shallow-water test cases with forcing mechanisms are introduced to mimic the strengthening of tropical cyclone-like vortices and to include simplified moisture and convection processes. The forced shallow-water experiments quantify the improvements gained from AMR grids, assess how well transient features are preserved across grid boundaries, and determine effective refinement criteria. In addition, results from idealized 3D test cases are shown to characterize the accuracy and stability of the non-hydrostatic 3D AMR dynamical core.

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.

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

NASA Technical Reports Server (NTRS)

Morris, C. I.

2013-01-01

The last two decades have witnessed tremendous growth in computational power, the development of computational fluid dynamics (CFD) codes which scale well over thousands of processors, and the refinement of unstructured grid-generation tools which facilitate rapid surface and volume gridding of complex geometries. Thus, engineering calculations of 10(exp 7) - 10(exp 8) finite-volume cells have become routine for some types of problems. Although the Reynolds Averaged Navier Stokes (RANS) approach to modeling turbulence is still in extensive and wide use, increasingly large-eddy simulation (LES) and hybrid RANS-LES approaches are being applied to resolve the largest scales of turbulence in many engineering problems. However, it has also become evident that LES places different requirements on the numerical approaches for both the spatial and temporal discretization of the Navier Stokes equations than does RANS. In particular, LES requires high time accuracy and minimal intrinsic numerical dispersion and dissipation over a wide spectral range. In this paper, the performance of both central-difference and upwind-biased spatial discretizations is examined for a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem, and the turbulent channel fl ow problem.

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

NASA Technical Reports Server (NTRS)

Morris, Christopher I.

2013-01-01

The last two decades have witnessed tremendous growth in computational power, the development of computational fluid dynamics (CFD) codes which scale well over thousands of processors, and the refinement of unstructured grid-generation tools which facilitate rapid surface and volume gridding of complex geometries. Thus, engineering calculations of 10(exp 7) - 10(exp 8) finite-volume cells have become routine for some types of problems. Although the Reynolds Averaged Navier Stokes (RANS) approach to modeling turbulence is still in extensive and wide use, increasingly large-eddy simulation (LES) and hybrid RANS-LES approaches are being applied to resolve the largest scales of turbulence in many engineering problems. However, it has also become evident that LES places different requirements on the numerical approaches for both the spatial and temporal discretization of the Navier Stokes equations than does RANS. In particular, LES requires high time accuracy and minimal intrinsic numerical dispersion and dissipation over a wide spectral range. In this paper, the performance of both central-difference and upwind-biased spatial discretizations is examined for a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem, and the turbulent channel ow problem.

Multi-scale damage modelling in a ceramic matrix composite using a finite-element microstructure meshfree methodology

PubMed Central

2016-01-01

The problem of multi-scale modelling of damage development in a SiC ceramic fibre-reinforced SiC matrix ceramic composite tube is addressed, with the objective of demonstrating the ability of the finite-element microstructure meshfree (FEMME) model to introduce important aspects of the microstructure into a larger scale model of the component. These are particularly the location, orientation and geometry of significant porosity and the load-carrying capability and quasi-brittle failure behaviour of the fibre tows. The FEMME model uses finite-element and cellular automata layers, connected by a meshfree layer, to efficiently couple the damage in the microstructure with the strain field at the component level. Comparison is made with experimental observations of damage development in an axially loaded composite tube, studied by X-ray computed tomography and digital volume correlation. Recommendations are made for further development of the model to achieve greater fidelity to the microstructure. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’. PMID:27242308

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Ash, Robert L.

1992-01-01

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.

3D Finite Element Analysis of Particle-Reinforced Aluminum

NASA Technical Reports Server (NTRS)

Shen, H.; Lissenden, C. J.

2002-01-01

Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem

NASA Astrophysics Data System (ADS)

Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.

2009-04-01

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Newman, James C., III; Barnwell, Richard W.

1997-01-01

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

NASA Astrophysics Data System (ADS)

Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek

2018-01-01

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.

Stackable differential mobility analyzer for aerosol measurement

DOEpatents

Cheng, Meng-Dawn [Oak Ridge, TN; Chen, Da-Ren [Creve Coeur, MO

2007-05-08

A multi-stage differential mobility analyzer (MDMA) for aerosol measurements includes a first electrode or grid including at least one inlet or injection slit for receiving an aerosol including charged particles for analysis. A second electrode or grid is spaced apart from the first electrode. The second electrode has at least one sampling outlet disposed at a plurality different distances along its length. A volume between the first and the second electrode or grid between the inlet or injection slit and a distal one of the plurality of sampling outlets forms a classifying region, the first and second electrodes for charging to suitable potentials to create an electric field within the classifying region. At least one inlet or injection slit in the second electrode receives a sheath gas flow into an upstream end of the classifying region, wherein each sampling outlet functions as an independent DMA stage and classifies different size ranges of charged particles based on electric mobility simultaneously.

Accurate finite difference methods for time-harmonic wave propagation

NASA Technical Reports Server (NTRS)

Harari, Isaac; Turkel, Eli

1994-01-01

Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

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.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 2: Unsteady ducted propfan analysis computer program users manual

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1991-01-01

The primary objective of this study was the development of a time-dependent three-dimensional Euler/Navier-Stokes aerodynamic analysis to predict unsteady compressible transonic flows about ducted and unducted propfan propulsion systems at angle of attack. The computer codes resulting from this study are referred to as Advanced Ducted Propfan Analysis Codes (ADPAC). This report is intended to serve as a computer program user's manual for the ADPAC developed under Task 2 of NASA Contract NAS3-25270, Unsteady Ducted Propfan Analysis. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. A time-accurate implicit residual smoothing operator was utilized for unsteady flow predictions. For unducted propfans, a single H-type grid was used to discretize each blade passage of the complete propeller. For ducted propfans, a coupled system of five grid blocks utilizing an embedded C-grid about the cowl leading edge was used to discretize each blade passage. Grid systems were generated by a combined algebraic/elliptic algorithm developed specifically for ducted propfans. Numerical calculations were compared with experimental data for both ducted and unducted propfan flows. The solution scheme demonstrated efficiency and accuracy comparable with other schemes of this class.

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.

Sprocket- Chain Simulation: Modelling and Simulation of a Multi Physics problem by sequentially coupling MotionSolve and nanoFluidX

NASA Astrophysics Data System (ADS)

Jayanthi, Aditya; Coker, Christopher

2016-11-01

In the last decade, CFD simulations have transitioned from the stage where they are used to validate the final designs to the main stream development of products driven by the simulation. However, there are still niche areas of applications liking oiling simulations, where the traditional CFD simulation times are probative to use them in product development and have to rely on experimental methods, which are expensive. In this paper a unique example of Sprocket-Chain simulation will be presented using nanoFluidx a commercial SPH code developed by FluiDyna GmbH and Altair Engineering. The grid less nature of the of SPH method has inherent advantages in the areas of application with complex geometry which pose severe challenge to classical finite volume CFD methods due to complex moving geometries, moving meshes and high resolution requirements leading to long simulation times. The simulations times using nanoFluidx can be reduced from weeks to days allowing the flexibility to run more simulation and can be in used in main stream product development. The example problem under consideration is a classical Multiphysics problem and a sequentially coupled solution of Motion Solve and nanoFluidX will be presented. This abstract is replacing DFD16-2016-000045.

