EUPDF: An Eulerian-Based Monte Carlo Probability Density Function (PDF) Solver. User's Manual
NASA Technical Reports Server (NTRS)
Raju, M. S.
1998-01-01
EUPDF is an Eulerian-based Monte Carlo PDF solver developed for application with sprays, combustion, parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with the coding required to couple the PDF code to any given flow code and a basic understanding of the EUPDF code structure as well as the models involved in the PDF formulation. The source code of EUPDF will be available with the release of the National Combustion Code (NCC) as a complete package.
Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver
NASA Astrophysics Data System (ADS)
Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind
2016-09-01
Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid Eulerian- Lagrangian approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.
NASA Astrophysics Data System (ADS)
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
NASA Astrophysics Data System (ADS)
Pathak, Ashish; Raessi, Mehdi
2016-04-01
We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented.
NASA Technical Reports Server (NTRS)
Raju, M. S.
1998-01-01
The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic
Hybrid Eulerian-Lagrangian Vortex Model for Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Royero, John; Ahmed, Kareem
2016-11-01
A hybrid Eulerian-Lagrangian model for three dimensional large eddy simulations of turbulent reacting flows is presented. The method utilizes a Eulerian grid to resolve large scale flow features and the Lagrangian vortex element method to capture smaller subgrid scale effects and carry out reactions which are then communicated back to the Eulerian grid after a set number of Lagrangian time steps. Lagrangian influences are localized in order to reduce computational cost. The Lagrangian vortex method which utilizes the Helmholtz decomposition of the velocity into potential, expansive, and solenoidal components allows the separation of the various mechanisms contributing to vorticity including gas expansion, diffusion, external body forces and baroclinic torque and is coupled with the Eulerian solver allowing easier implementation in arbitrary reacting flows at a reduced computational cost compared to a pure Lagrangian solver.
Eulerian computational methods
NASA Astrophysics Data System (ADS)
McGlaun, M.
Continuum dynamics codes are categorized as Lagrangian or Eulerian according to the motion of the mesh. A Lagrangian code's mesh moves with the material, so no mass flows between cells. An Eulerian code's mesh is stationary, so mass flows between the cells. Eulerian codes have improved to the point where they are routinely used to solve a broad variety of large deformation solid and fluid dynamics problems ranging from air flow over an airplane wing to meteor impact on space structures. This presentation will concentrate on multi-fluid Eulerian codes capable of modeling transient wave propagation in solids. These codes use a two-step process to integrate the physics across a time step. The first step, referred to as the Lagrangian step, integrates the physics on a Lagrangian mesh across the time step. The field values are then at the new time, but they are on the distorted Lagrangian mesh. The second step, referred to as the remap step, remaps the data on the distorted Lagrangian mesh back to the original Eulerian mesh thus completing one time step. The algorithms used in the first step are similar to those used in modern Lagrangian codes but they must be extended to handle multi-material cells. The algorithms used in the second step are complex and must be very carefully chosen to minimize errors. These algorithms include second-order, monotone advection equations to calculate the quantities flowing between cells. They also require algorithms that construct material interfaces inside multi-material cells. The strength and limitations of currently used numerical techniques will be discussed. New code development activities that combine the best features of both Lagrangian and Elurian codes will also be discussed. These new codes will employ the strengths of both technologies to address problems that cannot be adequately solved at this time.
A compressible real gas eulerian model for LES of fuel sprays
NASA Astrophysics Data System (ADS)
Knudsen, Edward; Doran, Eric
2015-11-01
A compressible solver for eulerian multiphase spray simulations is presented. This large eddy simulation solver employs a Peng-Robinson (PR) equation of state to describe mixtures of two species such as liquid dodecane and gaseous nitrogen. Modeling challenges associated with the use of PR are discussed, as are the resource requirements associated with using a compressible formulation to describe liquids when full fuel injector applications are considered. The solver is analyzed using canonical cases and the Spray A experiment from the Engine Combustion Network.
NASA Astrophysics Data System (ADS)
Parmentier, Philippe; Winckelmans, Gregoire; Chatelain, Philippe; Hillewaert, Koen
2015-11-01
A hybrid approach, coupling a compressible vortex particle-mesh method (CVPM, also with efficient Poisson solver) and a high order compressible discontinuous Galerkin Eulerian solver, is being developed in order to efficiently simulate flows past bodies; also in the transonic regime. The Eulerian solver is dedicated to capturing the anisotropic flow structures in the near-wall region whereas the CVPM solver is exploited away from the body and in the wake. An overlapping domain decomposition approach is used. The Eulerian solver, which captures the near-body region, also corrects the CVPM solution in that region at every time step. The CVPM solver, which captures the region away from the body and the wake, also provides the outer boundary conditions to the Eulerian solver. Because of the coupling, a boundary element method is also required for consistency. The approach is assessed on typical 2D benchmark cases. Supported by the Fund for Research Training in Industry and Agriculture (F.R.I.A.).
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
NASA Astrophysics Data System (ADS)
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Comparison of Joint Modeling Approaches Including Eulerian Sliding Interfaces
Lomov, I; Antoun, T; Vorobiev, O
2009-12-16
Accurate representation of discontinuities such as joints and faults is a key ingredient for high fidelity modeling of shock propagation in geologic media. The following study was done to improve treatment of discontinuities (joints) in the Eulerian hydrocode GEODYN (Lomov and Liu 2005). Lagrangian methods with conforming meshes and explicit inclusion of joints in the geologic model are well suited for such an analysis. Unfortunately, current meshing tools are unable to automatically generate adequate hexahedral meshes for large numbers of irregular polyhedra. Another concern is that joint stiffness in such explicit computations requires significantly reduced time steps, with negative implications for both the efficiency and quality of the numerical solution. An alternative approach is to use non-conforming meshes and embed joint information into regular computational elements. However, once slip displacement on the joints become comparable to the zone size, Lagrangian (even non-conforming) meshes could suffer from tangling and decreased time step problems. The use of non-conforming meshes in an Eulerian solver may alleviate these difficulties and provide a viable numerical approach for modeling the effects of faults on the dynamic response of geologic materials. We studied shock propagation in jointed/faulted media using a Lagrangian and two Eulerian approaches. To investigate the accuracy of this joint treatment the GEODYN calculations have been compared with results from the Lagrangian code GEODYN-L which uses an explicit treatment of joints via common plane contact. We explore two approaches to joint treatment in the code, one for joints with finite thickness and the other for tight joints. In all cases the sliding interfaces are tracked explicitly without homogenization or blending the joint and block response into an average response. In general, rock joints will introduce an increase in normal compliance in addition to a reduction in shear strength. In the
Development of multiphase CFD flow solver in OpenFOAM
NASA Astrophysics Data System (ADS)
Rollins, Chad; Luo, Hong; Dinh, Nam
2016-11-01
We are developing a pressure-based multiphase (Eulerian) CFD solver using OpenFOAM with Reynolds-averaged turbulence stress modeling. Our goal is the evaluation and improvement of the current OpenFOAM two-fluid (Eulerian) solver in boiling channels with a motivation to produce a more consistent modeling and numerics treatment. The difficulty lies in the prescense of the many forces and models that are tightly non-linearly coupled in the solver. Therefore, the solver platform will allow not only the modeling, but the tracking as well, of the effects of the individual components (various interfacial forces/heat transfer models) and their interactions. This is essential for the development of a robust and efficient solution method. There has be a lot of work already performed in related areas that generally indicates a lack of robustness of the solution methods. The objective here is therefore to identify and develop remedies for numerical/modeling issues through a systematic approach to verification and validation, taking advantage of the open source nature of OpenFOAM. The presentation will discuss major findings, and suggest strategies for robust and consistent modeling (probably, a more consistent treatment of heat transfer models with two-fluid models in the near-wall cells).
A robust HLLC-type Riemann solver for strong shock
NASA Astrophysics Data System (ADS)
Shen, Zhijun; Yan, Wei; Yuan, Guangwei
2016-03-01
It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.
Parallel processing of Eulerian-Lagrangian, cell-based adaptive method for moving boundary problems
NASA Astrophysics Data System (ADS)
Kuan, Chih-Kuang
In this study, issues and techniques related to the parallel processing of the Eulerian-Lagrangian method for multi-scale moving boundary computation are investigated. The scope of the study consists of the Eulerian approach for field equations, explicit interface-tracking, Lagrangian interface modification and reconstruction algorithms, and a cell-based unstructured adaptive mesh refinement (AMR) in a distributed-memory computation framework. We decomposed the Eulerian domain spatially along with AMR to balance the computational load of solving field equations, which is a primary cost of the entire solver. The Lagrangian domain is partitioned based on marker vicinities with respect to the Eulerian partitions to minimize inter-processor communication. Overall, the performance of an Eulerian task peaks at 10,000-20,000 cells per processor, and it is the upper bound of the performance of the Eulerian- Lagrangian method. Moreover, the load imbalance of the Lagrangian task is not as influential as the communication overhead of the Eulerian-Lagrangian tasks on the overall performance. To assess the parallel processing capabilities, a high Weber number drop collision is simulated. The high convective to viscous length scale ratios result in disparate length scale distributions; together with the moving and topologically irregular interfaces, the computational tasks require temporally and spatially resolved treatment adaptively. The techniques presented enable us to perform original studies to meet such computational requirements. Coalescence, stretch, and break-up of satellite droplets due to the interfacial instability are observed in current study, and the history of interface evolution is in good agreement with the experimental data. The competing mechanisms of the primary and secondary droplet break up, along with the gas-liquid interfacial dynamics are systematically investigated. This study shows that Rayleigh-Taylor instability on the edge of an extruding sheet
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-10-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
Examination of Eulerian and Lagrangian Coordinate Systems.
ERIC Educational Resources Information Center
Remillard, Wilfred J.
1978-01-01
Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)
Parallel Multigrid Equation Solver
Adams, Mark
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
DG-FDF solver for large eddy simulation of compressible flows
NASA Astrophysics Data System (ADS)
Sammak, Shervin; Brazell, Michael; Mavriplis, Dimitri; Givi, Peyman
2016-11-01
A new computational scheme is developed for large eddy simulation (LES) of compressible turbulent flows with the filtered density function (FDF) subgrid scale closure. This is a hybrid scheme, combining the discontinuous Galerkin (DG) Eulerian solver with a Lagrangian Monte Carlo FDF simulator. The methodology is shown to be suitable for LES, as a larger portion of the resolved energy is captured as the order of spectral approximation increases. Simulations are conducted of both subsonic and supersonic flows. The consistency and the overall performance of the DG-FDF solver are demonstrated, together with its shock capturing capabilities.
Nonlinear Eulerian Thermoelasticity for Anisotropic Crystals
2013-08-01
Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys . Int. J. Solids Struct. 42, 4613–4640. Clayton, J., 2006. Continuum...strain and linear in entropy ; results are analyzed for quartz, sapphire, and diamond. When elastic constants of up to order four are included, both...Lagrangian or Eulerian strain and linear in entropy ; results are analyzed for quartz, sapphire, and diamond. When elastic constants of up to order four
Scalable solvers and applications
Ribbens, C J
2000-10-27
The purpose of this report is to summarize research activities carried out under Lawrence Livermore National Laboratory (LLNL) research subcontract B501073. This contract supported the principal investigator (P1), Dr. Calvin Ribbens, during his sabbatical visit to LLNL from August 1999 through June 2000. Results and conclusions from the work are summarized below in two major sections. The first section covers contributions to the Scalable Linear Solvers and hypre projects in the Center for Applied Scientific Computing (CASC). The second section describes results from collaboration with Patrice Turchi of LLNL's Chemistry and Materials Science Directorate (CMS). A list of publications supported by this subcontract appears at the end of the report.
Mixed Lagrangian-Eulerian and Eulerian Approach to Discretizing Richards' Equation
NASA Astrophysics Data System (ADS)
Yeh, G. T.; Tsai, C. H.
2014-12-01
This paper presents a robust, efficient numerical solution involving the use of the mixed Lagrangian-Eulerian (LE) method and the Eulerian (L) approach for three dimensional simulations of variably saturated subsurface flow that is described by Richard's equation. The LE approach with its particle tracking algorithm and/or finite element methods (FEM) were employed to discretize interior nodes while the finite element method is selected to set up algebraic equations for boundary nodes. The use of FEM for boundary nodes alleviate the difficulty in dealing with flux and gradient types of boundary conditions. Extrapolations are no longer needed to handle flux or gradient type boundary conditions. In this new mixed LE&E approach, subsurface flow in variably saturated media can be efficiently dealt with. Three examples are provided to demonstrate the efficiency of the proposed approach. First, a one-dimensional column problem is used to compare the accuracy of the mixed LE&E approach versus the traditional Eulerian approach. Second, a three-dimensional drainage problem was simulated to compare the CPU time between two approaches. Third, a three-dimensional pumping well problem was simulated. In all three examples, the mixed LE&E using relatively large time steps yielded superior results in terms of the accuracy and computational efficiency in comparison with the conventional Eulerian approach. The proposed mixed LE&E approach may contribute to the efficient numerical solutions of problems involving moving sharp fronts problems such as groundwater in real-world watersheds.
ESES: Software for Eulerian solvent excluded surface.
Liu, Beibei; Wang, Bao; Zhao, Rundong; Tong, Yiying; Wei, Guo-Wei
2017-03-15
Solvent excluded surface (SES) is one of the most popular surface definitions in biophysics and molecular biology. In addition to its usage in biomolecular visualization, it has been widely used in implicit solvent models, in which SES is usually immersed in a Cartesian mesh. Therefore, it is important to construct SESs in the Eulerian representation for biophysical modeling and computation. This work describes a software package called Eulerian solvent excluded surface (ESES) for the generation of accurate SESs in Cartesian grids. ESES offers the description of the solvent and solute domains by specifying all the intersection points between the SES and the Cartesian grid lines. Additionally, the interface normal at each intersection point is evaluated. Furthermore, for a given biomolecule, the ESES software not only provides the whole surface area, but also partitions the surface area according to atomic types. Homology theory is utilized to detect topological features, such as loops and cavities, on the complex formed by the SES. The sizes of loops and cavities are measured based on persistent homology with an evolutionary partial differential equation-based filtration. ESES is extensively validated by surface visualization, electrostatic solvation free energy computation, surface area and volume calculations, and loop and cavity detection and their size estimation. We used the Amber PBSA test set in our electrostatic solvation energy, area, and volume validations. Our results are either calibrated by analytical values or compared with those from the MSMS software. © 2017 Wiley Periodicals, Inc.
Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame
Azarnykh, Dmitrii Litvinov, Sergey; Adams, Nikolaus A.
2016-06-01
A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.
Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame
NASA Astrophysics Data System (ADS)
Azarnykh, Dmitrii; Litvinov, Sergey; Adams, Nikolaus A.
2016-06-01
A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.
A computational Lagrangian-Eulerian advection remap for free surface flows
NASA Astrophysics Data System (ADS)
Ashgriz, Nasser; Barbat, Tiberiu; Wang, Gang
2004-01-01
A VOF-based algorithm for advecting free surfaces and interfaces across a 2-D unstructured grid is presented. This algorithm is based on a combination of a Computational Lagrangian-Eulerian Advection Remap and the Volume of the Fluid method (CLEAR-VOF). A set of geometric tools are used to remap the advected shape of the volume fraction from one cell onto the Eulerian fixed unstructured grid. The geometric remapping is used to compute the fluxes onto a group of neighbouring cells of the mesh. These fluxes are then redistributed and corrected to satisfy the conservation of mass. Here, we present methods for developing identification algorithms for surface cells and incorporating them with CLEAR-VOF. The CLEAR-VOF algorithm is then tested for translation of several geometries. It is also incorporated in a finite element based flow solver and tested in a laminar flow over a broad-crested weir and a turbulent flow over a semi-circular obstacle.
Eulerian BAO reconstructions and N -point statistics
NASA Astrophysics Data System (ADS)
Schmittfull, Marcel; Feng, Yu; Beutler, Florian; Sherwin, Blake; Chu, Man Yat
2015-12-01
As galaxy surveys begin to measure the imprint of baryonic acoustic oscillations (BAO) on large-scale structure at the subpercent level, reconstruction techniques that reduce the contamination from nonlinear clustering become increasingly important. Inverting the nonlinear continuity equation, we propose an Eulerian growth-shift reconstruction algorithm that does not require the displacement of any objects, which is needed for the standard Lagrangian BAO reconstruction algorithm. In real-space dark matter-only simulations the algorithm yields 95% of the BAO signal-to-noise obtained from standard reconstruction. The reconstructed power spectrum is obtained by adding specific simple 3- and 4-point statistics to the prereconstruction power spectrum, making it very transparent how additional BAO information from higher-point statistics is included in the power spectrum through the reconstruction process. Analytical models of the reconstructed density for the two algorithms agree at second order. Based on similar modeling efforts, we introduce four additional reconstruction algorithms and discuss their performance.
NASA Technical Reports Server (NTRS)
Ilin, Andrew V.
2006-01-01
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Sherlock Holmes, Master Problem Solver.
ERIC Educational Resources Information Center
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
2D Resistive Magnetohydrodynamics Calculations with an Arbitrary Lagrange Eulerian Code
NASA Astrophysics Data System (ADS)
Rousculp, C. L.; Gianakon, T. A.; Lipnikov, K. N.; Nelson, E. M.
2015-11-01
Single fluid resistive MHD is useful for modeling Z-pinch configurations in cylindrical geometry. One such example is thin walled liners for shock physics or HEDP experiments driven by capacitor banks such as the LANL's PHELIX or Sandia-Z. MHD is also useful for modeling high-explosive-driven flux compression generators (FCGs) and their high-current switches. The resistive MHD in our arbitrary Lagrange Eulerian (ALE) code operates in one and two dimensions in both Cartesian and cylindrical geometry. It is implemented as a time-step split operator, which consists of, ideal MHD connected to the explicit hydro momentum and energy equations and a second order mimetic discretization solver for implicit solution of the magnetic diffusion equation. In a staggered grid scheme, a single-component of cell-centered magnetic flux is conserved in the Lagrangian frame exactly, while magnetic forces are accumulated at the nodes. Total energy is conserved to round off. Total flux is conserved under the ALE relaxation and remap. The diffusion solver consistently computes Ohmic heating. Both Neumann and Dirichlet boundary conditions are available with coupling to external circuit models. Example calculations will be shown.
Eulerian Formulation of Spatially Constrained Elastic Rods
NASA Astrophysics Data System (ADS)
Huynen, Alexandre
Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional Lagrangian formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the Eulerian framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed Eulerian reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-15
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
AUTOMATIC DIFFERENTIATION OF AN EULERIAN HYDROCODE
R. HENNINGER; A. CARLE; P. MAUDLIN
2000-11-01
Automatic differentiation (AD) is applied to a two-dimensional Eulerian hydrodynamics computer code (hydrocode) to provide gradients that will be used for design optimization and uncertainty analysis. We examine AD in both the forward and adjoint (reverse) mode using Automatic Differentiation of Fortran (ADIFOR, version 3.0). Setup time, accuracy, and run times are described for three problems. The test set consists of a one-dimensional shock-propagation problem, a two-dimensional metal-jet-formation problem and a two-dimensional shell-collapse problem. Setup time for ADIFOR was approximately one month starting from a simplified, fixed-dimension version of the original code. ADIFOR produced accurate (as compared to finite difference) gradients in both modes for all of the problems. These test problems had 17 independent variables. We find that the forward mode is up to 39% slower and the adjoint mode is at least 11% faster than finding the gradient by means of finite differences. Problems of real interest will certainly have more independent variables. The adjoint mode is thus favored since the computational time increases only slightly for additional independent variables.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...of coastal ocean fields by assimilation of Eulerian and Lagrangian flow data. - Apply our DO and GMM-DO schemes, as well as their theoretical
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
NASA Astrophysics Data System (ADS)
Erzincanli, Belkis; Sahin, Mehmet
2013-12-01
An Arbitrary Lagrangian-Eulerian (ALE) formulation based on the unstructured finite volume method is proposed for solving moving boundary problems with large displacements and rotations. The numerical method is based on the side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. The continuity equation is satisfied within each element at machine precision and the summation of the continuity equations can be exactly reduced to the domain boundary, which is important for the global mass conservation. A special attention is given to construct an ALE algorithm obeying the discrete geometric conservation law (DGCL). The mesh deformation algorithm is based on the indirect Radial Basis Function (RBF) algorithm at each time level while avoiding remeshing in order to enhance numerical robustness. For the parallel solution of resulting large-scale algebraic equations in a fully coupled form, a matrix factorization is introduced similar to that of the projection method for the whole system and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the decaying Taylor-Green vortex flow, the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wings in hover flight. The time variation of the Eulerian coherent structures in the near wake is shown along with the aerodynamic loads.
Grid adaptation and remapping for arbitrary lagrangian eulerian (ALE) methods
Lapenta, G. M.
2002-01-01
Methods to include automatic grid adaptation tools within the Arbitrary Lagrangian Eulerian (ALE) method are described. Two main developments will be described. First, a new grid adaptation approach is described, based on an automatic and accurate estimate of the local truncation error. Second, a new method to remap the information between two grids is presented, based on the MPDATA approach. The Arbitrary Lagrangian Eulerian (ALE) method solves hyperbolic equations by splitting the operators is two phases. First, in the Lagrangian phase, the equations under consideration are written in a Lagrangian frame and are discretized. In this phase, the grid moves with the solution, the velocity of each node being the local fluid velocity. Second, in the Eulerian phase, a new grid is generated and the information is transferred to the new grid. The advantage of considering this second step is the possibility of avoiding mesh distortion and tangling typical of pure Lagrangian methods. The second phase of the ALE method is the primary topic of the present communication. In the Eulerian phase two tasks need to be completed. First, a new grid need to be created (we will refer to this task as rezoning). Second, the information is transferred from the grid available at the end of the Lagrangian phase to the new grid (we will refer to this task as remapping). New techniques are presented for the two tasks of the Eulerian phase: rezoning and remapping.
Robust and Efficient Riemann Solvers for MHD
NASA Astrophysics Data System (ADS)
Miyoshi, T.; Kusano, K.
2008-04-01
Robust and efficient approximate Riemann solvers for magnetohydrodynamics (MHD) are constructed. Particularly, a family of positively conservative Harten-Lax-van Leer (HLL)-type Riemann solvers, the so-called HLLD (`D' denotes Discontinuities), HLLR (`R' denotes Rotational), HLLC (`C' denotes Contact), and HLL solvers, is systematically considered.
Ice Accretion Modeling using an Eulerian Approach for Droplet Impingement
NASA Technical Reports Server (NTRS)
Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.
2012-01-01
A three-dimensional Eulerian analysis has been developed for modeling droplet impingement on lifting bodes. The Eulerian model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the Eulerian approach is more efficient because the Lagrangian approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the Lagrangian approach used in an industry standard analysis called LEWICE.
Numerical Simulation of Drophila Flight Based on Arbitrary Langrangian-Eulerian Method
NASA Astrophysics Data System (ADS)
Erzincanli, Belkis; Sahin, Mehmet
2012-11-01
A parallel unstructured finite volume algorithm based on Arbitrary Lagrangian Eulerian (ALE) method has been developed in order to investigate the wake structure around a pair of flapping Drosophila wings. The numerical method uses a side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. A radial basis function (RBF) interpolation method is also implemented in order to achieve large mesh deformations. For the parallel solution of resulting large-scale algebraic equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and two-cycle of BoomerAMG solver is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wing in hover flight. The time variation of the near wake structure is shown along with the aerodynamic loads and particle traces. The authors acknowledge financial support from Turkish National Scientific and Technical Research Council (TUBITAK) through project number 111M332. The authors would like to thank Michael Dickinson and Michael Elzinga for providing the experimental data.
Two Phase Compressible Flow Fields in One Dimensional and Eulerian Grid Framework
NASA Astrophysics Data System (ADS)
Lee, Sungsu; Park, Chan Wook
2008-11-01
Numerical investigation for two phase compressible flow fields of air-water in one dimensional tube are performed in the fixed Eulerian grid framework. Using an equation of states of Tait's type for a multiphase cell, the two phase compressible flow is modeled as equivalent single phase which is discretized using the Roe`s approximate Riemann solver, while the phase interface is captured via volume fractions of each phase. The most common problem found in the computational approaches in compressible multiphase flow is occurrence of the pressure oscillation at the phase interface. In order to suppress that phenomenon, tried are two approaches; a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The results show that the direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. This work was supported by a research fund granted from Agency for Defense Development, South Korea
Crystal level simulations using Eulerian finite element methods
Becker, R; Barton, N R; Benson, D J
2004-02-06
Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations.
QUANTIFYING SUBGRID POLLUTANT VARIABILITY IN EULERIAN AIR QUALITY MODELS
In order to properly assess human risk due to exposure to hazardous air pollutants or air toxics, detailed information is needed on the location and magnitude of ambient air toxic concentrations. Regional scale Eulerian air quality models are typically limited to relatively coar...
Eulerian-Lagrangian solution of the convection-dispersion equation in natural co-ordinates.
Cheng, R.T.; Casulli, V.; Milford, S.N.
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system.-from Authors
2014-11-01
Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories by JD Clayton ARL-RP-0513...of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories JD Clayton Weapons and Materials Research Directorate, ARL...SUBTITLE Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories 5a. CONTRACT NUMBER 5b. GRANT
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Parallel Performance of Linear Solvers and Preconditioners
2014-01-01
MUMPS libraries to identify the combination with the shortest wall clock time for large-scale linear systems. The linear system of equations in this...during initialization. Our results show that for system sizes of less than three million degrees of freedom (DOF), the MUMPS direct solver is 20...solver with various iterative solver – preconditioner combinations. Both solve time and setup time for MUMPS are included. Ideal refers to the solve
Analysis Tools for CFD Multigrid Solvers
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Diskin, Boris
2004-01-01
Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.
Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick
2016-01-01
In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798
Accurate direct Eulerian simulation of dynamic elastic-plastic flow
Kamm, James R; Walter, John W
2009-01-01
The simulation of dynamic, large strain deformation is an important, difficult, and unsolved computational challenge. Existing Eulerian schemes for dynamic material response are plagued by unresolved issues. We present a new scheme for the first-order system of elasto-plasticity equations in the Eulerian frame. This system has an intrinsic constraint on the inverse deformation gradient. Standard Godunov schemes do not satisfy this constraint. The method of Flux Distributions (FD) was devised to discretely enforce such constraints for numerical schemes with cell-centered variables. We describe a Flux Distribution approach that enforces the inverse deformation gradient constraint. As this approach is new and novel, we do not yet have numerical results to validate our claims. This paper is the first installment of our program to develop this new method.
Asymptotic shape of the region visited by an Eulerian walker
NASA Astrophysics Data System (ADS)
Kapri, Rajeev; Dhar, Deepak
2009-11-01
We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3 , for large N , and the width of the boundary region grows as Nα/3 , with α=0.40±0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, ⟨RN2⟩˜N2ν , shows a crossover from the Eulerian (ν=1/3) to a simple random-walk (ν=1/2) behavior.
A domain decomposition scheme for Eulerian shock physics codes
Bell, R.L.; Hertel, E.S. Jr.
1994-08-01
A new algorithm which allows for complex domain decomposition in Eulerian codes was developed at Sandia National Laboratories. This new feature allows a user to customize the zoning for each portion of a calculation and to refine volumes of the computational space of particular interest This option is available in one, two, and three dimensions. The new technique will be described in detail and several examples of the effectiveness of this technique will also be discussed.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
On the Eulerian AFTON Equations for Axisymmetric Fluid Flow,
The AFTON codes are based on a method for constructing finite difference equations that describe the evolution of classical fields, and more...by the AFTON 2A code, one of whose versions has been specialized for solution of the time-dependent Navier-Stokes equations for compressible flow, in...Eulerian form. The version of AFTON 2A in question has now been used to compute many viscous compressible flow fields. This report discusses the
MACSYMA's symbolic ordinary differential equation solver
NASA Technical Reports Server (NTRS)
Golden, J. P.
1977-01-01
The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.
Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Zhou, Ye
1998-01-01
Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Vital sign monitoring utilizing Eulerian video magnification and thermography.
Aubakir, Bauyrzhan; Nurimbetov, Birzhan; Tursynbek, Iliyas; Varol, Huseyin Atakan
2016-08-01
In this paper we present a proof of concept for non-contact extraction of vital signs using RGB and thermal images obtained from a smart phone. Using our method, heart rate, respiratory rate and forehead temperature can be measured concurrently. Face detection and tracking is leveraged in order to allow natural motion of patients. Heart rate is estimated via processing of visible band RGB video using Eulerian Video Magnification technique. Respiratory rate and the temperature is measured using thermal video. Experiments conducted with 11 healthy subjects indicate that heart rate and respiration rate can be measured with 92 and 94 percent accuracy, respectively.
MESA: A 3-D Eulerian hydrocode for penetration mechanics studies
Mandell, D.A.; Holian, K.S.; Henninger, R.
1991-01-01
We describe an explicit, finite-difference hydrocode, called MESA, and compare calculations to metal and ceramic plate impacts with spall and to Taylor cylinder tests. The MESA code was developed with support from DARPA, the Army and the Marine Corps for use in armor/anti-armor problems primarily, but the code has been used for a number of other applications. MESA includes 2-D and 3-D Eulerian hydrodynamics, a number of material strength and fracture models, and a programmed burn high explosives model. 15 refs., 4 figs.
Prospects for Eulerian CFD analysis of helicopter vortex flows
NASA Technical Reports Server (NTRS)
Drela, Mark; Murman, Earll M.
1987-01-01
The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel Eulerian/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.
Lagrangian and Eulerian statistics in homogeneous, anisotropic flows
NASA Astrophysics Data System (ADS)
Iyer, Kartik; Bonaccorso, Fabio; Toschi, Federico; Biferale, Luca
2016-11-01
We report results from highly resolved direct numerical simulations of anisotropic homogeneous flows using up to 20483 collocations points. We examine a turbulent Kolmogorov flow with randomly correlated phases in order to recover space homogeneity on average. We present Eulerian and Lagrangian measurements concerning the universality of isotropic and anisotropic contributions using a systematic decomposition based on the eigenfunctions of the SO (3) group of rotations in three dimensions. Additionally, we discuss absolute dispersion statistics of particles in flows subjected to different large-scale anisotropies. ERC ADG NewTURB 2013.
Parallelizing alternating direction implicit solver on GPUs
Technology Transfer Automated Retrieval System (TEKTRAN)
We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree.
Improved Stiff ODE Solvers for Combustion CFD
NASA Astrophysics Data System (ADS)
Imren, A.; Haworth, D. C.
2016-11-01
Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look at stiff ODE solvers is taken that includes how the solver is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based solvers in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.
Eulerian hydrocode modeling of a dynamic tensile extrusion experiment (u)
Burkett, Michael W; Clancy, Sean P
2009-01-01
Eulerian hydrocode simulations utilizing the Mechanical Threshold Stress flow stress model were performed to provide insight into a dynamic extrusion experiment. The dynamic extrusion response of copper (three different grain sizes) and tantalum spheres were simulated with MESA, an explicit, 2-D Eulerian continuum mechanics hydrocode and compared with experimental data. The experimental data consisted of high-speed images of the extrusion process, recovered extruded samples, and post test metallography. The hydrocode was developed to predict large-strain and high-strain-rate loading problems. Some of the features of the features of MESA include a high-order advection algorithm, a material interface tracking scheme and a van Leer monotonic advection-limiting. The Mechanical Threshold Stress (MTS) model was utilized to evolve the flow stress as a function of strain, strain rate and temperature for copper and tantalum. Plastic strains exceeding 300% were predicted in the extrusion of copper at 400 m/s, while plastic strains exceeding 800% were predicted for Ta. Quantitative comparisons between the predicted and measured deformation topologies and extrusion rate were made. Additionally, predictions of the texture evolution (based upon the deformation rate history and the rigid body rotations experienced by the copper during the extrusion process) were compared with the orientation imaging microscopy measurements. Finally, comparisons between the calculated and measured influence of the initial texture on the dynamic extrusion response of tantalum was performed.
Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities
NASA Technical Reports Server (NTRS)
Bendiksen, Oddvar O.
1994-01-01
This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.
Inductive ionospheric solver for magnetospheric MHD simulations
NASA Astrophysics Data System (ADS)
Vanhamäki, H.
2011-01-01
We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
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.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
NASA Astrophysics Data System (ADS)
Felici, Helene Marie
1992-06-01
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.
A Coupled Eulerian/lagrangian Method for the Solution of Three-Dimensional Vortical Flows
NASA Astrophysics Data System (ADS)
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 solution 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 procedure 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 a turbulent inlet velocity profile, the swirling flow in a pipe, 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. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2013-09-15
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.
Noninvasive Free Flap Monitoring Using Eulerian Video Magnification
Liu, Yuan Fang; Vuong, Christopher; Walker, Paul Charles; Peterson, Nathaniel Ray; Inman, Jared Christian; Filho, Pedro Alcantara Andrade; Lee, Steve Choon-Sung
2016-01-01
Eulerian Video Magnification (EVM) can enhance subtle changes in videos to reveal what was once invisible to the naked eye. In this proof of concept study, we investigated using EVM as a novel form of free flap monitoring. Free flaps with skin paddles were filmed in the operating room with manipulation of their pedicles. In a representative 77-year-old female who received a latissimus dorsi-serratus-rib composite free flap, EVM was able to detect blockage of arterial or venous supply instantaneously, providing a visible representation through degree of color change in videos. EVM has the potential to serve as a powerful free flap monitoring tool with the benefit of being noninvasive, sensitive, easy-to-use, and nearly cost-free. PMID:27092284
Relativistic perturbations in ΛCDM: Eulerian and Lagrangian approaches
Villa, Eleonora; Rampf, Cornelius E-mail: cornelius.rampf@port.ac.uk
2016-01-01
We study the relativistic dynamics of a pressure-less and irrotational fluid of dark matter (CDM) with a cosmological constant (Λ), up to second order in cosmological perturbation theory. In our analysis we also account for vector and tensor perturbations and include primordial non-Gaussianity. We consider three gauges: the synchronous-comoving gauge, the Poisson gauge and the total matter gauge, where the first is the unique relativistic Lagrangian frame of reference, and the latters are convenient gauge choices for Eulerian frames. Our starting point is the metric and fluid variables in the Poisson gauge up to second order. We then perform the gauge transformations to the synchronous-comoving gauge and subsequently to the total matter gauge. Our expressions for the metrics, densities, velocities, and the gauge generators are novel and coincide with known results in the limit of a vanishing cosmological constant.
Techniques to derive geometries for image-based Eulerian computations
Dillard, Seth; Buchholz, James; Vigmostad, Sarah; Kim, Hyunggun; Udaykumar, H.S.
2014-01-01
Purpose The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based Eulerian fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted. Design/methodology/approach Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures. Findings While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics. Originality/value It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an Eulerian setting. PMID
Development and deployment of constitutive softening routines in Eulerian hydrocodes.
Fuller, Timothy Jesse; Dewers, Thomas A.; Swan, Matthew Scot
2013-03-01
The state of the art in failure modeling enables assessment of crack nucleation, propagation, and progression to fragmentation due to high velocity impact. Vulnerability assessments suggest a need to track material behavior through failure, to the point of fragmentation and beyond. This eld of research is particularly challenging for structures made of porous quasi-brittle materials, such as ceramics used in modern armor systems, due to the complex material response when loading exceeds the quasi-brittle material's elastic limit. Further complications arise when incorporating the quasi-brittle material response in multi-material Eulerian hydrocode simulations. In this report, recent e orts in coupling a ceramic materials response in the post-failure regime with an Eulerian hydro code are described. Material behavior is modeled by the Kayenta material model [2] and Alegra as the host nite element code [14]. Kayenta, a three invariant phenomenological plasticity model originally developed for modeling the stress response of geologic materials, has in recent years been used with some success in the modeling of ceramic and other quasi-brittle materials to high velocity impact. Due to the granular nature of ceramic materials, Kayenta allows for signi cant pressures to develop due to dilatant plastic ow, even in shear dominated loading where traditional equations of state predict little or no pressure response. When a material's ability to carry further load is compromised, Kayenta allows the material's strength and sti ness to progressively degrade through the evolution of damage to the point of material failure. As material dilatation and damage progress, accommodations are made within Alegra to treat in a consistent manner the evolving state.
New iterative solvers for the NAG Libraries
Salvini, S.; Shaw, G.
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Using SPARK as a Solver for Modelica
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
An approximate Riemann solver for hypervelocity flows
NASA Technical Reports Server (NTRS)
Jacobs, Peter A.
1991-01-01
We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.
Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion
NASA Technical Reports Server (NTRS)
Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.
2012-01-01
demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current
Equation solvers for distributed-memory computers
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1994-01-01
A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
Wang, C.Y.; Zeuch, W.R.
1982-01-01
This paper describes an arbitrary Lagrangian-Eulerian method for analyzing fluid-structure interactions in fast-reactor containment with complex internal structures. The fluid transient can be calculated either implicitly or explicitly, using a finite-difference mesh with vertices that may be moved with the fluid (Lagrangian), held fixed (Eulerian), or moved in any other prescribed manner (hybrid Lagrangian Eulerian). The structural response is computed explicitly by two nonlinear, elastic-plastic finite-element modules formulated in corotational coordinates. Interaction between fluid and structure is accounted for by enforcing the interface boundary conditions. The method has convincing advantages in treating complicated phenomena such as flow through perforated structures, large material distortions, flow around corners and irregularities, and highly contorted fluid boundaries. Several sample problems are given to illustrate the effectiveness of this arbitrary Lagrangian-Eulerian method.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
Leung Shingyu; Qian Jianliang
2010-11-20
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
A Note on the Total Number of Double Eulerian Circuits in Multigraphs
NASA Astrophysics Data System (ADS)
Liskovets, Valery
2002-12-01
We formulate explicitly and discuss a simple new enumerative formula for double (directed) eulerian circuits in n-edged labeled multigraphs. The formula follows easily from a recent 2-parametric formula of B. Lass.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
NASA Astrophysics Data System (ADS)
Lind, S. J.; Stansby, P. K.
2016-12-01
The incompressible Smoothed Particle Hydrodynamics (ISPH) method is derived in Eulerian form with high-order smoothing kernels to provide increased accuracy for a range of steady and transient internal flows. Periodic transient flows, in particular, demonstrate high-order convergence and accuracies approaching, for example, spectral mesh-based methods. The improved accuracies are achieved through new high-order Gaussian kernels applied over regular particle distributions with time stepping formally up to 2nd order for transient flows. The Eulerian approach can be easily extended to model free surface flows by merging from Eulerian to Lagrangian regions in an Arbitrary-Lagrangian-Eulerian (ALE) fashion, and a demonstration with periodic wave propagation is presented. In the long term, it is envisaged that the method will greatly increase the accuracy and efficiency of SPH methods, while retaining the flexibility of SPH in modelling free surface and multiphase flows.
Eulerian-Lagrangian Simulation of an Explosive Dispersal of Particles
NASA Astrophysics Data System (ADS)
Rollin, Bertrand; Ouellet, Frederick; Koneru, Rahul; Annamalai, Subramanian
2016-11-01
Explosive dispersal of solid particles can be observed in a wide variety of contexts, notably in natural phenomenon such as volcanic eruptions or in engineering applications such as detonation of multiphase explosives. As the initial blast wave crosses the surrounding layer of particles, compaction occurs shortly before particles disperse radially outward at high speed. During the dispersion phase, complex multiphase interactions occurs between particles and detonation products of the explosive. Using a Eulerian-Lagrangian approach, namely point particle simulations, we study the case of a bed of particles of cylindrical shape surrounding an explosive chord. Our interest lies in predicting the behavior of particles after detonation. In particular, capturing and describing the mechanisms responsible for late-time formation of stable particle jets is sought. Therefore, detonation of the explosive material is not simulated. Instead an equivalent energy source is used to initiate the simulation. We present a detailed description of our approach to solving this problem, and our most recent progress in the analysis of particles explosive dispersal. This work was supported by the U.S. DoE, 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.
Comparison between Eulerian and Lagrangian Atmospheric Transport Models
NASA Astrophysics Data System (ADS)
Heinrich, P.; Grillon, Y.
2001-05-01
Two numerical atmospheric models are tested and compared both in backward and forward modes to study the transport and dispersion of radioactive gases in the framework of the Comprehensive Test Ban Treaty. The first one (LMDZ) has been developed at the Laboratoire de Meteorologie Dynamique in Paris,it calculates eulerian large-scale advection based upon finite-volume methods and parametrization of turbulent mixing and convection. The second one (HYSPLIT), developed by the Air Resources Laboratory of NOAA, is lagrangian and calculated 3D trajectories of particules, taking also into account dispersion due to wind shear. Concentrations of particules are compared at stations of the CTBT network for a fictitious source in the Pacific Ocean, that is assumed to be punctual in time and space. In the backward mode, concentrations are calculated and compared over 15 days from a point source at Tahiti to determine the field of regard for this station. Sensitivity tests are carried out by varying the spatial resolution of models.
Lagrangian and Eulerian description of bed-load particle kinematics
NASA Astrophysics Data System (ADS)
Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio
2016-04-01
The motion of bed-load sediment particles transported by a flow can be analyzed within a Lagrangian or an Eulerian framework. In the former case, we consider the particles as individual objects in motion and we study their kinematic properties. The latter approach is instead referred to suitably chosen control volumes. Quantities describing sediment motion in the two frameworks are different, and the relationships among the two approaches are not straightforward. In this work, we intend to discuss the kinematic properties of sediment transport: first, a set of quantities is univocally defined; then, relationships among different representations are explored. Proof-of-concept results presented in the study are from a recent experiment involving weak bed-load sediment transport, where the moving particles were released over a fixed rough bed. The bulk flow velocity was 1.4 times the critical value for incipient particle motion, and particles were mostly moving by rolling and sliding, with limited saltation. The particle motion was filmed from the top and the measurements were conducted by image-based methods, obtaining extensive samples of virtually-instantaneous quantities.
Currents in the Dead Sea: Lagrangian and Eulerian observations
NASA Astrophysics Data System (ADS)
Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav
2015-04-01
The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (Eulerian) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.
NASA Astrophysics Data System (ADS)
Wang, Bin; Hirose, Naoki; Moon, Jae-Hong; Yuan, Dongliang
2013-05-01
The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.
Aleph Field Solver Challenge Problem Results Summary
Hooper, Russell; Moore, Stan Gerald
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Implicit Riemann solvers for the Pn equations.
Mehlhorn, Thomas Alan; McClarren, Ryan; Brunner, Thomas A.; Holloway, James Paul
2005-03-01
The spherical harmonics (P{sub n}) approximation to the transport equation for time dependent problems has previously been treated using Riemann solvers and explicit time integration. Here we present an implicit time integration method for the P n equations using Riemann solvers. Both first-order and high-resolution spatial discretization schemes are detailed. One facet of the high-resolution scheme is that a system of nonlinear equations must be solved at each time step. This nonlinearity is the result of slope reconstruction techniques necessary to avoid the introduction of artifical extrema in the numerical solution. Results are presented that show auspicious agreement with analytical solutions using time steps well beyond the CFL limit.
A perspective on unstructured grid flow solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1995-01-01
This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.
Domain Decomposition for the SPN Solver MINOS
NASA Astrophysics Data System (ADS)
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-12-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3® code.