3D inversion based on multi-grid approach of magnetotelluric data from Northern Scandinavia

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Smirnov, M.; Korja, T. J.; Egbert, G. D.

2012-12-01

In this work we investigate the geoelectrical structure of the cratonic margin of Fennoscandian Shield by means of magnetotelluric (MT) measurements carried out in Northern Norway and Sweden during summer 2011-2012. The project Magnetotellurics in the Scandes (MaSca) focuses on the investigation of the crust, upper mantle and lithospheric structure in a transition zone from a stable Precambrian cratonic interior to a passive continental margin beneath the Caledonian Orogen and the Scandes Mountains in western Fennoscandia. Recent MT profiles in the central and southern Scandes indicated a large contrast in resistivity between Caledonides and Precambrian basement. The alum shales as a highly conductive layers between the resistive Precambrian basement and the overlying Caledonian nappes are revealed from this profiles. Additional measurements in the Northern Scandes were required. All together data from 60 synchronous long period (LMT) and about 200 broad band (BMT) sites were acquired. The array stretches from Lofoten and Bodo (Norway) in the west to Kiruna and Skeleftea (Sweden) in the east covering an area of 500x500 square kilometers. LMT sites were occupied for about two months, while most of the BMT sites were measured during one day. We have used new multi-grid approach for 3D electromagnetic (EM) inversion and modelling. Our approach is based on the OcTree discretization where the spatial domain is represented by rectangular cells, each of which might be subdivided (recursively) into eight sub-cells. In this simplified implementation the grid is refined only in the horizontal direction, uniformly in each vertical layer. Using multi-grid we manage to have a high grid resolution near the surface (for instance, to tackle with galvanic distortions) and lower resolution at greater depth as the EM fields decay in the Earth according to the diffusion equation. We also have a benefit in computational costs as number of unknowns decrease. The multi-grid forward solver is implemented within the framework of the modular system for EM inversion (ModEM by G. Egbert, A. Kelbert, N. Meqbel), using the ModEM 3D finite difference staggered grid forward solver (second order PDE in the electric field, with divergence correction) as a starting point for our development. The first 3D inversion model for the crust and upper mantle shows the highly conducting bodies in the crust which can be interpreted as alum shales. The eastern and central parts are presented by resistive Precambrian rocks of the Svecofennian and Archaean domains. The upper mantle is resistive and relates to the Baltica basement. We also compare 3D inversion model with the results of 2D inversion along several profiles. We are able to explain some of the features in the data (out of quadrant phase) with 3D model, thus providing more reliable results compared to routine 2D approach.

Edge equilibrium code for tokamaks

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

Li, Xujing; Zakharov, Leonid E.; Drozdov, Vladimir V.

2014-01-15

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids.

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.

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene Marie

1992-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Advances in Chimera Grid Tools for Multi-Body Dynamics Simulations and Script Creation

NASA Technical Reports Server (NTRS)

Chan, William M.

2004-01-01

This viewgraph presentation contains information about (1) Framework for multi-body dynamics - Geometry Manipulation Protocol (GMP), (2) Simulation procedure using Chimera Grid Tools (CGT) and OVERFLOW-2 (3) Further recent developments in Chimera Grid Tools OVERGRID, Grid modules, Script library and (4) Future work.

A finite volume method for trace element diffusion and partitioning during crystal growth

NASA Astrophysics Data System (ADS)

Hesse, Marc A.

2012-09-01

A finite volume method on a uniform grid is presented to compute the polythermal diffusion and partitioning of a trace element during the growth of a porphyroblast crystal in a uniform matrix and in linear, cylindrical and spherical geometry. The motion of the crystal-matrix interface and the thermal evolution are prescribed functions of time. The motion of the interface is discretized and it advances from one cell boundary to next as the prescribed interface position passes the cell center. The appropriate conditions for the flux across the crystal-matrix interface are derived from discrete mass conservation. Numerical results are benchmarked against steady and transient analytic solutions for isothermal diffusion with partitioning and growth. Two applications illustrate the ability of the model to reproduce observed rare-earth element patterns in garnets (Skora et al., 2006) and water concentration profiles around spherulites in obsidian (Watkins et al., 2009). Simulations with diffusion inside the growing crystal show complex concentration evolutions for trace elements with high diffusion coefficients, such as argon or hydrogen, but demonstrate that rare-earth element concentrations in typical metamorphic garnets are not affected by intracrystalline diffusion.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

The Blended Finite Element Method for Multi-fluid Plasma Modeling

DTIC Science & Technology

2016-07-01

Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model

Adaptive multiresolution modeling of groundwater flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Malenica, Luka; Gotovac, Hrvoje; Srzic, Veljko; Andric, Ivo

2016-04-01

Proposed methodology was originally developed by our scientific team in Split who designed multiresolution approach for analyzing flow and transport processes in highly heterogeneous porous media. The main properties of the adaptive Fup multi-resolution approach are: 1) computational capabilities of Fup basis functions with compact support capable to resolve all spatial and temporal scales, 2) multi-resolution presentation of heterogeneity as well as all other input and output variables, 3) accurate, adaptive and efficient strategy and 4) semi-analytical properties which increase our understanding of usually complex flow and transport processes in porous media. The main computational idea behind this approach is to separately find the minimum number of basis functions and resolution levels necessary to describe each flow and transport variable with the desired accuracy on a particular adaptive grid. Therefore, each variable is separately analyzed, and the adaptive and multi-scale nature of the methodology enables not only computational efficiency and accuracy, but it also describes subsurface processes closely related to their understood physical interpretation. The methodology inherently supports a mesh-free procedure, avoiding the classical numerical integration, and yields continuous velocity and flux fields, which is vitally important for flow and transport simulations. In this paper, we will show recent improvements within the proposed methodology. Since "state of the art" multiresolution approach usually uses method of lines and only spatial adaptive procedure, temporal approximation was rarely considered as a multiscale. Therefore, novel adaptive implicit Fup integration scheme is developed, resolving all time scales within each global time step. It means that algorithm uses smaller time steps only in lines where solution changes are intensive. Application of Fup basis functions enables continuous time approximation, simple interpolation calculations across different temporal lines and local time stepping control. Critical aspect of time integration accuracy is construction of spatial stencil due to accurate calculation of spatial derivatives. Since common approach applied for wavelets and splines uses a finite difference operator, we developed here collocation one including solution values and differential operator. In this way, new improved algorithm is adaptive in space and time enabling accurate solution for groundwater flow problems, especially in highly heterogeneous porous media with large lnK variances and different correlation length scales. In addition, differences between collocation and finite volume approaches are discussed. Finally, results show application of methodology to the groundwater flow problems in highly heterogeneous confined and unconfined aquifers.

Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature

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

Brito, K. D.; Sprague, M. A.