Domain decomposition for the SPN solver MINOS
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-07-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)
A multigrid solver for the semiconductor equations
NASA Technical Reports Server (NTRS)
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
Voids in modified gravity reloaded: Eulerian void assignment
NASA Astrophysics Data System (ADS)
Lam, Tsz Yan; Clampitt, Joseph; Cai, Yan-Chuan; Li, Baojiu
2015-07-01
We revisit the excursion set approach to calculate void abundances in chameleon-type modified gravity theories, which was previously studied by Clampitt, Cai & Li. We focus on properly accounting for the void-in-cloud effect, i.e. the growth of those voids sitting in overdense regions may be restricted by the evolution of their surroundings. This effect may change the distribution function of voids hence affect predictions on the differences between modified gravity (MG) and general relativity (GR). We show that the thin-shell approximation usually used to calculate the fifth force is qualitatively good but quantitatively inaccurate. Therefore, it is necessary to numerically solve the fifth force in both overdense and underdense regions. We then generalize the Eulerian-void-assignment method of Paranjape, Lam & Sheth to our modified gravity model. We implement this method in our Monte Carlo simulations and compare its results with the original Lagrangian methods. We find that the abundances of small voids are significantly reduced in both MG and GR due to the restriction of environments. However, the change in void abundances for the range of void radii of interest for both models is similar. Therefore, the difference between models remains similar to the results from the Lagrangian method, especially if correlated steps of the random walks are used. As Clampitt et al., we find that the void abundance is much more sensitive to MG than halo abundances. Our method can then be a faster alternative to N-body simulations for studying the qualitative behaviour of a broad class of theories. We also discuss the limitations and other practical issues associated with its applications.
Differential geometry based solvation model I: Eulerian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2010-11-01
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to
Differential geometry based solvation model I: Eulerian formulation
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-01-01
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to
Eulerian formulation of the interacting particle representation model of homogeneous turbulence
NASA Astrophysics Data System (ADS)
Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca
2016-10-01
The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the confines of a one-point model. In the original formulation [Kassinos and Reynolds, Center for Turbulence Research: Annual Research Briefs, 31-51 (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is reformulated in an Eulerian framework, and evolution equations are developed for the marginal probability density functions (PDFs). Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.
A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics
NASA Astrophysics Data System (ADS)
Clair, G.; Ghidaglia, J.-M.; Perlat, J.-P.
2016-12-01
In this paper we describe a second order multi-dimensional scheme, belonging to the class of direct Arbitrary Lagrangian-Eulerian (ALE) methods, for the solution of non-linear hyperbolic systems of conservation law. The scheme is constructed upon a cell-centered explicit Lagrangian solver completed with an edge-based upwinded formulation of the numerical fluxes, computed from the MUSCL-Hancock method, to obtain a full ALE formulation. Numerical fluxes depend on nodal grid velocities which are either set or computed to avoid most of the mesh problems typically encountered in purely Lagrangian simulations. In order to assess the robustness of the scheme, most results proposed in this paper have been obtained by computing the grid velocities as a fraction of the Lagrangian nodal velocities, the ratio being set before running the test case. The last part of the paper describes preliminary results about the triple point test case run in the ALE framework by computing the grid velocities with the fully adaptive Large Eddy Limitation (L.E.L.) method proposed in [1]. Such a method automatically computes the grid velocities at each node defining the mesh from the local characteristics of the flow. We eventually discuss the advantages and the drawback of the coupling.
Eulerian Gaussian beams for Schroedinger equations in the semi-classical regime
Leung, Shingyu Qian Jianliang
2009-05-01
We propose Gaussian-beam based Eulerian methods to compute semi-classical solutions of the Schroedinger equation. Traditional Gaussian beam type methods for the Schroedinger equation are based on the Lagrangian ray tracing. Based on the first Eulerian Gaussian beam framework proposed in Leung et al. [S. Leung, J. Qian, R. Burridge, Eulerian Gaussian beams for high frequency wave propagation, Geophysics 72 (2007) SM61-SM76], we develop a new Eulerian Gaussian beam method which uses global Cartesian coordinates, level-set based implicit representation and Liouville equations. The resulting method gives uniformly distributed phases and amplitudes in phase space simultaneously. To obtain semi-classical solutions to the Schroedinger equation with different initial wave functions, we only need to slightly modify the summation formula. This yields a very efficient method for computing semi-classical solutions to the Schroedinger equation. For instance, in the one-dimensional case the proposed algorithm requires only O(sNm{sup 2}) operations to compute s different solutions with s different initial wave functions under the influence of the same potential, where N=O(1/h),h is the Planck constant, and m<
Modeling and simulation challenges in Eulerian-Lagrangian computations of multiphase flows
NASA Astrophysics Data System (ADS)
Diggs, Angela; Balachandar, S.
2017-01-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Grid-Based (GB) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Particle-Based (PB) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of PB methods. By evaluating the total error and its components we compare the performance of GB and PB methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities.
Updates to the NEQAIR Radiation Solver
NASA Technical Reports Server (NTRS)
Cruden, Brett A.; Brandis, Aaron M.
2014-01-01
The NEQAIR code is one of the original heritage solvers for radiative heating prediction in aerothermal environments, and is still used today for mission design purposes. This paper discusses the implementation of the first major revision to the NEQAIR code in the last five years, NEQAIR v14.0. The most notable features of NEQAIR v14.0 are the parallelization of the radiation computation, reducing runtimes by about 30×, and the inclusion of mid-wave CO2 infrared radiation.
A finite different field solver for dipole modes
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL.
A 3D approximate maximum likelihood localization solver
2016-09-23
A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with acoustic transmitters and vocalizing marine mammals to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives and support Marine Renewable Energy. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Simulation on gasification of forestry residues in fluidized beds by Eulerian-Lagrangian approach.
Xie, Jun; Zhong, Wenqi; Jin, Baosheng; Shao, Yingjuan; Liu, Hao
2012-10-01
A comprehensive three-dimensional numerical model is developed to simulate forestry residues gasification in a fluidized bed reactor using Eulerian-Lagrangian approach. The complex granular flow behaviors and chemical reaction characteristics are addressed simultaneously. The model uses an Eulerian method for fluid phase and a discrete particle method for solid phase, which takes particle contact force into account. Heterogeneous and homogenous reaction rates are solved on the Eulerian grid. The numerical model is employed to study the gasification performance in a lab-scale pine gasifier. A series of simulations have been performed with some critical parameters including temperature, equivalence ratio and steam to biomass ratio. The model predicts product gas composition and carbon conversion efficiency in good agreement with experimental data. The formation and development of flow regimes, profiles of particle species, and distributions of gas compositions inside the reactor are also discussed.
Representation of measured ejector characteristics by simple Eulerian bond graph models
NASA Astrophysics Data System (ADS)
Paynter, H. M.
1985-12-01
For some time, a purely fluidic type of pump or compressor has existed. This device possesses no solid moving parts. Such an ejector of jet-pump employs the momentum of a high velocity jet from the drive flow to entrain and pressurize a secondary suction flow stream. One application of such ejectors is related to an employment by the nuclear industry. Certain accidents have drawn attention to the grossly inadequate data base for ejectors operating under extreme pathological conditions including reverse flows. In connection with these developments, extensive tests were conducted. The present paper uses primarily data obtained in these tests. Attention is given to an analysis of the test results, aspects of bond graph representation, internal Eulerian flows satisfying a condition of Eulerian similitude, a canonical model, moduli functions, a near-perfect Eulerian device, and constant and variable paramter models. The considered tests and studies made it possible to establish a structured performance model for ejectors.
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
NASA Astrophysics Data System (ADS)
Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.
2016-01-01
An approach for Eulerian-Lagrangian large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian and Lagrangian frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted Eulerian and Lagrangian velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.
Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows
NASA Technical Reports Server (NTRS)
He, Guowei; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Optimising a parallel conjugate gradient solver
Field, M.R.
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
Linear iterative solvers for implicit ODE methods
NASA Technical Reports Server (NTRS)
Saylor, Paul E.; Skeel, Robert D.
1990-01-01
The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.
Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers
NASA Technical Reports Server (NTRS)
Guru Prasad, K.; Kane, J. H.
1992-01-01
The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.
A real-time impurity solver for DMFT
NASA Astrophysics Data System (ADS)
Kim, Hyungwon; Aron, Camille; Han, Jong E.; Kotliar, Gabriel
Dynamical mean-field theory (DMFT) offers a non-perturbative approach to problems with strongly correlated electrons. The method heavily relies on the ability to numerically solve an auxiliary Anderson-type impurity problem. While powerful Matsubara-frequency solvers have been developed over the past two decades to tackle equilibrium situations, the status of real-time impurity solvers that could compete with Matsubara-frequency solvers and be readily generalizable to non-equilibrium situations is still premature. We present a real-time solver which is based on a quantum Master equation description of the dissipative dynamics of the impurity and its exact diagonalization. As a benchmark, we illustrate the strengths of our solver in the context of the equilibrium Mott-insulator transition of the one-band Hubbard model and compare it with iterative perturbation theory (IPT) method. Finally, we discuss its direct application to a nonequilibrium situation.
General purpose nonlinear system solver based on Newton-Krylov method.
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
Eulerian simulation of the perforation of aluminum plates by nondeforming projectiles
Silling, S.A.
1992-03-01
A new algorithm for the treatment of sliding interfaces between solids with or without friction in an Eulerian wavecode is described. The algorithm has been implemented in the two-dimensional version of the CTH code. The code was used to simulate penetration and perforation of aluminum plates by rigid, conical-nosed tungsten projectiles. Comparison with experimental data is provided.
The "Preface to the Special Edition on Model Evaluation: Evaluation of Urban and Regional Eulerian Air Quality Models" is a brief introduction to the papers included in a special issue of Atmospheric Environment. The Preface provides a background for the papers, which have thei...
A 3D radiative transfer framework . VII. Arbitrary velocity fields in the Eulerian frame
NASA Astrophysics Data System (ADS)
Seelmann, A. M.; Hauschildt, P. H.; Baron, E.
2010-11-01
Aims: A solution of the radiative-transfer problem in 3D with arbitrary velocity fields in the Eulerian frame is presented. The method is implemented in our 3D radiative transfer framework and used in the PHOENIX/3D code. It is tested by comparison to our well-tested 1D co-moving frame radiative transfer code, where the treatment of a monotonic velocity field is implemented in the Lagrangian frame. The Eulerian formulation does not need much additional memory and is useable on state-of-the-art computers, even large-scale applications with 1000's of wavelength points are feasible. Methods: In the Eulerian formulation of the problem, the photon is seen by the atom at a Doppler-shifted wavelength depending on its propagation direction, which leads to a Doppler-shifted absorption and emission. This leads to a different source function and a different Λ^* operator in the radiative transfer equations compared to the static case. Results: The results of the Eulerian 3D spherical calculations are compared to our well-tested 1D Lagrangian spherical calculations, the agreement is, up to vmax = 1 × 103 km s-1 very good. Test calculation in other geometries are also shown.
Implementation of a friction model in an Eulerian viscoplastic formulation for steady flow
Dawson, P.R.; Boyce, D.E.
1996-04-01
The goal of this project was to implement the routines necessary to use the friction model of Wilson and Korzekwa into the finite element analysis program {ital hickory}, in the case of an Eulerian reference frame. {ital hickory} is a deformation simulation code based on finite element modeling of viscoplastic deformation When using {ital hickory}, time-dependent problems are modeled from a Lagrangian reference frame; while steady-state problems are modeled from an Eulerian reference frame. The friction model had been implemented in earlier versions of {ital hickory}, for use with a Lagrangian reference frame. Additional modifications were required, however, to extend this capability to the case of an Eulerian reference frame. That is the subject of this report. The necessary modifications were related to the time integration of the friction state variables. The application of an Eulerian reference frame to study a steady-state flow requires that each specified boundary segment be a streamline of the flow. As such, an initial value for each state variable must be given at the first point of the streamline, and subsequent values must be determined by previous values by integration along the streamline. Additional routines were added to {ital hickory} to implement the streamline integration along the boundary. A plane strain rolling problem was used both to test the implementation and as a source of comparison among friction models.
SMITE - A Second Order Eulerian Code for Hydrodynamic and Elastic-Plastic Problems
1975-08-01
et al Mathematical Applications Group, Incorporated Prepared for: Ballistic Research Laboratories August 1975 DISTRIBI,TED BY: mi] National...SMITE - A SECOND ORDER EULERIAN CODE FOR HYDRODYNAMIC AND ELASTIC-PLASTIC PROBLEMS Prepared by Mathematical Applications Group, Inc. 3...AODRcis jMathematical Applications Group, Inc. 13 Westchester Plaza IFlmsford, New York 10523 10. PROGRAM ELEMENT, PROJECT, TASK AREA t WORK
NASA Astrophysics Data System (ADS)
Xiao, Heng; Bruhns, Otto T.; Meyers, Albert
2007-02-01
Recently it has been demonstrated that, on the basis of the separation D=De+Dp arising from the split of the stress power and two consistency criteria for objective Eulerian rate formulations, it is possible to establish a consistent Eulerian rate formulation of finite elastoplasticity in terms of the Kirchhoff stress and the stretching, without involving additional deformation-like variables labelled "elastic" or "plastic". It has further been demonstrated that this consistent formulation leads to a simple essential structure implied by the work postulate, namely, both the normality rule for plastic flow Dp and the convexity of the yield surface in Kirchhoff stress space. Here, we attempt to place such an Eulerian formulation on the thermodynamic grounds by extending it to a general case with thermal effects, where the consistency requirements are treated in a twofold sense. First, we propose a general constitutive formulation based on the foregoing separation as well as the two consistency criteria. This is accomplished by employing the corotational logarithmic rate and by incorporating an exactly integrable Eulerian rate equation for De for thermo-elastic behaviour. Then, we study the consistency of the formulation with thermodynamic laws. Towards this goal, simple forms of restrictions are derived, and consequences are discussed. It is shown that the proposed Eulerian formulation is free in the sense of thermodynamic consistency. Namely, a Helmholtz free energy function in explicit form may be found such that the restrictions from the thermodynamic laws can be fulfilled with positive internal dissipation for arbitrary forms of constitutive functions included in the constitutive formulation. In particular, that is the case for the foregoing essential constitutive structure in the purely mechanical case. These results eventually lead to a complete, explicit constitutive theory for coupled fields of deformation, stress and temperature in thermo
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
GPU accelerated kinetic solvers for rarefied gas dynamics
NASA Astrophysics Data System (ADS)
Zabelok, Sergey A.; Kolobov, Vladimir I.; Arslanbekov, Robert R.
2012-11-01
GPU-acceleration is applied to the Boltzmann solver with adaptive Cartesian mesh in the Unified Flow Solver framework. NVIDIA CUDA technology is used with threads being grouped in thread blocks by points of Korobov sequences in each cell for computing the collision integral and by points in coordinate space for the free-molecular flow stage. GPU-accelerated Boltzmann solver with octree Cartesian mesh has been tested on several computer systems. Speedup of several times for GPU-based code compared to single-core CPU computations on the same machines has been observed.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Advanced Multigrid Solvers for Fluid Dynamics
NASA Technical Reports Server (NTRS)
Brandt, Achi
1999-01-01
The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A.
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
Performance of NASA Equation Solvers on Computational Mechanics Applications
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1996-01-01
This paper describes the performance of a new family of NASA-developed equation solvers used for large-scale (i.e. 551,705 equations) structural analysis. To minimize computer time and memory, the solvers are divided by application and matrix characteristics (sparse/dense, real/complex, symmetric/nonsymmetric, size: in-core/out of core) and exploit the hardware features of current and future computers. In this paper, the equation solvers, which are written in FORTRAN, and are therefore easily transportable, are shown to be faster than specialized computer library routines utilizing assembly code. Twenty NASA structural benchmark models with NASA solver timings reside on World Wide Web with a challenge to beat them.
Experiences Running a Parallel Answer Set Solver on Blue Gene
NASA Astrophysics Data System (ADS)
Schneidenbach, Lars; Schnor, Bettina; Gebser, Martin; Kaminski, Roland; Kaufmann, Benjamin; Schaub, Torsten
This paper presents the concept of parallelisation of a solver for Answer Set Programming (ASP). While there already exist some approaches to parallel ASP solving, there was a lack of a parallel version of the powerful clasp solver. We implemented a parallel version of clasp based on message-passing. Experimental results on Blue Gene P/L indicate the potential of such an approach.
Transient molecular electro-optics Cartesian rotation vector versus Eulerian angles.
Evensen, Tom Richard; Elgsaeter, Arnljot; Naess, Stine Nalum
2007-04-15
Comparing the Euler angles, the classical choice of generalized coordinates describing the three rotational degrees of freedom of a rigid body, and the Cartesian rotation vector, we show that they both have their advantages and disadvantages in kinetic theory and Brownian dynamics analysis of molecular electro-optics. The Eulerian angles often yield relatively simple, yet singular, equations of motion, while their counterparts expressed in terms of Cartesian rotation vector are non-singular but more complex. In a special case, we show that the generalized force associated with the Cartesian rotation vector equals the torque. In addition, we introduce a new graphical approach to qualitatively track how changes in the Eulerian angles affect the Cartesian rotation vector.
Eulerian CFD modeling and X-ray validation of non-evaporating diesel spray
NASA Astrophysics Data System (ADS)
Xue, Qingluan; Som, Sibendu; Quan, Shaoping; Pomraning, Eric; Senecal, P. K.
2013-11-01
This work implemented an Eulerian single-phase approach by Vallet et al. into CFD software (Convergent) for diesel spray simulations. This Eulerian approach considers liquid and gas phase as a complex mixture of a single flow with a highly variable density to describe the near nozzle dense sprays. The mean density is obtained form the Favre-averaged liquid mass fraction. Liquid mass fraction is transported with a model for the turbulent liquid diffusion flux into the gas. A mean gradient-based model is employed for the diffusion flux in this study. A non-evaporating diesel spray was measured using x-ray radiography at Argonne National Laboratory. The quantitative and time-resolved data of liquid penetration and mass distribution in the dense spray region are used to validate this approach. The different turbulence models are also used for the simulations. The comparison between the simulated results and experimental data and the turbulence model effect are discussed.
Comparison of Direct Eulerian Godunov and Lagrange Plus Remap, Artificial Viscosity Schemes
Pember, R B; Anderson, R W
2001-03-30
The authors compare two algorithms for solving the equations of unsteady inviscid compressible flow in an Eulerian frame: a staggered grid, Lagrange plus remap artificial viscosity scheme and a cell-centered, direct Eulerian higher-order Godunov scheme. They use the two methods to compute solutions to a number of one- and two-dimensional problems. The results show the accuracy of the two schemes to be generally equivalent. In a 1984 survey paper by Woodward and Colella, the Lagrange plus remap approach did not compare favorably with the higher-order Godunov methodology. They examine, therefore, how certain features of the staggered grid scheme considered here contribute to its improved accuracy. The critical features are shown to be the use of a monotonic artificial viscosity in the Lagrange step and, in the remap step, the use of a corner transport upwind scheme with van Leer limiters in conjunction with separate advection of internal and kinetic energies.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
NASA Astrophysics Data System (ADS)
Darlington, Rebecca Mattson
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
Darlington, Rebecca Mattson
1999-12-01
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.
NASA Astrophysics Data System (ADS)
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2016-10-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.
Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
Villa, Eleonora; Maino, Davide; Matarrese, Sabino E-mail: sabino.matarrese@pd.infn.it
2014-06-01
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the Eulerian to the Lagrangian frame in the Newtonian approximation.
A Comparison of Two Intermediate State HLLC Solvers for Ideal Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Gurski, K. F.
2008-04-01
This paper compares a solver based on the HLLC (Harten-Lax-van Leer-contact wave) approximate nonlinear Riemann solver for gas dynamics for ideal magnetohydrodynamics (MHD) with the HLL, Roe, Linde, and Li solvers. Simulation results are given for three one-dimensional test cases not previously shown in the original paper presenting the smooth HLLC solver for MHD.
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-05-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
NASA Astrophysics Data System (ADS)
Antón, Luis; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Aloy, Miguel A.; Mimica, Petar
2010-05-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Lagrangian and Eulerian Methods for the Identification of Water Vapour Sources and Transport
NASA Astrophysics Data System (ADS)
Sodemann, H.; Schwierz, C.; Wernli, H.
2006-12-01
Diagnostics of the hydrological cycle are an important component of detection and attribution of climate variability. The hydrological cycle is a key component of the climate system, but due to the scale of evaporation and condensation processes, NWP models rely heavily on parameterizations. Evaluations of reanalysis datasets show biases of the hydrological cycle that are created during data assimilation, rendering these data one of the less reliable components of reanalysis products. We present two novel approaches to identify the sources and transport paths of atmospheric water vapor from analysis or reanalysis data, one of Lagrangian, and one of Eulerian nature. The Lagrangian method is based on back-trajectories, and diagnoses the evaporative sources of water vapor in high spatial detail. The method is exemplified with an examination of the inter-annual variability of the moisture sources for winter-time precipitation in Greenland, and the seasonality of the moisture sources for Alpine precipitation, based on ECMWF's ERA-40 reanalysis data. The Eulerian method makes use of a regional climate model that has been fitted with a mass-conservative water vapor tracer. This provides a novel possibility to evaluate the representation of the model's hydrological cycle in detail, and on a regional scale. The capabilities of the Eulerian method are exemplified with an identification of the moisture sources of the August 2002 flood, one of the strongest flood events in Central Europe in recent decades. A comparison of the two method indicates different preferential areas of application: the Lagrangian method being more suitable for gaining a large-scale picture, while the Eulerian method could provide detailed process understanding and be useful for NWP model evaluation. This in turn implies that a complementary view could potentially be gained when using such methods for evaluation purposes in combination with new observational data of the atmospheric hydrological cycle.
2011-01-01
DSMC) method17 was used to compute the gas flow . A Lagrangian technique was applied to model cluster evolution. Similar to Ref. 7, new clusters were...Eulerian approach for monomer gas flow based on the solution of Euler/Navier–Stokes equations, with the Lagrangian approach for cluster formation and...method is to cal- culate gas flow solving the compressible Euler or Navier– Stokes equation, model the nucleation process starting from the dimer
2012-09-30
codes are parallelized using message passing interface (MPI) based on domain decomposition. For SPH , graphics processing unit (GPU) computing, which is...aims at developing a numerical capability using a Lagrangian Smoothed Particle Hydrodynamics ( SPH ) method and an Eulerian Level-Set Method (LSM) for...the SPH and LSM with environmental input provided by coupled wind and wave simulations at far field; (2) Use the numerical method developed in (1
A robust multilevel simultaneous eigenvalue solver
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
Benchmarking transport solvers for fracture flow problems
NASA Astrophysics Data System (ADS)
Olkiewicz, Piotr; Dabrowski, Marcin
2015-04-01
Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in geothermal systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. For example, geothermal energy is primarily transported by the flow of the heated water or steam rather than by the thermal diffusion. The geometry of the fracture network and the distribution of the mean apertures of individual fractures are the key parameters with regard to the fracture network transmissivity. Transport in fractures can occur through the combination of advection and diffusion processes like in the case of dissolved chemical components. The local distribution of the fracture aperture may play an important role for both flow and transport processes. In this work, we benchmark various numerical solvers for flow and transport processes in a single fracture in 2D and 3D. Fracture aperture distributions are generated by a number of synthetic methods. We examine a single-phase flow of an incompressible viscous Newtonian fluid in the low Reynolds number limit. Periodic boundary conditions are used and a pressure difference is imposed in the background. The velocity field is primarly found using the Stokes equations. We systematically compare the obtained velocity field to the results obtained by solving the Reynolds equation. This allows us to examine the impact of the aperture distribution on the permeability of the medium and the local velocity distribution for two different mathematical descriptions of the fracture flow. Furthermore, we analyse the impact of aperture distribution on the front characteristics such as the standard deviation and the fractal dimension for systems in 2D and 3D.
Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments
NASA Astrophysics Data System (ADS)
Chitta, Subhashini; Steinhoff, John
2015-11-01
In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.
Eulerian laser Doppler vibrometry: Online blade damage identification on a multi-blade test rotor
NASA Astrophysics Data System (ADS)
Oberholster, A. J.; Heyns, P. S.
2011-01-01
Laser Doppler vibrometry enables the telemetry-free measurement of online turbomachinery blade vibration. Specifically, the Eulerian or fixed reference frame implementation of laser vibrometry provides a practical solution to the condition monitoring of rotating blades. The short data samples that are characteristic of this measurement approach do however negate the use of traditional frequency domain signal processing techniques. It is therefore necessary to employ techniques such as time domain analysis and non-harmonic Fourier analysis to obtain useful information from the blade vibration signatures. The latter analysis technique allows the calculation of phase angle trends which can be used as indicators of blade health deterioration, as has been shown in previous work for a single-blade rotor. This article presents the results from tests conducted on a five-blade axial-flow test rotor at different rotor speeds and measurement positions. With the aid of artificial neural networks, it is demonstrated that the parameters obtained from non-harmonic Fourier analysis and time domain signal processing on Eulerian laser Doppler vibrometry signals can successfully be used to identify and quantify blade damage from among healthy blades. It is also shown that the natural frequencies of individual blades can be approximated from the Eulerian signatures recorded during rotor run-up and run-down.
An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces
NASA Astrophysics Data System (ADS)
Pooley, Benjamin C.; Robinson, James C.
2016-12-01
In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-Lagrangian" form which involves the back-to-labels map (the inverse of the trajectory map for each fixed time). In the same paper a local existence result is proved in certain Hölder spaces {C^{1,μ}}. We review the Eulerian-Lagrangian formulation of the equations and prove that given initial data in H s for {n ≥ 2} and {s > n/2+1}, a unique local-in-time solution exists on the n-torus that is continuous into H s and C 1 into H s-1. These solutions automatically have C 1 trajectories. The proof here is direct and does not appeal to results already known about the classical formulation. Moreover, these solutions are regular enough that the classical and Eulerian-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.
Unit physics performance of a mix model in Eulerian fluid computations
Vold, Erik; Douglass, Rod
2011-01-25
In this report, we evaluate the performance of a K-L drag-buoyancy mix model, described in a reference study by Dimonte-Tipton [1] hereafter denoted as [D-T]. The model was implemented in an Eulerian multi-material AMR code, and the results are discussed here for a series of unit physics tests. The tests were chosen to calibrate the model coefficients against empirical data, principally from RT (Rayleigh-Taylor) and RM (Richtmyer-Meshkov) experiments, and the present results are compared to experiments and to results reported in [D-T]. Results show the Eulerian implementation of the mix model agrees well with expectations for test problems in which there is no convective flow of the mass averaged fluid, i.e., in RT mix or in the decay of homogeneous isotropic turbulence (HIT). In RM shock-driven mix, the mix layer moves through the Eulerian computational grid, and there are differences with the previous results computed in a Lagrange frame [D-T]. The differences are attributed to the mass averaged fluid motion and examined in detail. Shock and re-shock mix are not well matched simultaneously. Results are also presented and discussed regarding model sensitivity to coefficient values and to initial conditions (IC), grid convergence, and the generation of atomically mixed volume fractions.
NASA Astrophysics Data System (ADS)
Fox, Rodney O.; Vie, Aymeric; Laurent, Frederique; Chalons, Christophe; Massot, Marc
2012-11-01
Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, Eulerian methods can be used to solve for the moments of the NDF resulting in an unclosed Eulerian system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the Eulerian models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. Research carried out at the Center for Turbulence Research 2012 Summer Program.
A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing
NASA Technical Reports Server (NTRS)
Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo
2009-01-01
The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.
2005-12-01
IMPACT AND 5b. GRANT NUMBER SHOCK LOADING USING A SHARP-INTERFACE EULERIAN METHODOLOGY 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER H. S...ABSTRACT Numerical methods and a computer code have been developed for the simulation of multimaterial interactions in a general setting...by ANSI Std. Z39.18 FINAL REPORT PREDICTION AND ANALYSIS OF MATERIAL RESPONSE TO IMPACT AND SHOCK LOADING USING A SHARP-INTERFACE EULERIAN METHODOLOGY
A Comparison of Stiff ODE Solvers for Astrochemical Kinetics Problems
NASA Astrophysics Data System (ADS)
Nejad, Lida A. M.
2005-09-01
The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE solver packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE solvers. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct solver routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of solvers, the ordering and the chosen options. It is also shown that though a particular solver with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another solver can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE
Quantitative analysis of numerical solvers for oscillatory biomolecular system models
Quo, Chang F; Wang, May D
2008-01-01
Background This article provides guidelines for selecting optimal numerical solvers for biomolecular system models. Because various parameters of the same system could have drastically different ranges from 10-15 to 1010, the ODEs can be stiff and ill-conditioned, resulting in non-unique, non-existing, or non-reproducible modeling solutions. Previous studies have not examined in depth how to best select numerical solvers for biomolecular system models, which makes it difficult to experimentally validate the modeling results. To address this problem, we have chosen one of the well-known stiff initial value problems with limit cycle behavior as a test-bed system model. Solving this model, we have illustrated that different answers may result from different numerical solvers. We use MATLAB numerical solvers because they are optimized and widely used by the modeling community. We have also conducted a systematic study of numerical solver performances by using qualitative and quantitative measures such as convergence, accuracy, and computational cost (i.e. in terms of function evaluation, partial derivative, LU decomposition, and "take-off" points). The results show that the modeling solutions can be drastically different using different numerical solvers. Thus, it is important to intelligently select numerical solvers when solving biomolecular system models. Results The classic Belousov-Zhabotinskii (BZ) reaction is described by the Oregonator model and is used as a case study. We report two guidelines in selecting optimal numerical solver(s) for stiff, complex oscillatory systems: (i) for problems with unknown parameters, ode45 is the optimal choice regardless of the relative error tolerance; (ii) for known stiff problems, both ode113 and ode15s are good choices under strict relative tolerance conditions. Conclusions For any given biomolecular model, by building a library of numerical solvers with quantitative performance assessment metric, we show that it is possible
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
NASA Astrophysics Data System (ADS)
Daude, F.; Galon, P.
2016-01-01
Computation of compressible two-phase flows with the unsteady compressible Baer-Nunziato model in conjunction with the moving grid approach is discussed in this paper. Both HLL- and HLLC-type Finite-Volume methods are presented and implemented in the context of Arbitrary Lagrangian-Eulerian formulation in a multidimensional framework. The construction of suitable numerical methods is linked to proper approximations of the non-conservative terms on moving grids. The HLL discretization follows global conservation properties such as free-stream preservation and uniform pressure and velocity profiles preservation on moving grids. The HLLC solver initially proposed by Tokareva and Toro [1] for the Baer-Nunziato model is based on an approximate solution of local Riemann problems containing all the characteristic fields present in the exact solution. Both ;subsonic; and ;supersonic; configurations are considered in the construction of the present HLLC solver. In addition, an adaptive 6-wave HLLC scheme is also proposed for computational efficiency. The methods are first assessed on a variety of 1-D Riemann problems including both fixed and moving grids applications. The methods are finally tested on 2-D and 3-D applications: 2-D Riemann problems, a 2-D shock-bubble interaction and finally a 3-D fluid-structure interaction problem with a good agreement with the experiments.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the
Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
1997-01-01
Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.
EUPDF-II: An Eulerian Joint Scalar Monte Carlo PDF Module : User's Manual
NASA Technical Reports Server (NTRS)
Raju, M. S.; Liu, Nan-Suey (Technical Monitor)
2004-01-01
EUPDF-II provides the solution for the species and temperature fields based on an evolution equation for PDF (Probability Density Function) and it is developed mainly for application with sprays, combustion, parallel computing, and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase CFD and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with an understanding of the various models involved in the PDF formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. The source code of EUPDF-II will be available with National Combustion Code (NCC) as a complete package.
Performance Models for the Spike Banded Linear System Solver
Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...
2011-01-01
With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated
The novel high-performance 3-D MT inverse solver
NASA Astrophysics Data System (ADS)
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
Adaptive kinetic-fluid solvers for heterogeneous computing architectures
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2015-12-01
We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24 × 24 × 24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.
Two Solvers for Tractable Temporal Constraints with Preferences
NASA Technical Reports Server (NTRS)
Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)
2002-01-01
A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time on the basis of preferences. Soft temporal constraints problems allow to describe in a natural way scenarios where events happen over time and preferences are associated to event distances and durations. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. We describe two solvers based on two different approaches for solving the same tractable subclass. For each solver we present the theoretical results it stands on, a description of the algorithm and some experimental results. The random generator used to build the problems on which tests are performed is also described. Finally, we compare the two solvers highlighting the tradeoff between performance and representational power.
Overset Techniques for Hypersonic Multibody Configurations with the DPLR Solver
NASA Technical Reports Server (NTRS)
Hyatt, Andrew James; Prabhu, Dinesh K.; Boger, David A.
2010-01-01
Three unit problems in shock-shock/shock-boundary layer interactions are considered in the evaluation overset techniques with the Data Parallel Line Relaxation (DPLR) computational fluid dynamics solver, a three dimensional Navier-Stokes solver . The unit problems considered are those of two stacked hemispherical cylinders (of different diameters and lengths, and at various orientations relative to each other or relative to the nozzle axis) tested in a hypersonic wind tunnel. These problems are taken as representative of a Two-Stage-To-Orbit design. The objective of the present presentation would be to discuss the techniques used to develop suitable overset grid systems and then evaluate their respective solutions by comparing to corresponding point matched grid solutions and experimental data. Both successful and unsuccessful techniques would be discussed. All solutions would be calculated using the DPLR solver and SUGGAR will be used to develop the domain connectivity information.
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
NASA Astrophysics Data System (ADS)
Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel
2017-01-01
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and
Numerical System Solver Developed for the National Cycle Program
NASA Technical Reports Server (NTRS)
Binder, Michael P.
1999-01-01
As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.
Convergence acceleration of an aeroelastic Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Obayashi, S.; Guruswamy, G.
1994-01-01
New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.
A Eulerian-Lagrangian Model to Simulate Two-Phase/Particulate Flows
NASA Technical Reports Server (NTRS)
Apte, S. V.; Mahesh, K.; Lundgren, T.
2003-01-01
Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an Eulerian-Lagrangian technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on Eulerian-Lagrangian technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on Eulerian-Lagrangian techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.
Inferring methane fluxes at a larch forest using Lagrangian, Eulerian, and hybrid inverse models
NASA Astrophysics Data System (ADS)
Ueyama, Masahito; Takanashi, Satoru; Takahashi, Yoshiyuki
2014-10-01
Measuring methane (CH4) flux at upland forests is challenging due to high levels of heterogeneity in upscaling chamber measurements and the detection limits of currently available micrometeorological methods. We estimated CH4 fluxes in an upland forest from vertical concentration profiles using three different inverse multilayer models: the Lagrangian localized near field theory, Eulerian, and hybrid Lagrangian-Eulerian models. The approach could estimate spatially representative fluxes, and use of higher gradients within canopies than above them could minimize uncertainties associated with sensor noises. Comparing fluxes by the models and measurements by the micrometeorological hyperbolic relaxed eddy accumulation and chamber methods, daytime fluxes were reasonably reproduced, but nighttime fluxes were overestimated most likely due to an underestimation of stable conditions and storage effects. The models and measurements show that the forest acted as a CH4 sink during the study period, and the soil acted as the dominant sink. The estimated sink increased with increasing soil temperatures and decreasing soil water content. The CH4 sink estimated during the study period were 1.5 ± 0.2 nmol m-2 s-1 by the micrometeorological method, 2.4 ± 0.5 nmol m-2 s-1 by chambers, 2.8 ± 1.1 nmol m-2 s-1 by the Lagrangian model, 2.7 ± 1.0 nmol m-2 s-1 by the Eulerian model, and 3.7 ± 2.8 nmol m-2 s-1 by the hybrid model. The performance of the Lagrangian and hybrid models increased when the CH4 sink/source was assumed to only exist in the soil.
NASA Astrophysics Data System (ADS)
Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.
2011-04-01
This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, to improve the reproducibility of tracer-gas variations affected by the near-field surface emissions and transport around observation sites. The ability to resolve variability in atmospheric composition on an hourly time-scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and from upcoming space-based observations. The coupled model yields an increase in the horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling computationally efficient global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at three sites: two operated by the National Oceanic and Atmospheric Administration, USA, and one operated by the National Institute for Environmental Studies, Japan. As the goal of this study is limited to introducing the new modeling approach, we selected a transport simulation at these three sites to demonstrate how the model may perform at various geographical areas. The coupled model provides improved agreement between modeled and observed CO2 concentrations in comparison to the Eulerian model. In an area where variability in CO2 concentration is dominated by a fossil fuel signal, the correlation coefficient between modeled and observed concentrations increases by between 0.05 to 0.1 from the original values of 0.5-0.6 achieved with the Eulerian model.
Computational Transonic Flutter Solutions for Cranked Wings by the Direct Eulerian-Lagrangian Method
NASA Astrophysics Data System (ADS)
Mellquist, Erik Charles
In this dissertation, a three-dimensional computational aeroelastic simulation for cranked, highly-swept wings is developed, and solutions are presented for several wing models. The computational model is a fully nonlinear coupled fluid-structure simulation based on the Direct Eulerian-Lagrangian coupling methodology. The wing is modeled using nonlinear modified von Karman plate finite elements. Large deformation is accounted for through the use of element-attached local coordinate systems referenced to a single global coordinate system. The fluid is modeled using the mixed Eulerian-Lagrangian formulation of the classical Euler equations and is discretized using a Galerkin finite element approach on an unstructured tetrahedral mesh. The fluid and structural models are coupled by the Direct Eulerian-Lagrangian method where the finite-element shape functions and the local element coordinate systems are used to describe the fluid-structure boundary without approximation. Time synchronization and spatial accuracy are maintained to ensure accurate exchange of energy between the fluid and the structure. The computational solutions exhibit multiple types of aeroelastic response including transonic limit cycle flutter at a wide range of dynamic pressures, subsonic and supersonic bending-torsion flutter at higher dynamic pressures and a wide range of Mach numbers, and limit cycle oscillation dependent on both Mach number and angle of attack. Shock motion dependent on wing deformation is shown to play a major role in determining the response of the wings, and, depending on the flow conditions, can either stabilize or destabilize the response. Results from the simulations correlate closely with observed wind tunnel test responses.
Preliminary Benchmarking of Plinian Eruption Simulations Using an Adaptive Grid Eulerian Technique
NASA Astrophysics Data System (ADS)
Peterson, A. H.; Ogden, D. E.; Wohletz, K. H.; Gisler, G.; Glatzmaier, G. A.
2005-12-01
The SAGE (SAIC Adaptive Grid Eulerian) code is an Eulerian hydrodynamics numerical technique employing adaptive mesh refinement at each cycle for every cell in 1-, 2-, and 3-D grids. It is primarily designed to solve high deformation flow of multiple materials and thus provides important capabilities for simulating volcanic eruption phenomena. Its multimaterial equation of state libraries includes a comprehensive coverage of water from solid ice through two-phase liquid and vapor to supercritical states approaching the Hugoniot, and extremely important aspect for simulating volcanic gases in general. In development are strength and failure rules that model non-Newtonian fluid/solid deformation. Because of the low effective sound speeds of eruptive mixtures, the facts that SAGE uses a piecewise, linear, multi-material, Gudonov numerical method to resolve shocks with second-order precision and exactly conserves mass, momentum, and energy, are a highly desirable attributes. Although this code has been previously used to simulate a volcanic eruption (i.e., eruption through a crater lake at Ruapehu volcano by Morrissey and Gisler), we are embarking in an effort to benchmark the code with CFDLib, a well-validated arbitrary Lagrangian-Eulerian code developed at Los Alamos National Laboratory. Through this effort we expect to better understand the strengths and weaknesses, the limitations, and provide direction for important enhancement of SAGE, and potentially provide the volcanological community with a powerful alternative to numerical codes currently available. At this point in our benchmarking, we demonstrate some results for fluid convection within a chamber and fluid jetting through a conduit.
Assimilation of drifter observations for the reconstruction of eulerian circulation field.
NASA Astrophysics Data System (ADS)
Molcard, A.; Ozgokmen, T.; Piterbarg, L.; Griffa, A.
2003-04-01
In light of the increasing number of drifting buoys in the ocean, and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin-experiments using a reduced-gravity, quasi-geostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation and uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of Eulerian data, such as fixed-point velocities. Overall the results are very favorable for the assimilation of Lagrangian observations to improve the Eulerian velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in the range of 20-50% of the Lagrangian integral time scale of the flow field. The method is extended to primitive equation ocean models by using a dynamical relationship between velocity components and layer thickness based on geostrophy. The method is implemented in an idealized MICOM of midlatitude circulation, and performances of three different techniques, Pseudo-Lagrangian OI, Lagrangian OI and Pseudo-Lagrangian Kalman Filter (based on Chin et al., 1999) are compared using a comprehensive set of experiments. The main finding of this study is that two different strategies of data assimilation are simultaneously supported: (i) the strategy of adopting well
Turbidity Current Transport using DEM and FEM: a Hybrid Lagrangian-Eulerian Approach
NASA Astrophysics Data System (ADS)
Alves, J. L.; Guevara, N. O., Jr.; Silva, C. E.; Alves, F. T.; Gazoni, L. C.; Coutinho, A.; Camata, J.; Elias, R. N.; Paraizo, P.
2013-05-01
In this work we describe a contribution to the study of turbidity transport in scales smaller than TFM (two-fluid models), The intent of the work, part of a large scale simulation project, is to assess local, small scale parameters and their upscaling. The hybrid model is based on a Lagrangian-Eulerian approach under a class of the so called Unresolved Discrete Particle Method (UDPM). In this approach, a Lagrangian description is used for the particle system employing the Discrete Element Method (DEM) while a fixed Eulerian mesh is used for the fluid phase modeled by finite element method (FEM), Fluid motion is governed by Navier-Stokes equations which are solved by an appropriate FEM implementation. Closure equation are used to compute drag and lift forces over the particles in the DEM framework. Volume averaged momentum sink terms are included in the fluid equations. The resulting coupled DEM-FEM model is integrated in time with a subcycling scheme. The aforementioned scheme was applied in the simulation of a sedimentation basin as depicted in figures 1 and 2 to investigate flow and deposition features of the suspension in a finer scale. For this purpose a submodel of the basin was generated. Mapping variables back and forth the Eulerian (finite element) model and the Lagrangian (discrete element) model were performed during the subcycled integration of the hybrid model. References: [1] Hoomans, B.P.B., Kuipers, J.A.M., Swaaij, van W.P.M," Granular dynamics Simulation of segregation phenomena in bubbling gas-fluidised beds", Powder Technology, V 109, Issues 1-3, 3 April 2000, pp 41-48; [2] Cho, S.H., Choi,H.G, Yoo, J.Y.,"Direct numerical simulation of fluid flow laden with many particles", International Journal of Multiphase Flow, V 31, Issue 4, April 2005, pp 435-451;; Sedimentation basin: sectioning the turbidity plume in the Eulerian FE model for setting up the discrete particle model. ; Sedimentation Basin: section of the turbidity plume displaying the
Modeling erosion in a centrifugal pump in an Eulerian-Lagrangian frame using OpenFOAM®
NASA Astrophysics Data System (ADS)
Lopez, Alejandro; Stickland, Matthew; Dempster, William
2015-07-01
Erosion induced by solid particle impingement is a very commonwear mechanism in turbomachinery and Computational Fluid Dynamics is one of the most widely used tools for its prediction. In this article, erosion is modeled in one of the channels of a centrifugal pump using OpenFOAM®,which is an Open Source CFD package. A review of some of the most commonly used erosion models is carried out in an Eulerian-Lagrangian frame along with a comparative study of the erosion rates obtained with each model. Results yielded some disparities between models due to the different factors taken into consideration. The mesh is then deformed to obtain the resulting eroded geometry.