2012-10-01

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for amore » given model size or total computation time.« less

ACCURATE SOLUTION AND GRADIENT COMPUTATION FOR ELLIPTIC INTERFACE PROBLEMS WITH VARIABLE COEFFICIENTS

PubMed Central

LI, ZHILIN; JI, HAIFENG; CHEN, XIAOHONG

2016-01-01

A new augmented method is proposed for elliptic interface problems with a piecewise variable coefficient that has a finite jump across a smooth interface. The main motivation is not only to get a second order accurate solution but also a second order accurate gradient from each side of the interface. The key of the new method is to introduce the jump in the normal derivative of the solution as an augmented variable and re-write the interface problem as a new PDE that consists of a leading Laplacian operator plus lower order derivative terms near the interface. In this way, the leading second order derivatives jump relations are independent of the jump in the coefficient that appears only in the lower order terms after the scaling. An upwind type discretization is used for the finite difference discretization at the irregular grid points near or on the interface so that the resulting coefficient matrix is an M-matrix. A multi-grid solver is used to solve the linear system of equations and the GMRES iterative method is used to solve the augmented variable. Second order convergence for the solution and the gradient from each side of the interface has also been proved in this paper. Numerical examples for general elliptic interface problems have confirmed the theoretical analysis and efficiency of the new method. PMID:28983130

Simulating incompressible flow on moving meshfree grids using General Finite Differences (GFD)

NASA Astrophysics Data System (ADS)

Vasyliv, Yaroslav; Alexeev, Alexander

2016-11-01

We simulate incompressible flow around an oscillating cylinder at different Reynolds numbers using General Finite Differences (GFD) on a meshfree grid. We evolve the meshfree grid by treating each grid node as a particle. To compute velocities and accelerations, we consider the particles at a particular instance as Eulerian observation points. The incompressible Navier-Stokes equations are directly discretized using GFD with boundary conditions enforced using a sharp interface treatment. Cloud sizes are set such that the local approximations use only 16 neighbors. To enforce incompressibility, we apply a semi-implicit approximate projection method. To prevent overlapping particles and formation of voids in the grid, we propose a particle regularization scheme based on a local minimization principle. We validate the GFD results for an oscillating cylinder against the lattice Boltzmann method and find good agreement. Financial support provided by National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.

Integrated multidisciplinary design optimization using discrete sensitivity analysis for geometrically complex aeroelastic configurations

NASA Astrophysics Data System (ADS)

Newman, James Charles, III

1997-10-01

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In twodimensions, an initially symmetric NACA-0012 airfoil and a high-lift multielement airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in addition, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interaction compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented.

Geometry modeling and grid generation using 3D NURBS control volume

NASA Technical Reports Server (NTRS)

Yu, Tzu-Yi; Soni, Bharat K.; Shih, Ming-Hsin

1995-01-01

The algorithms for volume grid generation using NURBS geometric representation are presented. The parameterization algorithm is enhanced to yield a desired physical distribution on the curve, surface and volume. This approach bridges the gap between CAD surface/volume definition and surface/volume grid generation. Computational examples associated with practical configurations have shown the utilization of these algorithms.

Deep learning for classification of islanding and grid disturbance based on multi-resolution singular spectrum entropy

NASA Astrophysics Data System (ADS)

Li, Tie; He, Xiaoyang; Tang, Junci; Zeng, Hui; Zhou, Chunying; Zhang, Nan; Liu, Hui; Lu, Zhuoxin; Kong, Xiangrui; Yan, Zheng

2018-02-01

Forasmuch as the distinguishment of islanding is easy to be interfered by grid disturbance, island detection device may make misjudgment thus causing the consequence of photovoltaic out of service. The detection device must provide with the ability to differ islanding from grid disturbance. In this paper, the concept of deep learning is introduced into classification of islanding and grid disturbance for the first time. A novel deep learning framework is proposed to detect and classify islanding or grid disturbance. The framework is a hybrid of wavelet transformation, multi-resolution singular spectrum entropy, and deep learning architecture. As a signal processing method after wavelet transformation, multi-resolution singular spectrum entropy combines multi-resolution analysis and spectrum analysis with entropy as output, from which we can extract the intrinsic different features between islanding and grid disturbance. With the features extracted, deep learning is utilized to classify islanding and grid disturbance. Simulation results indicate that the method can achieve its goal while being highly accurate, so the photovoltaic system mistakenly withdrawing from power grids can be avoided.

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

NASA Technical Reports Server (NTRS)

Moghaddam, Masoud Ghorbani; Achuthan, A.; Bednacyk, B. A.; Arnold, S. M.; Pineda, E. J.

2014-01-01

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

NASA Technical Reports Server (NTRS)

Abramopoulos, Frank

1988-01-01

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Edge Equilibrium Code (EEC) For Tokamaks

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

Li, Xujling

2014-02-24

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids

Recent development of the Multi-Grid detector for large area neutron scattering instruments

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

Guerard, Bruno

2015-07-01

Most of the Neutron Scattering facilities are committed in a continuous program of modernization of their instruments, requiring large area and high performance thermal neutron detectors. Beside scintillators detectors, {sup 3}He detectors, like linear PSDs (Position Sensitive Detectors) and MWPCs (Multi-Wires Proportional Chambers), are the most current techniques nowadays. Time Of Flight instruments are using {sup 3}He PSDs mounted side by side to cover tens of m{sup 2}. As a result of the so-called '{sup 3}He shortage crisis{sup ,} the volume of 3He which is needed to build one of these instruments is not accessible anymore. The development of alternativemore » techniques requiring no 3He, has been given high priority to secure the future of neutron scattering instrumentation. This is particularly important in the context where the future ESS (European Spallation Source) will start its operation in 2019-2020. Improved scintillators represent one of the alternative techniques. Another one is the Multi-Grid introduced at the ILL in 2009. A Multi-Grid detector is composed of several independent modules of typically 0.8 m x 3 m sensitive area, mounted side by side in air or in a vacuum TOF chamber. One module is composed of segmented boron-lined proportional counters mounted in a gas vessel; the counters, of square section, are assembled with Aluminium grids electrically insulated and stacked together. This design provides two advantages: First, magnetron sputtering techniques can be used to coat B{sub 4}C films on planar substrates, and second, the neutron position along the anode wires can be measured by reading out individually the grid signals with fast shaping amplifiers followed by comparators. Unlike charge division localisation in linear PSDs, the individual readout of the grids allows operating the Multi-Grid at a low amplification gain, hence this detector is tolerant to mechanical defects and its production accessible to laboratories equipped with standard equipment. Prototypes of different configurations and sizes have been developed and tested. A demonstrator, with a sensitive area of 0.8 m x 3 m, has been studied during the CRISP European project; it contains 1024 grids, and a surface of isotopically enriched B{sub 4}C film close to 80 m{sup 2}. Its size represented a challenge in terms of fabrication and mounting of the detection elements. Another challenge was to make the gas chamber mechanically compatible with operation in a vacuum TOF chamber. Optimal working condition of this detector was achieved by flushing Ar-CO{sub 2} at a pressure of 50 mbar, and by applying 400 Volts on the anodes. This unusual gas pressure allows to greatly simplifying the mechanics of the gas vessel in vacuum. The detection efficiency has been measured with high precision for different film thicknesses. 52% has been measured at 2.5 Angstrom, in good agreement with the MC simulation. A high position resolution has been achieved by centre of gravity measurement of the TOT (Time-Over-Threshold) signals between neighbouring grids. These results, as well as other detection parameters, including gamma sensitivity and spatial uniformity, will be presented. (author)« less

Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

NASA Astrophysics Data System (ADS)

Gururaja Rao, C.; Nagabhushana Rao, V.; Krishna Das, C.

2008-04-01

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.

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

Modelling Near-Surface Metallic Clutter Without the Excruciating Pain

NASA Astrophysics Data System (ADS)

Downs, C. M.; Weiss, C. J.; Bach, J.; Williams, J. T.