NASA Astrophysics Data System (ADS)
Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Dlugokencky, E. J.; Tans, P. P.; Maksyutov, S. S.
2013-12-01
Global monthly CO2 flux distributions for 2001-2011 were estimated using an atmospheric inverse modeling system, which is based on combination of two transport models, called GELCA (Global Eulerian-Lagrangian Coupled Atmospheric model). This coupled model approach has several advantages over inversions to a single model alone: the use of Lagrangian particle dispersion model (LPDM) to simulate the transport in the vicinity of the observation points enables us to avoid numerical diffusion of Eulerian models, and is suitable to represent observations at high spatial and temporal resolutions. The global background concentration field generated by an Eulerian model is used as time-variant boundary conditions for an LPDM that performs backward simulations from each receptor point (observation event). In the GELCA inversion system, National Institute for Environmental Studies-Transport Model (NIES-TM) version 8.1i was used as an Eulerian global transport model coupled with FLEXPART version 8.0 as an LPDM. The meteorological fields for driving both models were taken from JMA Climate Data Assimilation System (JCDAS) with a spatial resolution of 1.25° x 1.25°, 40 vertical levels and a temporal resolution of 6 hours. Our prior CO2 fluxes consist of daily terrestrial biospheric fluxes, monthly oceanic fluxes, monthly biomass burning emissions, and monthly fossil fuel CO2 emissions. We employed a Kalman Smoother optimization technique with fixed lag of 3 months, estimating monthly CO2 fluxes for 42 land and 22 ocean regions. We have been using two different global networks of CO2 observations. The Observation Package (ObsPack) data products contain more measurement information in space and time than the NOAA global cooperative air sampling network which basically consists of approximately weekly sampling at background sites. The global total flux and its large-scale distribution optimized with two different global observation networks agreed overall with other previous
Covariant formulation of the governing equations of continuum mechanics in an Eulerian description
NASA Astrophysics Data System (ADS)
Schöberl, Markus; Schlacher, Kurt
2007-05-01
We present the balance relations for a continuum in the Eulerian formulation in a pure covariant fashion. Based on the analysis of nonrelativistic particle mechanics, we adapt the covariant description to the case of a continuum. The use of the covariant Nijenhuis differential as well as the splitting of the vertical configuration bundle are the key objects that allow a coordinate-free representation. We state the balance equations such that they are valid, also when time variant transformations are applied, which leads to a nontrivial space-time connection and a metric which explicitly depends on the time.
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
NASA Astrophysics Data System (ADS)
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.
A second order Lagrangian Eulerian momentum bounded method for multiphase flows
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Pitsch, Heinz
2011-11-01
A Lagrangian Eulerian framework relying on both Level Set and Volume of Fluid methods is presented in the context of multiphase flow computations. The resulting interface capturing scheme is shown to preserve planarity, and to conserve mass exactly for solenoidal and linear velocity fields. A novel fractional step approach for the incompressible Navier Stokes equation is also presented. The proposed scheme relies on a consistent transport of volume fraction and momentum fields, which also preserves velocity boundedness. A sharp interface projection step is derived accordingly. The algorithm is shown to conserve momentum exactly for solenoidal linear velocity, and to lead to robust computations. Supported by NASA under Subsonic Fixed Wing project.
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Andreussi, T.; Pegoraro, F.
2016-10-01
In a series of papers we have investigated general properties of equilibria and their stability in each of the Lagrangian, Eulerian, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. DOE DE-FG02-04ER-54742.
NASA Astrophysics Data System (ADS)
Cerminara, Matteo; Esposti Ongaro, Tomaso; Carlo Berselli, Luigi
2014-05-01
We have developed a compressible multiphase flow model to simulate the three-dimensional dynamics of turbulent volcanic ash plumes. The model describes the eruptive mixture as a polydisperse fluid, composed of different types of gases and particles, treated as interpenetrating Eulerian phases. Solid phases represent the discrete ash classes into which the total granulometric spectrum is discretized, and can differ by size and density. The model is designed to quickly and accurately resolve important physical phenomena in the dynamics of volcanic ash plumes. In particular, it can simulate turbulent mixing (driving atmospheric entrainment and controlling the heat transfer), thermal expansion (controlling the plume buoyancy), the interaction between solid particles and volcanic gas (including kinetic non-equilibrium effects) and the effects of compressibility (over-pressured eruptions and infrasonic measurements). The model is based on the turbulent dispersed multiphase flow theory for dilute flows (volume concentration <0.001, implying that averaged inter-particle distance is larger than 10 diameters) where particle collisions are neglected. Moreover, in order to speed up the code without losing accuracy, we make the hypothesis of fine particles (Stokes number <0.2 , i.e., volcanic ash particles finer then a millimeter), so that we are able to consider non-equilibrium effects only at the first order. We adopt LES formalism (which is preferable in transient regimes) for compressible flows to model the non-linear coupling between turbulent scales and the effect of sub-grid turbulence on the large-scale dynamics. A three-dimensional numerical code has been developed basing on the OpenFOAM computational framework, a CFD open source parallel software package. Numerical benchmarks demonstrate that the model is able to capture important non-equilibrium phenomena in gas-particle mixtures, such as particle clustering and ejection from large-eddy turbulent structures, as well
Intellectual Abilities That Discriminate Good and Poor Problem Solvers.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
1981-01-01
This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…
Time-varying Riemann solvers for conservation laws on networks
NASA Astrophysics Data System (ADS)
Garavello, Mauro; Piccoli, Benedetto
We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Elman, Howard C
2013-01-27
This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).
Coordinate Projection-based Solver for ODE with Invariants
Serban, Radu
2008-04-08
CPODES is a general purpose (serial and parallel) solver for systems of ordinary differential equation (ODE) with invariants. It implements a coordinate projection approach using different types of projection (orthogonal or oblique) and one of several methods for the decompositon of the Jacobian of the invariant equations.
Hypersonic simulations using open-source CFD and DSMC solvers
NASA Astrophysics Data System (ADS)
Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.
2016-11-01
Hypersonic hybrid hydrodynamic-molecular gas flow solvers are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics solver named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD solver. In this paper, further testing is performed, in particular with the CFD solver, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.
PSH3D fast Poisson solver for petascale DNS
NASA Astrophysics Data System (ADS)
Adams, Darren; Dodd, Michael; Ferrante, Antonino
2016-11-01
Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed a parallel solver of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear solver in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS solver does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.
Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers
Wang, Jun; Luo, Ray
2009-01-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
ERIC Educational Resources Information Center
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Parallel Solver for H(div) Problems Using Hybridization and AMG
Lee, Chak S.; Vassilevski, Panayot S.
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Modeling of combustion processes of stick propellants via combined Eulerian-Lagrangian approach
NASA Technical Reports Server (NTRS)
Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.
1988-01-01
This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined Eulerian-Lagrangian approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the Eulerian approach is obtained; governing equations for the stick propellants are formulated using the Lagrangian approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.
Two-way Interaction of Lagrangian Bubble Dynamics and Eulerian Mixture Flow Field
NASA Astrophysics Data System (ADS)
Choi, Jin-Keun; Hsiao, Chao-Tsung; Chahine, Georges
2007-11-01
Although under simple flow conditions a well dispersed bubble cloud in a liquid can be modeled with an Eulerian continuum model, the fine scale interactions between the two phases, the potential non-uniformities and high bubble concentrations in stiff gradient regions of complex flows can only be represented by more detailed numerical models such as Lagrangian tracking of individual bubbles. To meet both needs of describing individual bubbles and of including the collective effects in the two-phase continuum, we have developed a method coupling in a two-way fashion the two approaches. The bubble dynamics and tracking scheme is based on extensive studies on bubble dynamics and interactions at Dynaflow and is based on a Surface Averaged Pressure spherical model using a modified incompressible Rayleigh-Plesset equation or a modified compressible Gilmore equation. The bubbles presence in the Eulerian flow field is considered through a variable medium density formulation resulting from the instantaneous bubble population distribution in the field. The developed method is applicable to many practical flows in pipes, jets, pumps, propellers, ships, and the ocean. We present the method and its application to waterjet thrust augmentation by bubble injection.
NASA Astrophysics Data System (ADS)
Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.
2010-11-01
This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, for reproducibility of tracer gas variation affected by near field around observation sites. The ability to resolve variability in atmospheric composition on an hourly time scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and upcoming space-based observations. The coupled model yields increased horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at two sites operated by the National Oceanic and Atmospheric Administration, USA and one site operated by National Institute for Environmental Studies, Japan. As the purpose of this study is limited to demonstration of the new modeling approach, we select a small subset of 3 sites to highlight use of the model in various geographical areas. To explore the capability of the coupled model in simulating synoptic-scale meteorological phenomena, we calculate the correlation coefficients and variance ratios between deseasonalized model-simulated and observed CO2 concentrations. Compared with the Eulerian model alone, the coupled model yields improved agreement between modeled and observed CO2 concentrations.
Chaos in an Eulerian Based Model of Sickle Cell Blood Flow
NASA Astrophysics Data System (ADS)
Apori, Akwasi; Harris, Wesley
2001-11-01
A novel Eulerian model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This Eulerian model was based on extending previous models of sickle cell blood flow which were limited due to their Lagrangian formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.
Full-Eulerian fluid-structure coupling simulation of hyperelastic channel flow
NASA Astrophysics Data System (ADS)
Nagano, Naohiro; Sugiyama, Kazuyasu; Takeuchi, Shintaro; Satoshi, II; Takagi, Shu; Matsumoto, Yoichiro
2010-11-01
A full-Eulerian simulation for coupling a Newtonian fluid and hyperelastic material is conducted. The system involves an interaction problem between the fluid and hyperelastic walls and is driven by pressure difference, mimicking a blood flow in a blood vessel. A single set of the governing equations for the fluid and solid is employed, and a volume-of-fluid idea is employed to describe a multi-component geometry. The solid stress is defined in Eulerian frame by using a left Cauchy-Green deformation tensor, and the temporal change in the solid deformation is described by updating the tensor. The method employs a uniform fixed grid system for both fluid and solid and it does not require any mesh generation or reconstruction, aiming at facilitating the practical bio-mechanical fluid-structure analysis based on a medical image. The validity of the simulation results is established through comparison with a theoretical prediction. As an application of the present method, pulsating flows are simulated to demonstrate a nonlinear behavior of the flow rate on the pulsating amplitude, and an effect of employing an anisotropic hyperelastic material is discussed.
Numerical Simulation of the Friction Stir Welding Process Using Coupled Eulerian Lagrangian Method
NASA Astrophysics Data System (ADS)
Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.
2016-08-01
Friction Stir Welding (FSW) is a solid state joining process that relies on frictional heating and plastic deformation realized at the interaction between a non-consumable welding tool that rotates on the contact surfaces of the combined parts. The experiments are often time consuming and costly. To overcome these problems, numerical analysis has frequently been used in last years. Several simplified numerical models were designed to elucidate various aspects of the complex thermo-mechanical phenomena associated with FSW. This research investigates a thermo-mechanical finite element model based on Coupled Eulerian Lagrangian method to simulate the friction stir welding of the AA 6082-T6 alloy. Abaqus/cae software is used in order to simulate the welding stage of the Friction Stir Welding process. This paper presents the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Coupled Eulerian Lagrangian method.
NASA Astrophysics Data System (ADS)
Consalvi, Jean-Louis
2017-01-01
The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as `absorption Turbulence Radiation Interaction (TRI)' and `emission TRI'. Emission TRI is related to the non-linear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic Eulerian Field Model is used to solve the transport equation of the one-point one-time PDF. In this formulation, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic Eulerian Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed.
Simulation of brain mass effect with an arbitrary Lagrangian and Eulerian FEM.
Chen, Yasheng; Ji, Songbai; Wu, Xunlei; An, Hongyu; Zhu, Hongtu; Shen, Dinggang; Lin, Weili
2010-01-01
Estimation of intracranial stress distribution caused by mass effect is critical to the management of hemorrhagic stroke or brain tumor patients, who may suffer severe secondary brain injury from brain tissue compression. Coupling with physiological parameters that are readily available using MRI, eg, tissue perfusion, a non-invasive, quantitative and regional estimation of intracranial stress distribution could offer a better understanding of brain tissue's reaction under mass effect. A quantitative and sound measurement serving this particular purpose remains elusive due to multiple challenges associated with biomechanical modeling of the brain. One such challenge for the conventional Lagrangian frame based finite element method (LFEM) is that the mesh distortion resulted from the expansion of the mass effects can terminate the simulation prematurely before the desired pressure loading is achieved. In this work, we adopted an arbitrary Lagrangian and Eulerian FEM method (ALEF) with explicit dynamic solutions to simulate the expansion of brain mass effects caused by a pressure loading. This approach consists of three phases: 1) a Lagrangian phase to deform mesh like LFEM, 2) a mesh smoothing phase to reduce mesh distortion, and 3) an Eulerian phase to map the state variables from the old mesh to the smoothed one. In 2D simulations with simulated geometries, this approach is able to model substantially larger deformations compared to LFEM. We further applied this approach to a simulation with 3D real brain geometry to quantify the distribution of von Mises stress within the brain.
Migration of vectorized iterative solvers to distributed memory architectures
Pommerell, C.; Ruehl, R.
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
NASA Astrophysics Data System (ADS)
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
NASA Astrophysics Data System (ADS)
Bouttier, J.; Di Francesco, P.; Guitter, E.
2007-07-01
We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations.
ASHEE: a compressible, Equilibrium-Eulerian model for volcanic ash plumes
NASA Astrophysics Data System (ADS)
Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.
2015-10-01
A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations (Neri et al., 2003) for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model (Ferry and Balachandar, 2001), valid for low concentration regimes (particle volume fraction less than 10-3) and particles Stokes number (St, i.e., the ratio between their relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas-particle non-equilibrium effects. Direct numerical simulation accurately reproduce the dynamics of isotropic, compressible turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the
Eulerian frequency analysis of structural vibrations from high-speed video
NASA Astrophysics Data System (ADS)
Venanzoni, Andrea; De Ryck, Laurent; Cuenca, Jacques
2016-06-01
An approach for the analysis of the frequency content of structural vibrations from high-speed video recordings is proposed. The techniques and tools proposed rely on an Eulerian approach, that is, using the time history of pixels independently to analyse structural motion, as opposed to Lagrangian approaches, where the motion of the structure is tracked in time. The starting point is an existing Eulerian motion magnification method, which consists in decomposing the video frames into a set of spatial scales through a so-called Laplacian pyramid [1]. Each scale - or level - can be amplified independently to reconstruct a magnified motion of the observed structure. The approach proposed here provides two analysis tools or pre-amplification steps. The first tool provides a representation of the global frequency content of a video per pyramid level. This may be further enhanced by applying an angular filter in the spatial frequency domain to each frame of the video before the Laplacian pyramid decomposition, which allows for the identification of the frequency content of the structural vibrations in a particular direction of space. This proposed tool complements the existing Eulerian magnification method by amplifying selectively the levels containing relevant motion information with respect to their frequency content. This magnifies the displacement while limiting the noise contribution. The second tool is a holographic representation of the frequency content of a vibrating structure, yielding a map of the predominant frequency components across the structure. In contrast to the global frequency content representation of the video, this tool provides a local analysis of the periodic gray scale intensity changes of the frame in order to identify the vibrating parts of the structure and their main frequencies. Validation cases are provided and the advantages and limits of the approaches are discussed. The first validation case consists of the frequency content
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
NASA Astrophysics Data System (ADS)
Leung, Shingyu; Qian, Jianliang
2010-11-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2015-03-15
An algebraic mistake in the rendering of the Energy Casimir stability condition for a symmetric magnetohydrodynamics plasma configuration with flows made in the article Andreussi et al. “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected.
NASA Astrophysics Data System (ADS)
Tongne, A.; Robe, H.; Desrayaud, C.; Jahazi, M.; Feulvarch, E.
2016-10-01
A finite element model has been developed by means of a coupled Eulerian-Lagrangian approach. The banded structure which is related to the periodical material deposition is predicted in two dimensions as the experimental investigation shows that, during FSW with trigonal tool, the material flow operates mainly in the welded plates plan.
Carter, H H; Okubo, A; Wilson, R E; Sanderson, B; Pritchard, D W
1980-07-01
This research project addresses a fundamental problem in turbulence theory, the relation between Lagrangian and Eulerian statistics, by carrying out, analyzing, and interpreting a set of field experiments in the coastal waters off the south shore of Long Island. The study will not only provide information on the relation between the Lagrangian and Eulerian autocorrelations but also between the various experimental methods for quantitatively estimating turbulent diffusion. Two experiments, one in summer and one in winter, consisting of simultaneous measurements of dye diffusion, drogue dispersion, and Eulerian current velocities in a typical coastal locale were planned. In order to ensure a match between the Lagrangian (drogues, dye) scales of motion and the Eulerian (current meters) scales, however, a preliminary experiment, consisting of a 6 mooring current meter array and a short (approx. 3 hours) drogue experiment, was conducted during March 1980. Results of this preliminary experiment and their implications to the experimental program are discussed. The principal results were an improved design of our current meter array, and a wider variety of drogue experiments, i.e., multi-level, multi-scale, and continuous source simulation.
Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics
NASA Astrophysics Data System (ADS)
Spiegelman, M. W.; May, D.; Wilson, C. R.
2014-12-01
Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to
NASA Astrophysics Data System (ADS)
Haines, P. E.; Esler, J. G.
2014-02-01
A wide range of inverse problems in atmospheric transport and chemistry can be solved within the Eulerian backtracking framework. Here it is shown how a new and accurate numerical implementation can be used as an alternative to Lagrangian back trajectory methods in a wide class of process studies. As a key example, the question of how the (time-averaged) stratospheric flux of a finite lifetime chemical species depends upon the location(s) of its surface source(s) is addressed. The resulting sensitivity maps are demonstrated to be robust features of the global atmospheric circulation, with relatively low interannual variability. The maps serve as an at-a-glance resource for policymakers wishing to compare the likely impact of proposed emission locations for very short lived halogenated species on the total loading of stratospheric chlorine and bromine.
Convective weather events in high-frequency Eulerian observations and model column outputs
NASA Astrophysics Data System (ADS)
Mapes, B.
2006-05-01
Convective cloud systems produce large fractions of the Earth's rainfall. High-frequency Eulerian time-height datasets containing such convective storm passages permit clean, objective comparisons between observations and model output. Lagged regressions of these datasets vs. surface rainfall are used to depict the characteristic structure of precipitating disturbances, mainly in the wet tropics. Both observations and models have organized convective rain events with time scales of many hours, even though convection parameterizations (and arguably cumulus cells in nature) operate column by column and typically have no long-time memory. However, different models have very different characteristic structures: very different from observations (which are fairly similar from place to place), and very different from other models. Experiments with single-column versions suggest that this characteristic structure stems largely from the physical parameterizations.
NASA Astrophysics Data System (ADS)
Schroeder, Craig; Zheng, Wen; Fedkiw, Ronald
2012-02-01
We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels.
Recent developments of the arbitrary Lagrangian-Eulerian containment code ALICE-II. [LMFBR
Wang, C.Y.; Zeuch, W.R.
1983-01-01
The ANL arbitrary Lagrangian Eulerian containment code ALICE was developed for use in fast reactor containment studies and is particularly suited for problems involving complex fluid-structure interactions. Many improvements have been made which has resulted in a second version of the code, ALICE-II. A selection of some important improvements are given in this paper. To realistically analyze the above-core hydrodynamics containing a movable upper internal structure (UIS), a 3-D pipe element has been adopted to calculate the response of the UIS columns that connect the UIS to the vessel head. A corotational coordinate scheme for large displacement, small strain, elastic-plastic structural-dynamic analysis is utilized in the formulation. Both geometric and material nonlinearities are considered. The governing equations are integrated explicitly using a central difference procedure. Many sample problems are presented, including comparisons of ALICE-II and ICECO-CEL results on the APRICOT Phase 3 problems.
BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts
NASA Astrophysics Data System (ADS)
Polettini, Matteo
2015-09-01
We provide an exact expression for the statistics of the fluxes of Markov jump processes at all times, improving on asymptotic results from large deviation theory. The main ingredient is a generalization of the BEST theorem in enumeratoric graph theory to Eulerian tours with open ends. In the long-time limit we reobtain Sanov’s theorem for Markov processes, which expresses the exponential suppression of fluctuations in terms of relative entropy. The finite-time power-law term, increasingly important with the system size, is a spanning-tree determinant that, by introducing Grassmann variables, can be absorbed into the effective Lagrangian of a Fermionic ghost field on a metric space, coupled to a gauge potential. With reference to concepts in nonequilibrium stochastic thermodynamics, the metric is related to the dynamical activity that measures net communication between states, and the connection is made to a previous gauge theory for diffusion processes.
Anderson, R W; Pember, R B; Elliott, N S
2001-10-22
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
A new method that combines staggered grid arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
Pen, Ue-Yu; Chang, Mei-Chu; I, Lin
2013-02-01
We experimentally investigate the Lagrangian-Eulerian dynamics of fluid motion and wave-form evolution for a breaking shallow water wave approaching a slope by tracking tracer motions. It is found that, before breaking, the surface element can climb over the crest and exhibits cyclic oscillation with small forward drift. The increasing asymmetric tangential compression (accumulation) and rarefaction (depletion) in the crest front and the crest are the keys for the crest front steepening with the increasing particle cyclic excursion and forward Stoke drift. Eventually, the surface layer cannot climb over the crest with the vertical front. It curls up and forms an overhanging plunging jet leading the crest, while the lower flow still can reach the crest rear. This process leads to wave breaking with the rapid drop of crest height and the transition from slow divergence to rapid divergence of the adjacent fluid trajectories.
NASA Astrophysics Data System (ADS)
Schielicke, Lisa; Névir, Peter
2011-06-01
Various definitions of the intensity of atmospheric vortices exist. These definitions are often based on local parameters in a field. Otherwise, atmospheric vortices are analyzed concerning their geometric properties. A combination of both is rarely used. The aim of this publication is an expansion from a local, mass-specific view to a mass-related strength parameter, called atmospheric moment. The atmospheric moment is characterized by a combination of Eulerian parameters of intensity and Lagrangian aspects like track length and area of atmospheric vortices. The atmospheric moment is designed analogous to the seismic moment that describes the strength of earthquakes. Probability density distributions of tornadoes concerning their atmospheric moment show power law behavior. Compared with earthquakes, the scaling exponent is slightly smaller but of comparable order. In principle, this theoretical concept can also be applied to other atmospheric vortices like cyclones and hurricanes.
Benchmarking ICRF Full-wave Solvers for ITER
R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS
2011-01-06
Abstract Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.
Scalable Out-of-Core Solvers on Xeon Phi Cluster
D'Azevedo, Ed F; Chan, Ki Shing; Su, Shiquan; Wong, Kwai
2015-01-01
This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Kolev, Tzanio V.; Vassilevski, Panayot S.
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
A spectral Poisson solver for kinetic plasma simulation
NASA Astrophysics Data System (ADS)
Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf
2011-10-01
Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
A 3-D upwind Euler solver for unstructured meshes
NASA Technical Reports Server (NTRS)
Barth, Timothy J.
1991-01-01
A three-dimensional finite-volume upwind Euler solver is developed for unstructured meshes. The finite-volume scheme solves for solution variables at vertices of the mesh and satisfies the integral conservation law on nonoverlapping polyhedral control volumes surrounding vertices of the mesh. The schene achieves improved solution accuracy by assuming a piecewise linear variation of the solution in each control volume. This improved spatial accuracy hinges heavily upon the calculation of the solution gradient in each control volume given pointwise values of the solution at vertices of the mesh. Several algorithms are discussed for obtaining these gradients. Details concerning implementation procedures and data structures are discussed. Sample calculations for inviscid Euler flow about isolated aircraft wings at subsonic and transonic speeds are compared with established Euler solvers as well as experiment.
Verification and Validation Studies for the LAVA CFD Solver
NASA Technical Reports Server (NTRS)
Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.
2013-01-01
The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
An Upwind Solver for the National Combustion Code
NASA Technical Reports Server (NTRS)
Sockol, Peter M.
2011-01-01
An upwind solver is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new solver has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data.
On improving linear solver performance: a block variant of GMRES
Baker, A H; Dennis, J M; Jessup, E R
2004-05-10
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.
NASA Astrophysics Data System (ADS)
Georgiev, K.; Zlatev, Z.
2010-11-01
The Danish Eulerian Model (DEM) is an Eulerian model for studying the transport of air pollutants on large scale. Originally, the model was developed at the National Environmental Research Institute of Denmark. The model computational domain covers Europe and some neighbour parts belong to the Atlantic Ocean, Asia and Africa. If DEM model is to be applied by using fine grids, then its discretization leads to a huge computational problem. This implies that such a model as DEM must be run only on high-performance computer architectures. The implementation and tuning of such a complex large-scale model on each different computer is a non-trivial task. Here, some comparison results of running of this model on different kind of vector (CRAY C92A, Fujitsu, etc.), parallel computers with distributed memory (IBM SP, CRAY T3E, Beowulf clusters, Macintosh G4 clusters, etc.), parallel computers with shared memory (SGI Origin, SUN, etc.) and parallel computers with two levels of parallelism (IBM SMP, IBM BlueGene/P, clusters of multiprocessor nodes, etc.) will be presented. The main idea in the parallel version of DEM is domain partitioning approach. Discussions according to the effective use of the cache and hierarchical memories of the modern computers as well as the performance, speed-ups and efficiency achieved will be done. The parallel code of DEM, created by using MPI standard library, appears to be highly portable and shows good efficiency and scalability on different kind of vector and parallel computers. Some important applications of the computer model output are presented in short.
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
A contribution to the great Riemann solver debate
NASA Technical Reports Server (NTRS)
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
Menu-Driven Solver Of Linear-Programming Problems
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
A chemical reaction network solver for the astrophysics code NIRVANA
NASA Astrophysics Data System (ADS)
Ziegler, U.
2016-02-01
Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes
Scaling Algebraic Multigrid Solvers: On the Road to Exascale
Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M
2010-12-12
Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.
A Survey of Solver-Related Geometry and Meshing Issues
NASA Technical Reports Server (NTRS)
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
QED multi-dimensional vacuum polarization finite-difference solver
NASA Astrophysics Data System (ADS)
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M.; Walker, H.F.
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
Transonic Drag Prediction Using an Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Levy, David W.
2001-01-01
This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.
Error control of iterative linear solvers for integrated groundwater models.
Dixon, Matthew F; Bai, Zhaojun; Brush, Charles F; Chung, Francis I; Dogrul, Emin C; Kadir, Tariq N
2011-01-01
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of "forward error bound estimation" to explain the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed by the US Geological Survey and the California State Department of Water Resources, we observe that this error bound guides the choice of a practical measure for controlling the error in linear systems. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive Over-Relaxation (SOR) method, the most widely known iterative solver for nonsymmetric coefficient matrices. With forward error control, GMRES can easily replace the SOR method in legacy groundwater modeling packages, resulting in the overall simulation speedups as large as 7.74×. This research is expected to broadly impact groundwater modelers through the demonstration of a practical and general approach for setting the residual tolerance in line with the solution error tolerance and presentation of GMRES performance benchmarking results.
NASA Astrophysics Data System (ADS)
Winschall, A.; Pfahl, S.; Sodemann, H.; Wernli, H.
2014-07-01
Moisture convergence from different sources is an important prerequisite for a heavy-precipitation event. The contributions from different source regions can, however, hardly be quantified from observations, and their assessment based on model results is complex. Two conceptually different numerical methods are widely used for the quantification of moisture sources: Lagrangian approaches based on the analysis of humidity variations along backward trajectories and Eulerian methods based on the implementation of moisture tracers into a numerical model. In this study the moisture sources for a high-impact, heavy-precipitation event that affected eastern Europe in May 2010 are studied with both Eulerian and Lagrangian moisture source diagnostics. The precipitation event was connected to a cyclone that developed over northern Africa, moved over the Mediterranean towards eastern Europe and induced transport of moist air towards the Carpathian Mountains. Heavy precipitation and major flooding occurred in Poland, the Czech Republic and Slovakia between 16 and 18 May 2010. The Lagrangian and Eulerian diagnostics consistently indicate a wide spatial and temporal range of moisture sources contributing to the event. The source with the largest share is local evapotranspiration from the European land surface, followed by moisture from the North Atlantic. Further contributions come from tropical western Africa (10-20° N) and the Mediterranean Sea. Contrary to what could be expected, the Mediterranean contribution of about 10% is relatively small. A detailed analysis of exemplary trajectories corroborates the general consistency of the two approaches, and underlines their complementarity. The Lagrangian method allows for mapping out moisture source regions with computational efficiency, whereas the more elaborate Eulerian model requires predefined moisture sources, but includes also processes such as precipitation, evaporation and turbulent mixing. However, in the Eulerian model
Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.; Eder, D. C.; Gunney, B. T. N.; Masters, N. D.; Koniges, A. E.; Anderson, R. W.
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.; Sauer, Jeremy A.
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.
A New Robust Solver for Saturated-Unsaturated Richards' Equation
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Tartakovsky, D. M.
2012-12-01
We present a novel approach for the numerical integration of the saturated-unsaturated Richards' equation, a degenerate parabolic partial differential equation that models flow in porous media. The method is based on the mixed (pore pressure-water content) form of RE, written as a set of differential algebraic equations (DAEs) of index-1 for the fully saturated case and index-2 for the partially saturated case. A DAE-based approach allows us to overcome the numerical challenges posed by the degenerate nature of the Richards' equation. The resulting set of DAEs is solved using the stiffly-accurate, single-step, 3-stage implicit Runge-Kutta method Radau IIA, chosen for its favorable accuracy and stability properties, and its ease of implementation. For each time step a nonlinear system of equations on the intermediate Runge-Kutta states of the pore pressure is solved, written so to ensure that the next step pore pressure and water content correspond to one another correctly. The implementation of our approach compares favorably to state-of-the-art DAE-based solvers in both one- and two-dimensional simulations. These solvers use multi-step backward difference formulas together with a pressure-based form of Richards' equation. To the best of our knowledge, our method is the first instance of a successful DAE-based solver that uses the mixed form of Richards' equation. We consider this a promising line of research, with future work to be done on the use of globally convergent methods for the solution of the occurring nonlinear systems of equations.
Application of Aeroelastic Solvers Based on Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
2001-01-01
The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors
A Robust Compressible Flow Solver for Studies on Solar Fuel Production in Microwave Plasma
NASA Astrophysics Data System (ADS)
Tadayon Mousavi, Samaneh; Koelman, Peter; Groen, Pieter Willem; van Dijk, Jan; Epg/ Applied Physics/ Eindhoven University Of Technology Team; Dutch InstituteFundamental Energy Research (Differ) Team
2016-09-01
n order to simulate the dissociation of CO2 with H2O admixture by microwave plasma for the production of solar fuels, we need a multicomponent solver that is able to capture the complex nature of the plasma by combining the chemistry, flow, and electromagnetic field. To achieve this goal, first we developed a robust finite volume compressible flow solver in C++. The solver is implemented in the framework of the PLASIMO software and will be used in complete plasma simulations later on. Due to the compressible nature of the solver, it can be used for simulation of dissociation of CO2 with H2O admixture by supersonic expansion in microwave plasmas. A spatially second order version of this solver is able to reveal the vortex flow structure of the plasmas. Capabilities of this solver are presented by benchmarking against well-established analytical and numerical test cases.
A Simple Quantum Integro-Differential Solver (SQuIDS)
NASA Astrophysics Data System (ADS)
Argüelles Delgado, Carlos A.; Salvado, Jordi; Weaver, Christopher N.
2015-11-01
Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.
Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures
2008-10-01
iterations will be necessary to assure sufficient accuracy whenever we do not use a direct method to solve (1.3) or (1.5). The overall SPIKE algorithm...boosting is activated, SPIKE is not used as a direct solver but rather as a preconditioner. In this case outer iterations via a Krylov subspace method ...robustness. Preconditioning aims to improve the robustness of iterative methods by transforming the system into M−1Ax = M−1f, or AM−1(Mx) = f. (3.2
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring
NASA Technical Reports Server (NTRS)
Padovan, Joe; Kwang, Abel
1994-01-01
This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.
Algorithms for parallel flow solvers on message passing architectures
NASA Technical Reports Server (NTRS)
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
Reformulation of the Fourier-Bessel steady state mode solver
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.
NASA Astrophysics Data System (ADS)
Jarauta, Alex; Ryzhakov, Pavel; Secanell, Marc; Waghmare, Prashant R.; Pons-Prats, Jordi
2016-08-01
An embedded Eulerian-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an Eulerian formulation, whereas water is described with a Lagrangian framework. Using this framework, the gas-liquid interface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. The method naturally accounts for material property changes across the interface and accurately represents the pressure discontinuity. A sessile drop in a horizontal surface, a sessile drop in an inclined plane and droplets in a PEFC channel are solved for as numerical examples and compared to experimental data. Numerical results are in excellent agreement with experimental data. Numerical results are also compared to results obtained with the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach.
Pelanti, Marica; Bouchut, Francois; Mangeney, Anne
2011-02-01
We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2013-01-01
This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the Eulerian scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the Eulerian scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.
Implementation of the TEPLA Damage Model in a 3D Eulerian Hydrocode
NASA Astrophysics Data System (ADS)
Holian, Kathleen S.; Clancy, Sean P.; Maudlin, Paul J.
2007-06-01
A sophisticated damage model (TEPLA) has been implemented into a three-dimensional (Cartesian) computer code (Pagosa) used here at Los Alamos National Laboratory. TEPLA was originally an isotropic damage model based upon the Gurson flow surface (a potential function used in conjunction with the associated flow law) that models damage due to both porosity growth and plastic strain. It has since been modified to model anisotropic elastoplastic material strength as well. Pagosa is an Eulerian hydrodynamics code that has the following special features: a predictor-corrector Lagrangian step that advances the state variables in time, a high-order advection algorithm that remaps the problem back to the original mesh every time step, and a material interface tracking scheme with van Leer monotonic advection. It also includes a variety of equation of state, strength, fracture, and high explosive burn models. We will describe the physics of the TEPLA model (that models both strength and damage) and will show preliminary results of test problems that are used to validate the model. The four test problems (simple shear, stretching rod, Taylor anvil, and plate impact) can be compared with either analytic solutions or with experimental data.
NASA Astrophysics Data System (ADS)
Burkett, Michael W.; Clancy, Sean P.; Maudlin, Paul J.; Holian, Kathleen S.
2004-07-01
Previously developed constitutive models and solution algorithms for continuum-level anisotropic elastoplastic material strength and an isotropic damage model TEPLA have been implemented in the three-dimensional Eulerian hydrodynamics code known as CONEJO. The anisotropic constitutive modeling is posed in an unrotated material frame of reference using the theorem of polar decomposition to compute rigid-body rotation. TEPLA is based upon the Gurson flow surface (a potential function used in conjunction with the associated flow law). The original TEPLA equation set has been extended to include anisotropic elastoplasticity and has been recast into a new implicit solution algorithm based upon an eigenvalue scheme to accommodate the anisotropy. This algorithm solves a two-by-two system of nonlinear equations using a Newton-Raphson iteration scheme. Simulations of a shaped-charge jet formation, a Taylor cylinder impact, and an explosively loaded hemishell were selected to demonstrate the utility of this modeling capability. The predicted deformation topology, plastic strain, and porosity distributions are shown for the three simulations.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Staten, Matthew L.; Owen, Steven James
2010-09-01
Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.
Eulerian-Lagrangian Simulations of Bubbly Flows in A Vertical Square Duct
NASA Astrophysics Data System (ADS)
Liu, Rui; Vanka, Surya P.; Thomas, Brian G.
2013-11-01
We report results of Eulerian-Lagrangian simulations of developing upward and downward bubbly flows in a vertical square duct with a bulk Reynolds number of 5000. The continuous fluid is simulated with DNS, solving the Navier-Stokes equations by a second-order accurate finite volume fractional step method. Bubbles of sizes comparable to the Kolmogorov scale are injected at the duct entrance with a mean bulk volume fraction below 10-2. A two-way coupling approach is adopted for the interaction between the continuous fluid phase and dispersed bubble phase. The bubbles are tracked by a Lagrangian method including drag and lift forces due to buoyancy and Saffman lift. A in-house code, CU-FLOW, implemented on Graphic Processing Unit (GPU) is used for simulations in this work. The preferential distributions of bubbles and their impact on local turbulence structures and their effects on turbulent kinetic energy budgets are studied. Results between an upward flow and a downward flow with the bubbles are compared. Work Supported by Continuous Casting Consortium at UIUC.
Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics
NASA Astrophysics Data System (ADS)
Nazem, M.; Carter, J. P.; Airey, D. W.
2010-06-01
In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.
Flow-driven cloud formation and fragmentation: results from Eulerian and Lagrangian simulations
NASA Astrophysics Data System (ADS)
Heitsch, Fabian; Naab, Thorsten; Walch, Stefanie
2011-07-01
The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian smoothed particle hydrodynamics (SPH) code VINE and the Eulerian grid code PROTEUS. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydrodynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300 K. For clumps more massive than 1 M⊙ pc-1, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of magnitude smaller than their relative motion, rendering it subsonic with respect to the internal sound speed of the clumps but supersonic as seen by an external observer. For the SPH simulations most of the cold gas resides at temperatures below 100 K, while the grid-based models show an additional, substantial component between 100 and 300 K. Independent of the numerical method, our models confirm that converging flows of warm neutral gas fragment rapidly and form high-density, low-temperature clumps as possible seeds for star formation.
CFD transient simulation of the cough clearance process using an Eulerian wall film model.
Paz, Concepción; Suárez, Eduardo; Vence, Jesús
2017-02-01
In this study, a cough cycle is reproduced using a computational methodology. The Eulerian wall film approach is proposed to simulate airway mucus flow during a cough. The reproduced airway domain is based on realistic geometry from the literature and captures the deformation of flexible tissue. To quantify the overall performance of this complex phenomenon, cough efficiency (CE) was calculated, which provided an easily reproducible measurement parameter for the cough clearance process. Moreover, the effect of mucus layer thickness was examined. The relationship between the CE and the mucus viscosity was quantified using reductions from 20 to 80%. Finally, predictions of CE values based on healthy person inputs were compared with values obtained from patients with different respiratory diseases, including chronic obstructive pulmonary disease (COPD) and respiratory muscle weakness (RMW). It was observed that CE was reduced by 50% in patients with COPD compared with that of a healthy person. On average, CE was reduced in patients with RMW to 10% of the average value of a healthy person.
Eulerian and Lagrangian methods for vortex tracking in 2D and 3D flows
NASA Astrophysics Data System (ADS)
Huang, Yangzi; Green, Melissa
2014-11-01
Coherent structures are a key component of unsteady flows in shear layers. Improvement of experimental techniques has led to larger amounts of data and requires of automated procedures for vortex tracking. Many vortex criteria are Eulerian, and identify the structures by an instantaneous local swirling motion in the field, which are indicated by closed or spiral streamlines or pathlines in a reference frame. Alternatively, a Lagrangian Coherent Structures (LCS) analysis is a Lagrangian method based on the quantities calculated along fluid particle trajectories. In the current work, vortex detection is demonstrated on data from the simulation of two cases: a 2D flow with a flat plate undergoing a 45 ° pitch-up maneuver and a 3D wall-bounded turbulence channel flow. Vortices are visualized and tracked by their centers and boundaries using Γ1, the Q criterion, and LCS saddle points. In the cases of 2D flow, saddle points trace showed a rapid acceleration of the structure which indicates the shedding from the plate. For channel flow, saddle points trace shows that average structure convection speed exhibits a similar trend as a function of wall-normal distance as the mean velocity profile, and leads to statistical quantities of vortex dynamics. Dr. Jeff Eldredge and his research group at UCLA are gratefully acknowledged for sharing the database of simulation for the current research. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.
Efficient simulation of pitch angle collisions in a 2+2-D Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.
2014-10-01
Here we discuss pitch angle scattering collisions in the context of the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 12-ERD-061.
Modelling Cavitating Flows using an Eulerian-Lagrangian Approach and a Nucleation Model
NASA Astrophysics Data System (ADS)
Ma, Jingsen; Hsiao, Chao-Tsung; Chahine, Georges L.
2015-12-01
An Eulerian/Lagrangian multi-scale two-phase flow model is developed to simulate the various types of cavitation including bubble, sheet, and tip vortex cavitation. Sheet cavitation inception, unsteady breakup, and cloud shedding on a hydrofoil are used as an example here. No assumptions are needed on mass transfer between phases; instead, the method tracks bubble nuclei, which are in the bulk of the liquid and those generated by nucleation from solid boundaries and this is- sufficient to accurately capture the sheet dynamics. The multi-scale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics and a transition scheme to bridge the micro and macro scales. Nuclei are treated as flow singularities until they grow into large bubbles, which eventually merge to form a large scale discretised sheet cavity. The sheet performs large scale oscillations with a periodic reentrant jet forming under the sheet cavity, traveling upstream, and breaking the cavity. This results in bubble cloud formation and in high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The results for a NACA0015 foil are in good agreement with the experimental data.
NASA Astrophysics Data System (ADS)
Alver, Morten Omholt; Broch, Ole Jacob; Melle, Webjørn; Bagøien, Espen; Slagstad, Dag
2016-08-01
Calanus finmarchicus is an important zooplankton species in the Norwegian Sea, as a dominant food organism for pelagic fish larvae, and a potentially large source of marine lipids and proteins. Its position in the marine food web also makes it an important model species in assessing the risk posed by oil spills in the Norwegian and Arctic Seas. In this study, an Eulerian population model for C.finmarchicus, coupled to the physical and ecological model SINMOD, is presented. The model includes the full life cycle of C. finmarchicus with a representation of all developmental stages. The model has been validated against field measurements made in different areas of the Norwegian Sea in 1997 and 1998. The model displays geographical and temporal distributions of development stages that is in line with observed patterns. When comparing time series for selected regions, we see a high degree of variability both in the field samples and model output. On average, the model deviations are near half of the summed variability of the field data and model estimates. The model has applications within assessment of ecological production, and the potential for harvesting in the Norwegian and Arctic Seas, but in combination with other models, also for the assessment of ecological effects of oil spills and other types of pollution.
NASA Astrophysics Data System (ADS)
Yu, Qifeng; Pan, Tongyan
2017-03-01
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less
Bozorgi, Y; Keshavarz, P; Taheri, M; Fathikaljahi, J
2006-09-01
In this study, a mathematical model has been developed to simulate the performance of a spray scrubber in an industrial ammonium nitrate plant. The model is based on the Lagrangian approach for the droplets movement and particle source in cell (PSI-CELL) model for calculating the droplet concentration distribution. Consequently, unlike former research, the emphasis is on the droplet dynamic behavior. In the current study, for approaching a realistic model, a droplet size distribution rather than average diameter, and also liquid film formation rather than uniform and constant droplet flow rate has been applied. Also, the Eulerian method has been used for the calculation of the particles removal efficiency and energy balance has been applied on the gas to estimate the droplet size distribution. In the experimental section, the concentration of particles and their size distribution in both inlet and outlet gas of the studied scrubber has been measured for the validation of the predicted particles collection efficiency. In addition, the temperature of the gas at inlet, outlet and in the middle of the tower has been measured for the confirmation of the predicted droplet size distribution in the tower. A good consistency between the model and data has been observed. After the model is validated, it is used to investigate the various variable profiles such as liquid film, total projected surface area of the droplets, velocity profile of the droplets and some of the other parameters in the spray scrubbers.