2016-12-01

An ongoing problem in modeling electromagnetic (EM) interactions with the near-surface and related anthropogenic metal clutter is the large difference in length scale between the clutter dimensions and their resulting EM response. For example, observational evidence shows that cables, pipes and rail lines can have a strong influence far from where they are located, even in situations where these artefacts are volumetrically insignificant over the scale of the model. This poses a significant modeling problem for understanding geohazards in urban environments, for example, because of the very fine numerical discretization required for accurate representation of an artefact embedded in a larger computational domain. We adopt a sub-grid approximation and impose a boundary condition along grid edges to capture the vanishing fields of a perfect conductor. We work in a Cartesian system where the EM fields are solved via finite volumes in the frequency domain in terms of the Lorenz gauged magnetic vector (A) and electric scalar (Phi) potentials. The electric fied is given simply by A-grad(Phi), and set identically to zero along edges of the mesh that coincide with the center of long, slender metallic conductors. A simple extension to bulky artefacts like blocks or slabs involves endowing all such edges in their interior with the same "internal" boundary condition. In essence, we apply the "perfect electric conductor" boundary condition to select edges interior to the modeling domain. We note a few minor numerical consequences of this approach, namely: the zero-E field internal boundary condition destroys the symmetry of the finite volume coefficient matrix; and, the accuracy of the representation of the conducting artefact is restricted by the relatively coarse discretization mesh. The former is overcome with the use of preconditioned bi-conjugate gradient methods instead of the quasi-minimal-residual method. Both are matrix-free iterative solvers - thus avoiding unnecessary storage- and both exhibit generally good convergence for well-posed problems. The latter is more difficult to overcome without either modifying the mesh (potentially degrading the condition number of the coefficient matrix) or with novel mesh sub-gridding. Initial results show qualitative agreement with the expected physics.

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

NASA Astrophysics Data System (ADS)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings

NASA Astrophysics Data System (ADS)

Lashkajani, Kazem Hasanzadeh

This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil remeshing and field smoothing. The new coupling is fully automated and capable of multi-step ice accretion simulations via a quasi-steady approach. In addition, the framework allows for flow analysis and aerodynamic performance prediction of the iced airfoils. The convergence of the quasi-steady algorithm is verified and identifies the need for an order of magnitude increase in the number of multi-time steps in icing simulations to achieve solver independent solutions. Second, a Multi-Block Navier-Stokes code, NSMB, is coupled with the CANICE2D icing framework. Attention is paid to the roughness implementation of the ONERA roughness model within the Spalart-Allmaras turbulence model, and to the convergence of the steady and quasi-steady iterative procedure. Effects of uniform surface roughness in quasi-steady ice accretion simulation are analyzed through different validation test cases. The results of CANICE2D-NS show good agreement with experimental data both in terms of predicted ice shapes as well as aerodynamic analysis of predicted and experimental ice shapes. Third, an efficient single-block structured Navier-Stokes CFD code, NSCODE, is coupled with the CANICE2D-NS icing framework. Attention is paid to the roughness implementation of the Boeing model within the Spalart-Allmaras turbulence model, and to acceleration of the convergence of the steady and quasi-steady iterative procedures. Effects of uniform surface roughness in quasi-steady ice accretion simulation are analyzed through different validation test cases, including code to code comparisons with the same framework coupled with the NSMB Navier-Stokes solver. The efficiency of the J-multigrid approach to solve the flow equations on complex iced geometries is demonstrated. Since it was noted in all these calculations that the ICEM-CFD grid generation package produced a number of issues such as inefficient mesh quality and smoothing deficiencies (notably grid shocks), a fourth study proposes a new mesh generation algorithm. A PDE based multi-block structured grid generation code, NSGRID, is developed for this purpose. The study includes the developments of novel mesh generation algorithms over complex glaze ice shapes containing multi-curvature ice accretion geometries, such as single/double ice horns. The twofold approaches tackle surface geometry discretization as well as field mesh generation. An adaptive curvilinear curvature control algorithm is constructed solving a 1D elliptic PDE equation with periodic source terms. This method controls the arclength grid spacing so that high convex and concave curvature regions around ice horns are appropriately captured and is shown to effectively treat the grid shock problem. Then, a novel blended method is developed by defining combinations of source terms with 2D elliptic equations. The source terms include two common control functions, Sorenson and Spekreijse, and an additional third source term to improve orthogonality. This blended method is shown to be very effective for improving grid quality metrics for complex glaze ice meshes with RANS resolution. The performance in terms of residual reduction per non-linear iteration of several solution algorithms (Point-Jacobi, Gauss-Seidel, ADI, Point and Line SOR) are discussed within the context of a full Multi-grid operator. Details are given on the various formulations used in the linearization process. It is shown that the performance of the solution algorithm depends on the type of control function used. Finally, the algorithms are validated on standard complex experimental ice shapes, demonstrating the applicability of the methods. Finally, the automated framework of RANS based two-dimensional multi-step ice accretion, CANICE2D-NS is developed, coupled with a Multi-Block Navier-Stokes CFD code, NSCODE2D, a Multi-Block elliptic grid generation code, NSGRID2D, and a Multi-Block Eulerian droplet solver, NSDROP2D (developed at Polytechnique Montreal). The framework allows Lagrangian and Eulerian droplet computations within a chimera approach treating multi-elements geometries. The code was tested on public and confidential validation test cases including standard NATO cases. In addition, up to 10 times speedup is observed in the mesh generation procedure by using the implicit line SOR and ADI smoothers within a multigrid procedure. The results demonstrate the benefits and robustness of the new framework in predicting ice shapes and aerodynamic performance parameters.

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

NASA Astrophysics Data System (ADS)

Lai, Changliang; Wang, Junbiao; Liu, Chuang

2014-10-01

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

A coarse-grid-projection acceleration method for finite-element incompressible flow computations

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne; FiN Lab Team

2015-11-01

Coarse grid projection (CGP) methodology provides a framework for accelerating computations by performing some part of the computation on a coarsened grid. We apply the CGP to pressure projection methods for finite element-based incompressible flow simulations. Based on it, the predicted velocity field data is restricted to a coarsened grid, the pressure is determined by solving the Poisson equation on the coarse grid, and the resulting data are prolonged to the preset fine grid. The contributions of the CGP method to the pressure correction technique are twofold: first, it substantially lessens the computational cost devoted to the Poisson equation, which is the most time-consuming part of the simulation process. Second, it preserves the accuracy of the velocity field. The velocity and pressure spaces are approximated by Galerkin spectral element using piecewise linear basis functions. A restriction operator is designed so that fine data are directly injected into the coarse grid. The Laplacian and divergence matrices are driven by taking inner products of coarse grid shape functions. Linear interpolation is implemented to construct a prolongation operator. A study of the data accuracy and the CPU time for the CGP-based versus non-CGP computations is presented. Laboratory for Fluid Dynamics in Nature.

Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations

NASA Technical Reports Server (NTRS)

Moon, Young J.; Liou, Meng-Sing

1989-01-01

Conservative algorithms for boundary interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.

Continuum kinetic modeling of the tokamak plasma edge

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

Dorf, M. A.; Dorr, M. R.; Hittinger, J. A.