The detection of breathing behavior using Eulerian-enhanced thermal video.
Bennett, Stephanie L; Goubran, Rafik; Knoefel, Frank
2015-01-01
The current gold standard for detecting and distinguishing between types of sleep apnea is expensive and invasive. This paper aims to examine the potential of inexpensive and unobtrusive thermal cameras in the identification and distinction between types of sleep apnea. A thermal camera was used to gather video of a subject performing regular nasal breathing, nasal hyperventilation and an additional trial simulating one type of sleep apnea. Simultaneously, a respiratory inductance plethysmography (RIP) band gathered respiratory data. Thermal video of all three trials were subjected to Eulerian Video Magnification; a procedure developed at MIT for enhancing subtle color variations in video data. Post magnification, nasal regions of interest were defined and mean region intensities were found for each frame of each trial. These signals were compared to determine the best performing region and compared to RIP data to validate breathing behavior. While some regions performed better, all region intensity signals depicted correct breathing behavior. The mean intensity signals for normal breathing and hyperventilation were correct and correlated well with RIP data. Furthermore, the RIP data resulting from the sleep apnea simulation clearly depicted chest movement while the corresponding mean intensity signal depicted lack of cyclical air flow. These results indicate that a subject's breathing behavior can be captured using thermal video and suggest that, with further development and additional equipment, thermal video can be used to detect and distinguish between types of sleep apnea.
Simulation of atmospheric dispersion of radionuclides using an Eulerian-Lagrangian modelling system.
Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N
2008-12-01
In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a Lagrangian stochastic particle model (LSPM) coupled with an Eulerian regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a Lagrangian stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.
NASA Astrophysics Data System (ADS)
Dhir, Gaurav; Suman, Sawan
2015-11-01
Experimental evidence shows that aircrafts operating under heavy rainfall conditions face deterioration of lift and increase in drag. This scenario can be a critical design challenge especially for slow moving vehicles such as airships. Effective roughening of airfoil surface caused by an uneven water film, loss of flow momentum and the loss of vehicle momentum due to its collision with the raindrops are the primary reasons causing the drag to increase. Our work focuses primarily on the numerical quantification of boundary layer momentum loss caused due to raindrops. The collision of raindrops with a solid surface leads to formation of an ejecta fog of splashed back droplets with their sizes being of the order of micrometers and their acceleration leads to boundary layer momentum loss. We model the airflow within a flat plate boundary layer using a Lagrangian-Eulerian approach with the raindrops being considered as non-deformable, non-spinning and non-interacting droplets. We employ an inter-phase coupling term to account for the interaction between the boundary layer flow and the droplets. Our presentation will focus on several comparisons (velocity field, lift and drag at various angles of attack) with the results of the standard (rain-free) Prandtl boundary layer flow. Indian Institute of Technology, Delhi.
ICECO-CEL: a coupled Eulerian-Lagrangian code for analyzing primary system response in fast reactors
Wang, C.Y.
1981-02-01
This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the Eulerian hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made.
2015-06-17
BioCast User Manual Forecasting 3D Satellite Derived Optical Properties Using Eulerian Advection Procedure Version 1.0 Sean Mccarthy Sherwin Ladner JaSon...18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT TODS BioCast User Manual Forecasting 3D Satellite Derived Optical Properties Using Eulerian Advection...defined by the AOPS input file. BioCast is designed to apply a simple advection approach to satellite derived products in order to forecast the
A massively parallel fractional step solver for incompressible flows
Houzeaux, G. Vazquez, M. Aubry, R. Cela, J.M.
2009-09-20
This paper presents a parallel implementation of fractional solvers for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified 'continuity' equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler solvers and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CG, Deflated CG). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors.
Agglomeration Multigrid for an Unstructured-Grid Flow Solver
NASA Technical Reports Server (NTRS)
Frink, Neal; Pandya, Mohagna J.
2004-01-01
An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.
Riemann solvers and Alfven waves in black hole magnetospheres
NASA Astrophysics Data System (ADS)
Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip
2016-09-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.
A fast solver for systems of reaction-diffusion equations.
Garbey, M.; Kaper, H. G.; Romanyukha, N.
2001-04-20
In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, {partial_derivative}{sub t} u + a {center_dot} {del}u = {Delta}u + f(x,t,u), and x element of {Omega} contained in R{sup 3}, t > 0. Here, u is a vector-valued function, u triple bond u(x,t) element of R{sup m} is large, and the corresponding system of ODEs, {partial_derivative}{sub t}u = F(x,t,u), is stiff. Typical examples arise in air pollution studies, where a is the given wind field and the nonlinear function F models the atmospheric chemistry. The time integration of Eq. (1) is best handled by the method of characteristics. The problem is thus reduced to designing for the reaction-diffusion part a fast solver that has good stability properties for the given time step and does not require the computation of the full Jacobi matrix. An operator-splitting technique, even a high-order one, combining a fast nonlinear ODE solver with an efficient solver for the diffusion operator is less effective when the reaction term is stiff. In fact, the classical Strang splitting method may underperform a first-order source splitting method. The algorithm we propose in this paper uses an a posteriori filtering technique to stabilize the computation of the diffusion term. The algorithm parallelizes well, because the solution of the large system of ODEs is done pointwise; however, the integration of the chemistry may lead to load-balancing problems. The Tchebycheff acceleration technique proposed in offers an alternative that complements the approach presented here. To facilitate the presentation, we limit the discussion to domains {Omega} that either admit a regular discretization grid or decompose into subdomains that admit regular discretization grids. We describe the algorithm for one-dimensional domains in Section 2 and for multidimensional domains in Section 3. Section 4 briefly outlines future work.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources.
Evaluation of linear solvers for oil reservoir simulation problems. Part 2: The fully implicit case
Joubert, W.; Janardhan, R.
1997-12-01
A previous paper [Joubert/Biswas 1997] contained investigations of linear solver performance for matrices arising from Amoco`s Falcon parallel oil reservoir simulation code using the IMPES formulation (implicit pressure, explicit saturation). In this companion paper, similar issues are explored for linear solvers applied to matrices arising from more difficult fully implicit problems. The results of numerical experiments are given.
Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F
2016-02-07
The response of individual cells at the micro-scale in cell mechanics is important in understanding how they are affected by changing environments. To control cell stresses, microfluidics can be implemented since there is tremendous control over the geometry of the devices. Designing microfluidic devices to induce and manipulate stress levels on biological cells can be aided by computational modeling approaches. Such approaches serve as an efficient precursor to fabricating various microfluidic geometries that induce predictable levels of stress on biological cells, based on their mechanical properties. Here, a three-dimensional, multiphase computational fluid dynamics (CFD) modeling approach was implemented for soft biological materials. The computational model incorporates the physics of the particle dynamics, fluid dynamics and solid mechanics, which allows us to study how stresses affect the cells. By using an Eulerian-Lagrangian approach to treat the fluid domain as a continuum in the microfluidics, we are conducting studies of the cells' movement and the stresses applied to the cell. As a result of our studies, we were able to determine that a channel with periodically alternating columns of obstacles was capable of stressing cells at the highest rate, and that microfluidic systems can be engineered to impose heterogenous cell stresses through geometric configuring. We found that when using controlled geometries of the microfluidics channels with staggered obstructions, we could increase the maximum cell stress by nearly 200 times over cells flowing through microfluidic channels with no obstructions. Incorporating computational modeling in the design of microfluidic configurations for controllable cell stressing could help in the design of microfludic devices for stressing cells such as cell homogenizers.
NASA Astrophysics Data System (ADS)
Eastham, Sebastian D.; Jacob, Daniel J.
2017-02-01
Quasi-horizontal chemical plumes in the free troposphere can preserve their concentrated structure for over a week, enabling transport on intercontinental scales with important environmental impacts. Global Eulerian chemical transport models (CTMs) fail to preserve these plumes due to fast numerical dissipation. We examine the causes of this dissipation and how it can be cured. Goddard Earth Observing System (GEOS-5) meteorological data at 0.25° × 0.3125° horizontal resolution and ˜ 0.5 km vertical resolution in the free troposphere are used to drive a worldwide ensemble of GEOS-Chem CTM plumes at resolutions from 0.25° × 0.3125° to 4° × 5°, in both 2-D (horizontal) and 3-D. Two-dimensional simulations enable examination of the sensitivity of numerical dissipation to grid resolution. We show that plume decay is driven by flow divergence and shear, filamenting the plumes until GEOS-Chem's high-order advection scheme cannot resolve gradients and fast numerical diffusion ensues. This divergence can be measured by the Lyapunov exponent (λ) of the flow. Dissipation of plumes is much faster at extratropical latitudes than in the tropics and this can be explained by stronger divergence. The plume decay constant (α) is linearly related to λ, and increasing grid resolution provides only modest benefits toward plume preservation. Three-dimensional simulations show near-complete dissipation of plumes within a few days, independent of horizontal grid resolution and even in the tropics. This is because vertical grid resolution is inadequate in all cases to properly resolve plume gradients. We suggest that finer vertical grid resolution in the free troposphere is essential for models to resolve intercontinental plumes, while current horizontal resolution in these models (˜ 1°) is sufficient.
NASA Astrophysics Data System (ADS)
Vérèmes, H.; Cammas, J.-P.; Baray, J.-L.; Keckhut, P.; Barthe, C.; Posny, F.; Tulet, P.; Dionisi, D.; Bielli, S.
2016-12-01
Signatures of multiple stratospheric intrusions were observed on simultaneous and collocated ozone and water vapor profiles retrieved by lidars and radiosondes at the Maïdo Observatory, Reunion Island (21°S, 55°E, 2160 m above sea level), during MAïdo LIdar Calibration CAmpaign in April 2013. A singular structure of the ozone vertical profile with three peaks (in excess of 90 ppbv, at 8, 10, and 13 km altitude) embedded in a thick dry layer of air suggested stratospheric intrusions with multiple origins. The hypothesis is corroborated by a synoptic analysis based on re-analyses. European Centre for Medium-Range Weather Forecasts ERA-Interim temporal series associated with 5 days Lagrangian back trajectories initialized on each ozone peak allows to capture their stratospheric origin. The ozone peak at the lowest altitude is associated with an irreversible tropopause folding process along the polar jet stream during an extratropical cutoff low formation. Simultaneous lidar water vapor profiles of this peak show that the anticorrelation with ozone has been removed, due to mixing processes. Back trajectories indicate that the two other ozone peaks observed at higher altitudes are associated with the dynamics of the subtropical jet stream and the lower stratosphere. The observations confirm the recent stratospheric origins. The highest ozone peak is explained by the horizontal distribution of the intrusion. Use of a Lagrangian Reverse Domain Filling model and of the Meso-NH Eulerian mesoscale model with a passive stratospheric tracer allow to further document the stratosphere-troposphere transport processes and to describe the detailed potential vorticity and ozone structures in which are embedded in the observed multiple stratospheric intrusions.
SIMULATION OF GEOMATERIALS USING CONTINUUM DAMAGE MODELS ON AN EULERIAN GRID
Lomov, I; Antoun, T H
2004-09-17
A new continuum model for directional tensile failure has been developed that can simulate weakening and void formation due to directional tensile failure. The model is developed within the context of a properly invariant nonlinear thermomechanical theory. A second order damage tensor is introduced which allows simulation of weakening to tension applied in one direction, without weakening to subsequent tension applied in perpendicular directions. This damage tensor can be advected using standard methods in computer codes. Porosity is used as an isotropic measure of volumetric void strain and its evolution is influenced by tensile failure. The rate of dissipation due to directional tensile failure takes a particularly simple form, which can be analyzed easily. Specifically, the model can be combined with general constitutive equations for porous compaction and dilation, as well as viscoplasticity. A robust non-iterative numerical scheme for integrating these evolution equations is proposed. This constitutive model has been implemented into an Eulerian shock wave code with adaptive mesh refinement. A comparison of experimental results and computational simulations of spherical wave propagation in Danby marble was made. The experiment consisted of a 2-cm-diameter explosive charge detonated in the center of a cylindrical rock sample. Radial particle velocity histories were recorded at several concentric locations in the sample. An extensively damaged region near the charge cavity and two networks of cracks were evident in the specimen after the test. The first network consists of radial cracks emanating form the cavity and extending about halfway through the specimen. The second network consists of circumferential cracks occurring in a relatively narrow band that extends from the outer boundary of the radially cracked region toward the free surface. The calculations indicated load-induced anisotropy such as was observed in the experiment.
GPU accelerated FDTD solver and its application in MRI.
Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S
2010-01-01
The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD solver and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.
A Coupled Finite Volume Solver for Incompressible Flows
NASA Astrophysics Data System (ADS)
Moukalled, F.; Darwish, M.
2008-09-01
This paper reports on a pressure-based coupled algorithm for the solution of laminar incompressible flow problems. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. The superiority of the coupled approach over the segregated approach is demonstrated by solving the lid-driven flow in a square cavity problem using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver is grid independent. Moreover, recorded CPU time values reveal that the coupled approach substantially reduces the computational cost with the reduction rate for the problem solved increasing as the grid size increases and reaching a value as high as 115.
Blade design and analysis using a modified Euler solver
NASA Technical Reports Server (NTRS)
Leonard, O.; Vandenbraembussche, R. A.
1991-01-01
An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.
Large-scale linear nonparallel support vector machine solver.
Tian, Yingjie; Ping, Yuan
2014-02-01
Twin support vector machines (TWSVMs), as the representative nonparallel hyperplane classifiers, have shown the effectiveness over standard SVMs from some aspects. However, they still have some serious defects restricting their further study and real applications: (1) They have to compute and store the inverse matrices before training, it is intractable for many applications where data appear with a huge number of instances as well as features; (2) TWSVMs lost the sparseness by using a quadratic loss function making the proximal hyperplane close enough to the class itself. This paper proposes a Sparse Linear Nonparallel Support Vector Machine, termed as L1-NPSVM, to deal with large-scale data based on an efficient solver-dual coordinate descent (DCD) method. Both theoretical analysis and experiments indicate that our method is not only suitable for large scale problems, but also performs as good as TWSVMs and SVMs.
Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
NASA Technical Reports Server (NTRS)
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.
Extending the QUDA Library with the eigCG Solver
Strelchenko, Alexei; Stathopoulos, Andreas
2014-12-12
While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Performance evaluation of a parallel sparse lattice Boltzmann solver
Axner, L. Bernsdorf, J. Zeiser, T. Lammers, P. Linxweiler, J. Hoekstra, A.G.
2008-05-01
We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and/or complex topology such as porous media, fissured rocks and geometries from medical applications. The topology of the lattice nodes representing the fluid fraction of the computational domain is mapped on a graph. Graph decomposition is performed with both multilevel recursive-bisection and multilevel k-way schemes based on modified Kernighan-Lin and Fiduccia-Mattheyses partitioning algorithms. Performance results and optimization strategies are presented for a variety of platforms, showing a parallel efficiency of almost 80% for the largest problem size. A good agreement between the performance model and experimental results is demonstrated.
Polyurethanes: versatile materials and sustainable problem solvers for today's challenges.
Engels, Hans-Wilhelm; Pirkl, Hans-Georg; Albers, Reinhard; Albach, Rolf W; Krause, Jens; Hoffmann, Andreas; Casselmann, Holger; Dormish, Jeff
2013-09-02
Polyurethanes are the only class of polymers that display thermoplastic, elastomeric, and thermoset behavior depending on their chemical and morphological makeup. In addition to compact polyurethanes, foamed variations in particular are very widespread, and they achieve their targeted properties at very low weights. The simple production of sandwich structures and material composites in a single processing step is a key advantage of polyurethane technology. The requirement of energy and resource efficiency increasingly demands lightweight structures. Polyurethanes can serve this requirement by acting as matrix materials or as flexible adhesives for composites. Polyurethanes are indispensable when it comes to high-quality decorative coatings or maintaining the value of numerous objects. They are extremely adaptable and sustainable problem solvers for today's challenges facing our society, all of which impose special demands on materials.
Progress in developing Poisson-Boltzmann equation solvers
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-01-01
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185
Accurate derivative evaluation for any Grad–Shafranov solver
Ricketson, L.F.; Cerfon, A.J.; Rachh, M.; Freidberg, J.P.
2016-01-15
We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.
A Newton-Krylov solver for fast spin-up of online ocean tracers
NASA Astrophysics Data System (ADS)
Lindsay, Keith
2017-01-01
We present a Newton-Krylov based solver to efficiently spin up tracers in an online ocean model. We demonstrate that the solver converges, that tracer simulations initialized with the solution from the solver have small drift, and that the solver takes orders of magnitude less computational time than the brute force spin-up approach. To demonstrate the application of the solver, we use it to efficiently spin up the tracer ideal age with respect to the circulation from different time intervals in a long physics run. We then evaluate how the spun-up ideal age tracer depends on the duration of the physics run, i.e., on how equilibrated the circulation is.
High-performance equation solvers and their impact on finite element analysis
NASA Technical Reports Server (NTRS)
Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.
1990-01-01
The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Pernice, M.
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
A three-dimensional fast solver for arbitrary vorton distributions
Strickland, J.H.; Baty, R.S.
1994-05-01
A method which is capable of an efficient calculation of the three-dimensional flow field produced by a large system of vortons (discretized regions of vorticity) is presented in this report. The system of vortons can, in turn, be used to model body surfaces, container boundaries, free-surfaces, plumes, jets, and wakes in unsteady three-dimensional flow fields. This method takes advantage of multipole and local series expansions which enables one to make calculations for interactions between groups of vortons which are in well-separated spatial domains rather than having to consider interactions between every pair of vortons. In this work, series expansions for the vector potential of the vorton system are obtained. From such expansions, the three components of velocity can be obtained explicitly. A Fortran computer code FAST3D has been written to calculate the vector potential and the velocity components at selected points in the flow field. In this code, the evaluation points do not have to coincide with the location of the vortons themselves. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the magnitudes of the vector potential and velocity fields are on the order of 10{sup {minus}4}and 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities of up to 10{sup {minus}5}. For less than 1,000 to 2,000 vortons in the field, there is virtually no CPU time savings with the fast solver. For 100,000 vortons in the flow, the fast solver obtains solutions in 1 % to 10% of the time required for the direct solution technique depending upon the configuration.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
A Fast Poisson Solver with Periodic Boundary Conditions for GPU Clusters in Various Configurations
NASA Astrophysics Data System (ADS)
Rattermann, Dale Nicholas
Fast Poisson solvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson solver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson solver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in
NASA Astrophysics Data System (ADS)
Oberholster, A. J.; Heyns, P. S.
2009-07-01
The ability to monitor the vibration of blades online is of great importance to the structural health of turbomachinery. This paper focuses on the fixed reference frame or Eulerian implementation of laser Doppler vibrometry to perform this function. The way in which this measurement technique works is studied analytically and then a numerical simulation approach is proposed. Through experimental testing and finite element modeling, it is shown that this measurement approach is in principle viable for online blade condition monitoring when phase angles at reference frequencies are monitored, using non-harmonic Fourier analysis.
Exit of a blast wave from a conical nozzle. [flow field calculations by Eulerian computer code DORF
NASA Technical Reports Server (NTRS)
Kim, K.; Johnson, W. E.
1976-01-01
The Eulerian computer code DORF was used in the analysis of a two-dimensional, unsteady flow field resulting from semi-confined explosions for propulsive applications. Initially, the ambient gas inside the conical shaped nozzle is set into motion due to the expansion of the explosion product gas, forming a shock wave. When this shock front exits the nozzle, it takes almost a spherical form while a complex interaction between the nozzle and compression and rarefaction waves takes place behind the shock. The results show an excellent agreement with experimental data.
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael
2015-07-01
In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multi-dimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach
Long-term simulations of European air quality using the Danish Eulerian Hemispheric Model
NASA Astrophysics Data System (ADS)
Mantzius Hansen, Kaj
2010-05-01
Effects of air quality on nature and human health have been on the agenda for several decades. Air quality monitoring sites have been established throughout Europe and several of the sites have been operating for more than two decades. Long term evaluation of air quality from specific monitoring sites or smaller regions has been performed in several studies. For studies of larger regions, models with comprehensive chemistry schemes have been developed and applied to study atmospheric transport, transformation and deposition of various air pollutants. With faster and faster computers, the development over the years has been towards more complex chemistry schemes and higher spatial and temporal resolution of model output. This often limits the studied period to single or a few years. We will present a study of European air quality covering 18 years, simulated with a state-of-the-art atmospheric chemistry transport model. The Danish Eulerian Hemispheric Model (DEHM) covers the majority of the Northern Hemisphere with a horizontal grid resolution of 150 km X 150 km. DEHM has 29 vertical layers in terrain-following sigma-coordinates extending up to a height of 100 hPa. Two-way nesting options with a nesting factor of three can be applied with higher resolution over a limited area of the model. At present the model can be run without nests or with one, two or three nests, each with grid resolutions of 50 km X 50 km, 16.7 km X 16.7 km, and 5.6 km X 5.6 km, respectively. The model includes a comprehensive chemistry scheme with more than 100 reactions and 67 atmospheric constituents, of which 4 relate to primary particulates (PM2.5, PM10, TSP and sea salt); other species are SOx, NOx, NHx, VOCs, and secondary inorganic particulates. DEHM is driven by meteorological data from the numerical weather prediction model MM5v3. One long-term simulation was performed with DEHM covering the period from 1989 to 2006. The predicted concentrations were evaluated against measurements
GORRAM: Introducing accurate operational-speed radiative transfer Monte Carlo solvers
NASA Astrophysics Data System (ADS)
Buras-Schnell, Robert; Schnell, Franziska; Buras, Allan
2016-06-01
We present a new approach for solving the radiative transfer equation in horizontally homogeneous atmospheres. The motivation was to develop a fast yet accurate radiative transfer solver to be used in operational retrieval algorithms for next generation meteorological satellites. The core component is the program GORRAM (Generator Of Really Rapid Accurate Monte-Carlo) which generates solvers individually optimized for the intended task. These solvers consist of a Monte Carlo model capable of path recycling and a representative set of photon paths. Latter is generated using the simulated annealing technique. GORRAM automatically takes advantage of limitations on the variability of the atmosphere. Due to this optimization the number of photon paths necessary for accurate results can be reduced by several orders of magnitude. For the shown example of a forward model intended for an aerosol satellite retrieval, comparison with an exact yet slow solver shows that a precision of better than 1% can be achieved with only 36 photons. The computational time is at least an order of magnitude faster than any other type of radiative transfer solver. Merely the lookup table approach often used in satellite retrieval is faster, but on the other hand suffers from limited accuracy. This makes GORRAM-generated solvers an eligible candidate as forward model in operational-speed retrieval algorithms and data assimilation applications. GORRAM also has the potential to create fast solvers of other integrable equations.