2016-05-15

The first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalous radial transport.

Technical report series on global modeling and data assimilation. Volume 5: Documentation of the AIRES/GEOS dynamical core, version 2

NASA Technical Reports Server (NTRS)

Suarez, Max J. (Editor); Takacs, Lawrence L.

1995-01-01

A detailed description of the numerical formulation of Version 2 of the ARIES/GEOS 'dynamical core' is presented. This code is a nearly 'plug-compatible' dynamics for use in atmospheric general circulation models (GCMs). It is a finite difference model on a staggered latitude-longitude C-grid. It uses second-order differences for all terms except the advection of vorticity by the rotation part of the flow, which is done at fourth-order accuracy. This dynamical core is currently being used in the climate (ARIES) and data assimilation (GEOS) GCMs at Goddard.

A NASTRAN model of a large flexible swing-wing bomber. Volume 5: NASTRAN model development-fairing structure

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.

1982-01-01

The NASTRAN model plan for the fairing structure was expanded in detail to generate the NASTRAN model of this substructure. The grid point coordinates, element definitions, material properties, and sizing data for each element were specified. The fairing model was thoroughly checked out for continuity, connectivity, and constraints. The substructure was processed for structural influence coefficients (SIC) point loadings to determine the deflection characteristics of the fairing model. Finally, a demonstration and validation processing of this substructure was accomplished using the NASTRAN finite element program. The bulk data deck, stiffness matrices, and SIC output data were delivered.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Lightning Damage of Carbon Fiber/Epoxy Laminates with Interlayers Modified by Nickel-Coated Multi-Walled Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Dong, Qi; Wan, Guoshun; Xu, Yongzheng; Guo, Yunli; Du, Tianxiang; Yi, Xiaosu; Jia, Yuxi

2017-12-01

The numerical model of carbon fiber reinforced polymer (CFRP) laminates with electrically modified interlayers subjected to lightning strike is constructed through finite element simulation, in which both intra-laminar and inter-laminar lightning damages are considered by means of coupled electrical-thermal-pyrolytic analysis method. Then the lightning damage extents including the damage volume and maximum damage depth are investigated. The results reveal that the simulated lightning damages could be qualitatively compared to the experimental counterparts of CFRP laminates with interlayers modified by nickel-coated multi-walled carbon nanotubes (Ni-MWCNTs). With higher electrical conductivity of modified interlayer and more amount of modified interlayers, both damage volume and maximum damage depth are reduced. This work provides an effective guidance to the anti-lightning optimization of CFRP laminates.

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.

Tools for Analysis and Visualization of Large Time-Varying CFD Data Sets

NASA Technical Reports Server (NTRS)

Wilhelms, Jane; VanGelder, Allen

1997-01-01

In the second year, we continued to built upon and improve our scanline-based direct volume renderer that we developed in the first year of this grant. This extremely general rendering approach can handle regular or irregular grids, including overlapping multiple grids, and polygon mesh surfaces. It runs in parallel on multi-processors. It can also be used in conjunction with a k-d tree hierarchy, where approximate models and error terms are stored in the nodes of the tree, and approximate fast renderings can be created. We have extended our software to handle time-varying data where the data changes but the grid does not. We are now working on extending it to handle more general time-varying data. We have also developed a new extension of our direct volume renderer that uses automatic decimation of the 3D grid, as opposed to an explicit hierarchy. We explored this alternative approach as being more appropriate for very large data sets, where the extra expense of a tree may be unacceptable. We also describe a new approach to direct volume rendering using hardware 3D textures and incorporates lighting effects. Volume rendering using hardware 3D textures is extremely fast, and machines capable of using this technique are becoming more moderately priced. While this technique, at present, is limited to use with regular grids, we are pursuing possible algorithms extending the approach to more general grid types. We have also begun to explore a new method for determining the accuracy of approximate models based on the light field method described at ACM SIGGRAPH '96. In our initial implementation, we automatically image the volume from 32 equi-distant positions on the surface of an enclosing tessellated sphere. We then calculate differences between these images under different conditions of volume approximation or decimation. We are studying whether this will give a quantitative measure of the effects of approximation. We have created new tools for exploring the differences between images produced by various rendering methods. Images created by our software can be stored in the SGI RGB format. Our idtools software reads in pair of images and compares them using various metrics. The differences of the images using the RGB, HSV, and HSL color models can be calculated and shown. We can also calculate the auto-correlation function and the Fourier transform of the image and image differences. We will explore how these image differences compare in order to find useful metrics for quantifying the success of various visualization approaches. In general, progress was consistent with our research plan for the second year of the grant.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are 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 are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are 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 are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Radiation Solver for the National Combustion Code

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

2015-01-01

A methodology is given that converts an existing finite volume radiative transfer method that requires input of local absorption coefficients to one that can treat a mixture of combustion gases and compute the coefficients on the fly from the local mixture properties. The Full-spectrum k-distribution method is used to transform the radiative transfer equation (RTE) to an alternate wave number variable, g . The coefficients in the transformed equation are calculated at discrete temperatures and participating species mole fractions that span the values of the problem for each value of g. These results are stored in a table and interpolation is used to find the coefficients at every cell in the field. Finally, the transformed RTE is solved for each g and Gaussian quadrature is used to find the radiant heat flux throughout the field. The present implementation is in an existing cartesian/cylindrical grid radiative transfer code and the local mixture properties are given by a solution of the National Combustion Code (NCC) on the same grid. Based on this work the intention is to apply this method to an existing unstructured grid radiation code which can then be coupled directly to NCC.

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1987-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

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.

Unsteady flow simulations around complex geometries using stationary or rotating unstructured grids

NASA Astrophysics Data System (ADS)

Sezer-Uzol, Nilay

In this research, the computational analysis of three-dimensional, unsteady, separated, vortical flows around complex geometries is studied by using stationary or moving unstructured grids. Two main engineering problems are investigated. The first problem is the unsteady simulation of a ship airwake, where helicopter operations become even more challenging, by using stationary unstructured grids. The second problem is the unsteady simulation of wind turbine rotor flow fields by using moving unstructured grids which are rotating with the whole three-dimensional rigid rotor geometry. The three dimensional, unsteady, parallel, unstructured, finite volume flow solver, PUMA2, is used for the computational fluid dynamics (CFD) simulations considered in this research. The code is modified to have a moving grid capability to perform three-dimensional, time-dependent rotor simulations. An instantaneous log-law wall model for Large Eddy Simulations is also implemented in PUMA2 to investigate the very large Reynolds number flow fields of rotating blades. To verify the code modifications, several sample test cases are also considered. In addition, interdisciplinary studies, which are aiming to provide new tools and insights to the aerospace and wind energy scientific communities, are done during this research by focusing on the coupling of ship airwake CFD simulations with the helicopter flight dynamics and control analysis, the coupling of wind turbine rotor CFD simulations with the aeroacoustic analysis, and the analysis of these time-dependent and large-scale CFD simulations with the help of a computational monitoring, steering and visualization tool, POSSE.

Climate simulations and services on HPC, Cloud and Grid infrastructures

NASA Astrophysics Data System (ADS)

Cofino, Antonio S.; Blanco, Carlos; Minondo Tshuma, Antonio

2017-04-01

Cloud, Grid and High Performance Computing have changed the accessibility and availability of computing resources for Earth Science research communities, specially for Climate community. These paradigms are modifying the way how climate applications are being executed. By using these technologies the number, variety and complexity of experiments and resources are increasing substantially. But, although computational capacity is increasing, traditional applications and tools used by the community are not good enough to manage this large volume and variety of experiments and computing resources. In this contribution, we evaluate the challenges to run climate simulations and services on Grid, Cloud and HPC infrestructures and how to tackle them. The Grid and Cloud infrastructures provided by EGI's VOs ( esr , earth.vo.ibergrid and fedcloud.egi.eu) will be evaluated, as well as HPC resources from PRACE infrastructure and institutional clusters. To solve those challenges, solutions using DRM4G framework will be shown. DRM4G provides a good framework to manage big volume and variety of computing resources for climate experiments. This work has been supported by the Spanish National R&D Plan under projects WRF4G (CGL2011-28864), INSIGNIA (CGL2016-79210-R) and MULTI-SDM (CGL2015-66583-R) ; the IS-ENES2 project from the 7FP of the European Commission (grant agreement no. 312979); the European Regional Development Fund—ERDF and the Programa de Personal Investigador en Formación Predoctoral from Universidad de Cantabria and Government of Cantabria.

Volume of Valley Networks on Mars and Its Hydrologic Implications

NASA Astrophysics Data System (ADS)

Luo, W.; Cang, X.; Howard, A. D.; Heo, J.

2015-12-01

Valley networks on Mars are river-like features that offer the best evidence for water activities in its geologic past. Previous studies have extracted valley network lines automatically from digital elevation model (DEM) data and manually from remotely sensed images. The volume of material removed by valley networks is an important parameter that could help us infer the amount of water needed to carve the valleys. A progressive black top hat (PBTH) transformation algorithm has been adapted from image processing to extract valley volume and successfully applied to simulated landform and Ma'adim Valles, Mars. However, the volume of valley network excavation on Mars has not been estimated on a global scale. In this study, the PBTH method was applied to the whole Mars to estimate this important parameter. The process was automated with Python in ArcGIS. Polygons delineating the valley associated depressions were generated by using a multi-flow direction growth method, which started with selected high point seeds on a depth grid (essentially an inverted valley) created by PBTH transformation and grew outward following multi-flow direction on the depth grid. Two published versions of valley network lines were integrated to automatically select depression polygons that represent the valleys. Some crater depressions that are connected with valleys and thus selected in the previous step were removed by using information from a crater database. Because of large distortion associated with global dataset in projected maps, the volume of each cell within a valley was calculated using the depth of the cell multiplied by the spherical area of the cell. The volumes of all the valley cells were then summed to produce the estimate of global valley excavation volume. Our initial result of this estimate was ~2.4×1014 m3. Assuming a sediment density of 2900 kg/m3, a porosity of 0.35, and a sediment load of 1.5 kg/m3, the global volume of water needed to carve the valleys was estimated to be ~7.1×1017 m3. Because of the coarse resolution of MOLA data, this is a conservative lower bound. Comparing with the hypothesized northern ocean volume 2.3×1016 m3 estimated by Carr and Head (2003), our estimate of water volume suggests and confirms an active hydrologic cycle for early Mars. Further hydrologic analysis will improve the estimate accuracy.

Dynamic-contrast-enhanced-MRI with extravasating contrast reagent: Rat cerebral glioma blood volume determination

NASA Astrophysics Data System (ADS)

Li, Xin; Rooney, William D.; Várallyay, Csanád G.; Gahramanov, Seymur; Muldoon, Leslie L.; Goodman, James A.; Tagge, Ian J.; Selzer, Audrey H.; Pike, Martin M.; Neuwelt, Edward A.; Springer, Charles S.

2010-10-01

The accurate mapping of the tumor blood volume (TBV) fraction ( vb) is a highly desired imaging biometric goal. It is commonly thought that achieving this is difficult, if not impossible, when small molecule contrast reagents (CRs) are used for the T1-weighted (Dynamic-Contrast-Enhanced) DCE-MRI technique. This is because angiogenic malignant tumor vessels allow facile CR extravasation. Here, a three-site equilibrium water exchange model is applied to DCE-MRI data from the cerebrally-implanted rat brain U87 glioma, a tumor exhibiting rapid CR extravasation. Analyses of segments of the (and the entire) DCE data time-course with this "shutter-speed" pharmacokinetic model, which admits finite water exchange kinetics, allow TBV estimation from the first-pass segment. Pairwise parameter determinances were tested with grid searches of 2D parametric error surfaces. Tumor blood volume ( vb), as well as ve (the extracellular, extravascular space volume fraction), and Ktrans (a CR extravasation rate measure) parametric maps are presented. The role of the Patlak Plot in DCE-MRI is also considered.

The Volume Grid Manipulator (VGM): A Grid Reusability Tool

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

1997-01-01

This document is a manual describing how to use the Volume Grid Manipulation (VGM) software. The code is specifically designed to alter or manipulate existing surface and volume structured grids to improve grid quality through the reduction of grid line skewness, removal of negative volumes, and adaption of surface and volume grids to flow field gradients. The software uses a command language to perform all manipulations thereby offering the capability of executing multiple manipulations on a single grid during an execution of the code. The command language can be input to the VGM code by a UNIX style redirected file, or interactively while the code is executing. The manual consists of 14 sections. The first is an introduction to grid manipulation; where it is most applicable and where the strengths of such software can be utilized. The next two sections describe the memory management and the manipulation command language. The following 8 sections describe simple and complex manipulations that can be used in conjunction with one another to smooth, adapt, and reuse existing grids for various computations. These are accompanied by a tutorial section that describes how to use the commands and manipulations to solve actual grid generation problems. The last two sections are a command reference guide and trouble shooting sections to aid in the use of the code as well as describe problems associated with generated scripts for manipulation control.

Grid Generation Techniques Utilizing the Volume Grid Manipulator

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

1998-01-01

This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.

Pathloss Calculation Using the Transmission Line Matrix and Finite Difference Time Domain Methods With Coarse Grids

DOE PAGES

Nutaro, James; Kuruganti, Teja

2017-02-24

Numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data. However, calculations of radio signal pathloss generally do not require accurate time domain solutions. This paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength. The calculated pathloss can be kept close to the true value formore » freespace propagation with an appropriate selection of initial conditions. This method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing.« less

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Grid sensitivity capability for large scale structures

NASA Technical Reports Server (NTRS)

Nagendra, Gopal K.; Wallerstein, David V.

1989-01-01

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Analysis of the Multi Strategy Goal Programming for Micro-Grid Based on Dynamic ant Genetic Algorithm

NASA Astrophysics Data System (ADS)

Qiu, J. P.; Niu, D. X.

Micro-grid is one of the key technologies of the future energy supplies. Take economic planning. reliability, and environmental protection of micro grid as a basis for the analysis of multi-strategy objective programming problems for micro grid which contains wind power, solar power, and battery and micro gas turbine. Establish the mathematical model of each power generation characteristics and energy dissipation. and change micro grid planning multi-objective function under different operating strategies to a single objective model based on AHP method. Example analysis shows that in combination with dynamic ant mixed genetic algorithm can get the optimal power output of this model.

ION ACCELERATION SYSTEM

DOEpatents

Luce, J.S.; Martin, J.A.

1960-02-23

Well focused, intense ion beams are obtained by providing a multi- apertured source grid in front of an ion source chamber and an accelerating multi- apertured grid closely spaced from and in alignment with the source grid. The longest dimensions of the elongated apertures in the grids are normal to the direction of the magnetic field used with the device. Large ion currents may be withdrawn from the source, since they do not pass through any small focal region between the grids.

Apparatus for and method of simulating turbulence

DOEpatents

Dimas, Athanassios; Lottati, Isaac; Bernard, Peter; Collins, James; Geiger, James C.

2003-01-01

In accordance with a preferred embodiment of the invention, a novel apparatus for and method of simulating physical processes such as fluid flow is provided. Fluid flow near a boundary or wall of an object is represented by a collection of vortex sheet layers. The layers are composed of a grid or mesh of one or more geometrically shaped space filling elements. In the preferred embodiment, the space filling elements take on a triangular shape. An Eulerian approach is employed for the vortex sheets, where a finite-volume scheme is used on the prismatic grid formed by the vortex sheet layers. A Lagrangian approach is employed for the vortical elements (e.g., vortex tubes or filaments) found in the remainder of the flow domain. To reduce the computational time, a hairpin removal scheme is employed to reduce the number of vortex filaments, and a Fast Multipole Method (FMM), preferably implemented using parallel processing techniques, reduces the computation of the velocity field.

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.

3D Voronoi grid dedicated software for modeling gas migration in deep layered sedimentary formations with TOUGH2-TMGAS

NASA Astrophysics Data System (ADS)

Bonduà, Stefano; Battistelli, Alfredo; Berry, Paolo; Bortolotti, Villiam; Consonni, Alberto; Cormio, Carlo; Geloni, Claudio; Vasini, Ester Maria

2017-11-01

As is known, a full three-dimensional (3D) unstructured grid permits a great degree of flexibility when performing accurate numerical reservoir simulations. However, when the Integral Finite Difference Method (IFDM) is used for spatial discretization, constraints (arising from the required orthogonality between the segment connecting the blocks nodes and the interface area between blocks) pose difficulties in the creation of grids with irregular shaped blocks. The full 3D Voronoi approach guarantees the respect of IFDM constraints and allows generation of grids conforming to geological formations and structural objects and at the same time higher grid resolution in volumes of interest. In this work, we present dedicated pre- and post-processing gridding software tools for the TOUGH family of numerical reservoir simulators, developed by the Geothermal Research Group of the DICAM Department, University of Bologna. VORO2MESH is a new software coded in C++, based on the voro++ library, allowing computation of the 3D Voronoi tessellation for a given domain and the creation of a ready to use TOUGH2 MESH file. If a set of geological surfaces is available, the software can directly generate the set of Voronoi seed points used for tessellation. In order to reduce the number of connections and so to decrease computation time, VORO2MESH can produce a mixed grid with regular blocks (orthogonal prisms) and irregular blocks (polyhedron Voronoi blocks) at the point of contact between different geological formations. In order to visualize 3D Voronoi grids together with the results of numerical simulations, the functionality of the TOUGH2Viewer post-processor has been extended. We describe an application of VORO2MESH and TOUGH2Viewer to validate the two tools. The case study deals with the simulation of the migration of gases in deep layered sedimentary formations at basin scale using TOUGH2-TMGAS. A comparison between the simulation performances of unstructured and structured grids is presented.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

YAP Version 4.0

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

Nelson, Eric M.

2004-05-20

The YAP software library computes (1) electromagnetic modes, (2) electrostatic fields, (3) magnetostatic fields and (4) particle trajectories in 2d and 3d models. The code employs finite element methods on unstructured grids of tetrahedral, hexahedral, prism and pyramid elements, with linear through cubic element shapes and basis functions to provide high accuracy. The novel particle tracker is robust, accurate and efficient, even on unstructured grids with discontinuous fields. This software library is a component of the MICHELLE 3d finite element gun code.

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

DOE PAGES

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans; ...

2016-11-09

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

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

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

FANS-3D Users Guide (ESTEP Project ER 201031)

DTIC Science & Technology

2016-08-01

governing laminar and turbulent flows in body-fitted curvilinear grids. The code employs multi-block overset ( chimera ) grids, including fully matched...governing incompressible flow in body-fitted grids. The code allows for multi-block overset ( chimera ) grids, which can be fully matched, arbitrarily...interested reader may consult the Chimera Overset Structured Mesh-Interpolation Code (COSMIC) Users’ Manual (Chen, 2009). The input file used for

Computational Investigation and Validation of Twin-Tail Buffet Response Including Dynamics and Control

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.

A method of selecting grid size to account for Hertz deformation in finite element analysis of spur gears

NASA Technical Reports Server (NTRS)

Coy, J. J.; Chao, C. H. C.

1981-01-01

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

CFD Methods and Tools for Multi-Element Airfoil Analysis

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.; George, Michael W. (Technical Monitor)

1995-01-01

This lecture will discuss the computational tools currently available for high-lift multi-element airfoil analysis. It will present an overview of a number of different numerical approaches, their current capabilities, short-comings, and computational costs. The lecture will be limited to viscous methods, including inviscid/boundary layer coupling methods, and incompressible and compressible Reynolds-averaged Navier-Stokes methods. Both structured and unstructured grid generation approaches will be presented. Two different structured grid procedures are outlined, one which uses multi-block patched grids, the other uses overset chimera grids. Turbulence and transition modeling will be discussed.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

NASA Astrophysics Data System (ADS)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Stackable differential mobility analyzer for aerosol measurement

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

Cheng, Meng-Dawn; Chen, Da-Ren

2007-05-08

A multi-stage differential mobility analyzer (MDMA) for aerosol measurements includes a first electrode or grid including at least one inlet or injection slit for receiving an aerosol including charged particles for analysis. A second electrode or grid is spaced apart from the first electrode. The second electrode has at least one sampling outlet disposed at a plurality different distances along its length. A volume between the first and the second electrode or grid between the inlet or injection slit and a distal one of the plurality of sampling outlets forms a classifying region, the first and second electrodes for chargingmore » to suitable potentials to create an electric field within the classifying region. At least one inlet or injection slit in the second electrode receives a sheath gas flow into an upstream end of the classifying region, wherein each sampling outlet functions as an independent DMA stage and classifies different size ranges of charged particles based on electric mobility simultaneously.« less

Numerical simulation of convective heat transfer of nonhomogeneous nanofluid using Buongiorno model

NASA Astrophysics Data System (ADS)

Sayyar, Ramin Onsor; Saghafian, Mohsen

2017-08-01

The aim is to study the assessment of the flow and convective heat transfer of laminar developing flow of Al2O3-water nanofluid inside a vertical tube. A finite volume method procedure on a structured grid was used to solve the governing partial differential equations. The adopted model (Buongiorno model) assumes that the nanofluid is a mixture of a base fluid and nanoparticles, with the relative motion caused by Brownian motion and thermophoretic diffusion. The results showed the distribution of nanoparticles remained almost uniform except in a region near the hot wall where nanoparticles volume fraction were reduced as a result of thermophoresis. The simulation results also indicated there is an optimal volume fraction about 1-2% of the nanoparticles at each Reynolds number for which the maximum performance evaluation criteria can be obtained. The difference between Nusselt number and nondimensional pressure drop calculated based on two phase model and the one calculated based on single phase model was less than 5% at all nanoparticles volume fractions and can be neglected. In natural convection, for 4% of nanoparticles volume fraction, in Gr = 10 more than 15% enhancement of Nusselt number was achieved but in Gr = 300 it was less than 1%.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Geometry modeling and multi-block grid generation for turbomachinery configurations

NASA Technical Reports Server (NTRS)

Shih, Ming H.; Soni, Bharat K.

1992-01-01

An interactive 3D grid generation code, Turbomachinery Interactive Grid genERation (TIGER), was developed for general turbomachinery configurations. TIGER features the automatic generation of multi-block structured grids around multiple blade rows for either internal, external, or internal-external turbomachinery flow fields. Utilization of the Bezier's curves achieves a smooth grid and better orthogonality. TIGER generates the algebraic grid automatically based on geometric information provided by its built-in pseudo-AI algorithm. However, due to the large variation of turbomachinery configurations, this initial grid may not always be as good as desired. TIGER therefore provides graphical user interactions during the process which allow the user to design, modify, as well as manipulate the grid, including the capability of elliptic surface grid generation.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar Z.

2008-01-01

A new approach for distribution of grid points on the surface and in the volume has been developed and implemented in the NASA unstructured grid generation code VGRID. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.

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.

[Numerical modeling of shape memory alloy vascular stent's self-expandable progress and "optimized grid" of stent].

PubMed

Xu, Qiang; Liu, Yulan; Wang, Biao; He, Jin

2008-10-01

Vascular stent is an important medical appliance for angiocardiopathy. Its key deformation process is the expandable progress of stent in the vessel. The important deformation behaviour corresponds to two mechanics targets: deformation and stress. This paper is devoted to the research and development of vascular stent with proprietary intellectual property rights. The design of NiTinol self-expandable stent is optimized by means of finite element software. ANSYS is used to build the finite element simulation model of vascular stent; the molding material is NiTinol shape memory alloy. To cope with the factors that affect the structure of stent, the shape of grid and so on, the self-expanding process of Nitinol stent is simulated through computer. By making a comparison between two kinds of stents with similar grid structure, we present a new concept of "Optimized Grid" of stent.

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.

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

Two-Dimensional Grids About Airfoils and Other Shapes

NASA Technical Reports Server (NTRS)

Sorenson, R.

1982-01-01

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

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.

Multi-zonal Navier-Stokes code with the LU-SGS scheme

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Yoon, S.

1993-01-01

The LU-SGS (lower upper symmetric Gauss Seidel) algorithm has been implemented into the Compressible Navier-Stokes, Finite Volume (CNSFV) code and validated with a multizonal Navier-Stokes simulation of a transonic turbulent flow around an Onera M6 transport wing. The convergence rate and robustness of the code have been improved and the computational cost has been reduced by at least a factor of 2 over the diagonal Beam-Warming scheme.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Implementation of a Multi-Robot Coverage Algorithm on a Two-Dimensional, Grid-Based Environment

DTIC Science & Technology

2017-06-01

two planar laser range finders with a 180-degree field of view , color camera, vision beacons, and wireless communicator. In their system, the robots...Master’s thesis 4. TITLE AND SUBTITLE IMPLEMENTATION OF A MULTI -ROBOT COVERAGE ALGORITHM ON A TWO -DIMENSIONAL, GRID-BASED ENVIRONMENT 5. FUNDING NUMBERS...path planning coverage algorithm for a multi -robot system in a two -dimensional, grid-based environment. We assess the applicability of a topology

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar

2010-01-01

A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.

Excitations in the Yang–Gaudin Bose gas

DOE PAGES

Robinson, Neil J.; Konik, Robert M.

2017-06-01

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

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

Robinson, Neil J.; Konik, Robert M.

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

A new technique for simulating composite material

NASA Technical Reports Server (NTRS)

Volakis, John L.

1991-01-01

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Multi-scale modeling of multi-component reactive transport in geothermal aquifers

NASA Astrophysics Data System (ADS)

Nick, Hamidreza M.; Raoof, Amir; Wolf, Karl-Heinz; Bruhn, David

2014-05-01

In deep geothermal systems heat and chemical stresses can cause physical alterations, which may have a significant effect on flow and reaction rates. As a consequence it will lead to changes in permeability and porosity of the formations due to mineral precipitation and dissolution. Large-scale modeling of reactive transport in such systems is still challenging. A large area of uncertainty is the way in which the pore-scale information controlling the flow and reaction will behave at a larger scale. A possible choice is to use constitutive relationships relating, for example the permeability and porosity evolutions to the change in the pore geometry. While determining such relationships through laboratory experiments may be limited, pore-network modeling provides an alternative solution. In this work, we introduce a new workflow in which a hybrid Finite-Element Finite-Volume method [1,2] and a pore network modeling approach [3] are employed. Using the pore-scale model, relevant constitutive relations are developed. These relations are then embedded in the continuum-scale model. This approach enables us to study non-isothermal reactive transport in porous media while accounting for micro-scale features under realistic conditions. The performance and applicability of the proposed model is explored for different flow and reaction regimes. References: 1. Matthäi, S.K., et al.: Simulation of solute transport through fractured rock: a higher-order accurate finite-element finite-volume method permitting large time steps. Transport in porous media 83.2 (2010): 289-318. 2. Nick, H.M., et al.: Reactive dispersive contaminant transport in coastal aquifers: Numerical simulation of a reactive Henry problem. Journal of contaminant hydrology 145 (2012), 90-104. 3. Raoof A., et al.: PoreFlow: A Complex pore-network model for simulation of reactive transport in variably saturated porous media, Computers & Geosciences, 61, (2013), 160-174.

A NASTRAN model of a large flexible swing-wing bomber. Volume 3: NASTRAN model development-wing structure

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.

1982-01-01

The NASTRAN model plan for the wing structure was expanded in detail to generate the NASTRAN model for this substructure. The grid point coordinates were coded for each element. The material properties and sizing data for each element were specified. The wing substructure model was thoroughly checked out for continuity, connectivity, and constraints. This substructure was processed for structural influence coefficients (SIC) point loadings and the deflections were compared to those computed for the aircraft detail model. Finally, a demonstration and validation processing of this substructure was accomplished using the NASTRAN finite element program. The bulk data deck, stiffness matrices, and SIC output data were delivered.

Continuum kinetic modeling of the tokamak plasma edge

DOE PAGES

Dorf, M. A.; Dorr, M.; Rognlien, T.; ...

2016-03-10

In this study, the first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasmatransport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalousmore » radial transport.« less

A NASTRAN model of a large flexible swing-wing bomber. Volume 2: NASTRAN model development-horizontal stabilzer, vertical stabilizer and nacelle structures

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.; Tisher, E. D.

1982-01-01

The NASTRAN model plans for the horizontal stabilizer, vertical stabilizer, and nacelle structure were expanded in detail to generate the NASTRAN model for each of these substructures. The grid point coordinates were coded for each element. The material properties and sizing data for each element were specified. Each substructure model was thoroughly checked out for continuity, connectivity, and constraints. These substructures were processed for structural influence coefficients (SIC) point loadings and the deflections were compared to those computed for the aircraft detail models. Finally, a demonstration and validation processing of these substructures was accomplished using the NASTRAN finite element program installed at NASA/DFRC facility.