Acceleration of FDTD mode solver by high-performance computing techniques.
Han, Lin; Xi, Yanping; Huang, Wei-Ping
2010-06-21
A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.
A parallel 3D poisson solver for space charge simulation in cylindrical coordinates.
Xu, J.; Ostroumov, P. N.; Nolen, J.; Physics
2008-02-01
This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the (r,{theta}) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.
Oasis: A high-level/high-performance open source Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Mortensen, Mikael; Valen-Sendstad, Kristian
2015-03-01
Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.
The impact of improved sparse linear solvers on industrial engineering applications
Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
NASA Astrophysics Data System (ADS)
Marshall, David D.
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.
Robust large-scale parallel nonlinear solvers for simulations.
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write
A new set of direct and iterative solvers for the TOUGH2 family of codes
Moridis, G.J.
1995-04-01
Two new solvers are discussed. LUBAND, the first routine is a direct solver for banded systems and is based on a LU decomposition with partial pivoting and row interchange. BCGSTB, the second routine, is a Preconditioned Conjugate Gradient (PCG) solver with improved speed and convergence characteristics. Bandwidth minimization and gridblock ordering schemes are also introduced into TOUGH2 to improve speed and accuracy. TOUGH2 simulates fluid and heat flows in permeable media and is used for the evaluation of WIPP and TEVES (Thermal Enhanced Vapor Extraction System) that will be used to extract solvents from the Chemical Waste Landfill at Sandia National Laboratories.
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.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2012-01-01
This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.
NASA Astrophysics Data System (ADS)
Li, Linmin; Li, Baokuan
2016-08-01
In ladle metallurgy, bubble-liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The Eulerian volume of fluid model is adopted to track the liquid steel-slag-air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O'Rourke's algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air-liquid interface. The turbulent liquid flow that is induced by bubble-liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open-close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid Eulerian-Lagrangian-LES model provides a valid modeling framework to predict the unsteady gas bubble-slag layer coupled behaviors.
A generalized Poisson solver for first-principles device simulations
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost; Brück, Sascha; Luisier, Mathieu
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Incremental planning to control a blackboard-based problem solver
NASA Technical Reports Server (NTRS)
Durfee, E. H.; Lesser, V. R.
1987-01-01
To control problem solving activity, a planner must resolve uncertainty about which specific long-term goals (solutions) to pursue and about which sequences of actions will best achieve those goals. A planner is described that abstracts the problem solving state to recognize possible competing and compatible solutions and to roughly predict the importance and expense of developing these solutions. With this information, the planner plans sequences of problem solving activities that most efficiently resolve its uncertainty about which of the possible solutions to work toward. The planner only details actions for the near future because the results of these actions will influence how (and whether) a plan should be pursued. As problem solving proceeds, the planner adds new details to the plan incrementally, and monitors and repairs the plan to insure it achieves its goals whenever possible. Through experiments, researchers illustrate how these new mechanisms significantly improve problem solving decisions and reduce overall computation. They briefly discuss current research directions, including how these mechanisms can improve a problem solver's real-time response and can enhance cooperation in a distributed problem solving network.
Verification of continuum drift kinetic equation solvers in NIMROD
Held, E. D.; Ji, J.-Y.; Kruger, S. E.; Belli, E. A.; Lyons, B. C.
2015-03-15
Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
New numerical solver for flows at various Mach numbers
NASA Astrophysics Data System (ADS)
Miczek, F.; Röpke, F. K.; Edelmann, P. V. F.
2015-04-01
Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims: While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods: Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Results: Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions: Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y.
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations
NASA Astrophysics Data System (ADS)
Kudoh, Yuki; Hanawa, Tomoyuki
2016-11-01
We analyse the cosmic ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR `number' conservation, where the CR number density is defined as the three-fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second-order accuracy in space and time. Our numerical examples include an expansion of high-pressure sphere in a magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.
Cooperative solutions coupling a geometry engine and adaptive solver codes
NASA Technical Reports Server (NTRS)
Dickens, Thomas P.
1995-01-01
Follow-on work has progressed in using Aero Grid and Paneling System (AGPS), a geometry and visualization system, as a dynamic real time geometry monitor, manipulator, and interrogator for other codes. In particular, AGPS has been successfully coupled with adaptive flow solvers which iterate, refining the grid in areas of interest, and continuing on to a solution. With the coupling to the geometry engine, the new grids represent the actual geometry much more accurately since they are derived directly from the geometry and do not use refits to the first-cut grids. Additional work has been done with design runs where the geometric shape is modified to achieve a desired result. Various constraints are used to point the solution in a reasonable direction which also more closely satisfies the desired results. Concepts and techniques are presented, as well as examples of sample case studies. Issues such as distributed operation of the cooperative codes versus running all codes locally and pre-calculation for performance are discussed. Future directions are considered which will build on these techniques in light of changing computer environments.
Two-Dimensional Ffowcs Williams/Hawkings Equation Solver
NASA Technical Reports Server (NTRS)
Lockard, David P.
2005-01-01
FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.
Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver
NASA Astrophysics Data System (ADS)
Turnquist, Brian; Owkes, Mark
2016-11-01
Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.
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.
An optimal iterative solver for the Stokes problem
Wathen, A.; Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
An implicit-explicit flow solver for complex unsteady flows
NASA Astrophysics Data System (ADS)
Hsu, John Ming-Jey
2005-12-01
Current calculations of complex unsteady flows are prohibitively expensive for use in real engineering applications. Typical flow solvers for unsteady integration employ a fully implicit time stepping scheme, in which the equations are solved by an inner iteration. In order to achieve convergence within each physical time step, a substantial number of pseudo-time steps (typically between 30--100, depending on the case) are required. Another unfavorable characteristic of the dual time stepping method is that there are no available error estimates for time accuracy available unless the inner iterations are fully converged, although numerical experiments have demonstrated second order accuracy in time. The approach in this thesis is to construct hybrid type schemes by combining implicit and explicit schemes in a manner that guarantees second order accuracy in time. An initial time accurate ADI step is introduced, followed by a small number of cycles of the dual-time stepping scheme augmented by multigrid. The formal second order accuracy in time should be retained without the need for large numbers of inner iterations. The number of inner iterations required for convergence can thus be reduced while maintaining the same overall error levels. To investigate the effectiveness of the proposed scheme, several pitching airfoil test cases were examined, offering a close look at possible reductions in computational cost by adopting the present approach.
NASA Astrophysics Data System (ADS)
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
NASA Astrophysics Data System (ADS)
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2016-07-01
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu)
NASA Astrophysics Data System (ADS)
Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.
2016-05-01
Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
NASA Technical Reports Server (NTRS)
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-01-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-stream snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-streammore » snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.« less
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; Sun, Yannan; USA, Richland Washington; Martinez, Jayson J.; USA, Richland Washington; Fu, Tao; USA, Richland Washington; McMichael, Geoffrey A.; USA, Richland Washington; Carlson, Thomas J.; USA, Richland Washington
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Cognitive Distance Learning Problem Solver Reduces Search Cost through Learning Processes
NASA Astrophysics Data System (ADS)
Yamakawa, Hiroshi; Miyamoto, Yuji; Baba, Takayuki; Okada, Hiroyuki
Our proposed cognitive distance learning problem solver generates sequence of actions from initial state to goal states in problem state space. This problem solver learns cognitive distance (path cost) of arbitrary combination of two states. Action generation at each state is selection of next state that has minimum cognitive distance to the goal, like Q-learning agent. In this paper, first, we show that our proposed method reduces search cost than conventional search method by analytical simulation in spherical state space. Second, we show that an average search cost is more reduced more the prior learning term is long and our problem solver is familiar to the environment, by a computer simulation in a tile world state space. Third, we showed that proposed problem solver is superior to the reinforcement learning techniques when goal is changed by a computer simulation. Forth, we found that our simulation result consist with psychological experimental results.
Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; ...
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developedmore » using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.« less
Wavelet-based Poisson solver for use in particle-in-cell simulations.
Terzić, Balsa; Pogorelov, Ilya V
2005-06-01
We report on a successful implementation of a wavelet-based Poisson solver for use in three-dimensional particle-in-cell simulations. Our method harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and additional compression of relevant data sets. We present and discuss preliminary results relating to the application of the new solver to test problems in accelerator physics and astrophysics.
THE USE OF CLASSICAL LAX-FRIEDRICHS RIEMANN SOLVERS WITH DISCONTINUOUS GALERKIN METHODS
W. J. RIDER; R. B. LOWRIE
2001-03-01
While conducting a von Neumann stability analysis of discontinuous Galerkin methods we found that the standard Lax-Friedrichs (LxF) Riemann solver is unstable for all time-step sizes. A simple modification of the Riemann solver's dissipation returns the method to stability. Furthermore, the method has a smaller truncation error than the corresponding method with an upwind flux for the RK2-DG(1) method. These results are confirmed upon testing.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
2015-04-12
Avoiding communication in the Lanczos bidiagonalization routine and associated Least Squares QR solver Erin Carson Electrical Engineering and...Bidiagonalization Routine and Associated Least Squares QR Solver 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...throughout scienti c codes , are often the bottlenecks in application perfor- mance due to a low computation/communication ratio. In this paper we develop
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
Dynamic Linear Solver Selection for Transient Simulations Using Multi-label Classifiers
2012-01-01
Conference on Computational Science, ICCS 2012 Dynamic linear solver selection for transient simulations using multi-label classifiers Paul R. Eller ...preconditioned linear solver as the output. Email addresses: Paul.R.Eller@usace.army.mil (Paul R. Eller ), Ruth.C.Cheng@usace.army.mil (Jing-Ru C...unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 1524 Paul R. Eller et al. / Procedia
Implementation of a parallel unstructured Euler solver on the CM-5
NASA Technical Reports Server (NTRS)
Morano, Eric; Mavriplis, D. J.
1995-01-01
An efficient unstructured 3D Euler solver is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow solver is discussed.
A 3D Unstructured Mesh Euler Solver Based on the Fourth-Order CESE Method
2013-06-01
conservation in space and time without using a one-dimensional Riemann solver, (ii) genuinely multi-dimensional treatment without dimensional splitting (iii...of the original second-order CESE method, including: (i) flux conservation in space and time without using a one-dimensional Riemann solver, (ii...treated in a unified manner. The geometry for a three-dimensional CESE method is more difficult to visualize than the one- and two-dimensional methods
Development of a Flow Solver with Complex Kinetics on the Graphic Processing Units
2011-09-22
Physics 109, 11 (2011), 113308. [9] Klockner, A., Warburton, T., Bridge, J., and Hesthaven, J. Nodal Discontinuous Galerkin Methods on Graphics...Graphic Processing Units ( GPU ) to model reactive gas mixture with detailed chemical kinetics. The solver incorporates high-order finite volume methods...method. We explored different approaches in implementing a fast kinetics solver on the GPU . The detail of the implementation is discussed in the
Head and neck 192Ir HDR-brachytherapy dosimetry using a grid-based Boltzmann solver
Wolf, Sabine; Kóvacs, George
2013-01-01
Purpose To compare dosimetry for head and neck cancer patients, calculated with TG-43 formalism and a commercially available grid-based Boltzmann solver. Material and methods This study included 3D-dosimetry of 49 consecutive brachytherapy head and neck cancer patients, computed by a grid-based Boltzmann solver that takes into account tissue inhomogeneities as well as TG-43 formalism. 3D-treatment planning was carried out by using computed tomography. Results Dosimetric indices D90 and V100 for target volume were about 3% lower (median value) for the grid-based Boltzmann solver relative to TG-43-based computation (p < 0.01). The V150 dose parameter showed 1.6% increase from grid-based Boltzmann solver to TG-43 (p < 0.01). Conclusions Dose differences between results of a grid-based Boltzmann solver and TG-43 formalism for high-dose-rate head and neck brachytherapy patients to the target volume were found. Distinctions in D90 of CTV were low (2.63 Gy for grid-based Boltzmann solver vs. 2.71 Gy TG-43 in mean). In our clinical practice, prescription doses remain unchanged for high-dose-rate head and neck brachytherapy for the time being. PMID:24474973
A Wavelet Technique For Multi-grid Solver For Large Linear Systems
NASA Astrophysics Data System (ADS)
Keller, W.
In general, large systems of linear equations cannot be solved directly. An iterative solver has to be applied instead. Unfortunately, iterative solvers have a notouriously slow convergence rate, which in the worst case can prevent convergence at all, due to the inavoidable rounding errors. Multi-grid iteration schemes are meant to guarantee a sufficiently high convergence rate, independent from the dimension of the linear system. The idea behind the multi-grid solvers is that the traditional iterative solvers eliminate only the short-wavelength error constituents in the initial guess for the solution. For the elimination of the remaining long-wavelength error constituents a much coarser grid is sufficient. On the coarse grid the dimension of the problem is much smaller so that the elimination can be done by a direct solver. The paper shows that wavelet techniques successfully can be applied for following steps of a multi-grid procedure: · Generation of an approximation of the proplem on a coarse grid from a given approximation on the fine grid. · Restriction of a signal on a fine grid to its approximation on a co grid. · Uplift of a signal from the coarse to the fine grid. The paper starts with a theoretical explanation of the links between wavelets and multi-grid solvers. Based on this investigation the class o operators, which are suitable for a multi-grid solution strategy can be characterized. The numerical efficiency of the approach will be tested for the Planar Stokes problem.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
A Radiation Transfer Solver for Athena Using Short Characteristics
NASA Astrophysics Data System (ADS)
Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
NASA Astrophysics Data System (ADS)
Pokharna, Himanshu
The Particle-Fluid Model (PFM) is a modeling approach for two-phase flow which has promise for overcoming some of the limitations of the existing two-fluid models and leads to enhanced predictive capability. The model incorporates a Lagrangian representation for the dispersed phases and thus reduces the numerical diffusion associated with Eulerian schemes. In addition, it permits the interfacial interactions as well as inter-particle interactions to be modeled in a natural way. This thesis concerns further improvements to a PFM code called DISCON. In particular, stochastic models for bubble interactions such as bubble coalescence, turbulence, breakup and wall nucleation have been incorporated. Capability to model heat structures has also been added. The boiling model produces good agreement when compared to experiment data. A primary emphasis of the development was the quasi-multidimensional lateral phase distribution model and its incorporation into the Lagrangian-Eulerian single channel model. This phase distribution model is based on the physics of eddy-bubble interaction. Eddies are simulated using simple algebraic models and the bubble lateral motion is established by tracking the bubbles through a succession of eddies in turbulence. Results from the model are compared with experimental data and good agreement is obtained. Furthermore, the single channel code was extended to a pilot systems code to model branched flow passages. Models for merging and dividing flows were incorporated into the PFM code. Modeling results for a few conceptual problems have been obtained using this enhanced capability and are presented herein. Finally the modeling studies are augmented with theoretical dispersion and characteristics analysis of the conservation equations used in both the two-fluid model and in the PFM. It is shown that the Lagrangian-Eulerian system of equations results in a well posed problem. This is in contrast to the usual one-dimensional two-fluid model which
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
NASA Technical Reports Server (NTRS)
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
NASA Astrophysics Data System (ADS)
Naphon, P.; Arisariyawong, T.; Nualboonrueng, T.
2017-02-01
A computation fluid dynamics study has been performed to analyze the nanofluids heat transfer and flow characteristics in the spirally coiled tubes. Eulerian two-phase turbulent model is applied to simulate the heat transfer and flow characteristics in the vertical spirally coiled tube. The spirally coiled tubes are fabricated by bending a 8.50 mm inner diameter straight copper tube into a spiral-coil with two different curvature ratios of 0.035, 0.060. The predicted results are verified with the present measured data. Reasonable agreement is obtained from the comparison between the measured data and the predicted results. In addition, due to the centrifugal force, the induced secondary flow has significant effect on the heat transfer enhancement as flowing through the spirally coiled tube. Effects of curvature, nanofluids concentration and hot water temperature on the nanofluids heat transfer characteristics and pressure drop are considered.
NASA Technical Reports Server (NTRS)
De Jong, Frederik J.; Sabnis, Jayant S.; Mcconnaughey, Paul K.
1989-01-01
A computer code has been developed for the analysis of SSME (Space Shuttle Main Engine) HPOTP (High Pressure Oxidizer Turbo Pump) nozzle plug trajectories in the turnaround duct downstream of the turbine. The algorithm is based on a combined Eulerian-Lagrangian analysis originally developed for the study of two-phase flows. The Lagrangian part of this analysis has been enhanced to include three-dimensional particle motion and the effect of particle-wall collisions in complex geometries (with a large number of boundaries). The sensitivity of the nozzle plug trajectories to a variety of parameters has been determined, via the qualitative analysis of a select number of computed trajectories. The results of extensive parametric studies have been reported in a companion paper.
NASA Astrophysics Data System (ADS)
Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan
2016-12-01
Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The Eulerian approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the Lagrangian way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/h is larger than 0.4.
NASA Astrophysics Data System (ADS)
Sahin, Mehmet; Mohseni, Kamran
2009-07-01
A new geometrically conservative arbitrary Lagrangian-Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian-Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier-Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc library. The present ALE method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free-swimming hydromedusa Aequorea victoria (crystal jellyfish). The calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa. In addition, the propulsion efficiency of the free-swimming hydromedusa is computed and its value is compared with values from the literature for several other species.
NASA Astrophysics Data System (ADS)
Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan
2017-04-01
Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The Eulerian approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the Lagrangian way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/ h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/ h is larger than 0.4.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. I. HYDRODYNAMICS AND SELF-GRAVITY
Almgren, A. S.; Beckner, V. E.; Bell, J. B.; Day, M. S.; Lijewski, M. J.; Nonaka, A.; Howell, L. H.; Singer, M.; Joggerst, C. C.; Zingale, M.
2010-06-01
We present a new code, CASTRO, that solves the multicomponent compressible hydrodynamic equations for astrophysical flows including self-gravity, nuclear reactions, and radiation. CASTRO uses an Eulerian grid and incorporates adaptive mesh refinement (AMR). Our approach to AMR uses a nested hierarchy of logically rectangular grids with simultaneous refinement in both space and time. The radiation component of CASTRO will be described in detail in the next paper, Part II, of this series.
Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening
NASA Technical Reports Server (NTRS)
Diskin, Boris
1999-01-01
This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation
Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications
NASA Technical Reports Server (NTRS)
Sun, Xian-He
1997-01-01
Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm
Yeh, Gour-Tsyh; Carpenter, S.L.; Hopkins, P.L.; Siegel, M.D.
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
Wilson, John D.; Naff, Richard L.
2004-01-01
A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.
Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Storaasli, Olaf O.
2004-01-01
Of several iterative and direct equation solvers evaluated previously for computations in aeroacoustics, the most promising was the NASA-developed General-Purpose Solver (winner of NASA's 1999 software of the year award). This paper presents detailed, single-processor statistics of the performance of this solver, which has been tailored and optimized for large-scale aeroacoustic computations. The statistics, compiled using an SGI ORIGIN 2000 computer with 12 Gb available memory (RAM) and eight available processors, are the central processing unit time, RAM requirements, and solution error. The equation solver is capable of solving 10 thousand complex unknowns in as little as 0.01 sec using 0.02 Gb RAM, and 8.4 million complex unknowns in slightly less than 3 hours using all 12 Gb. This latter solution is the largest aeroacoustics problem solved to date with this technique. The study was unable to detect any noticeable error in the solution, since noise levels predicted from these solution vectors are in excellent agreement with the noise levels computed from the exact solution. The equation solver provides a means for obtaining numerical solutions to aeroacoustics problems in three dimensions.
Wu, Jue; Chung, Albert C S
2005-01-01
This paper introduces a novel solver, namely cross entropy (CE), into the MRF theory for medical image segmentation. The solver, which is based on the theory of rare event simulation, is general and stochastic. Unlike some popular optimization methods such as belief propagation and graph cuts, CE makes no assumption on the form of objective functions and thus can be applied to any type of MRF models. Furthermore, it achieves higher performance of finding more global optima because of its stochastic property. In addition, it is more efficient than other stochastic methods like simulated annealing. We tested the new solver in 4 series of segmentation experiments on synthetic and clinical, vascular and cerebral images. The experiments show that CE can give more accurate segmentation results.
Development of a parallel implicit solver of fluid modeling equations for gas discharges
NASA Astrophysics Data System (ADS)
Hung, Chieh-Tsan; Chiu, Yuan-Ming; Hwang, Feng-Nan; Wu, Jong-Shinn
2011-01-01
A parallel fully implicit PETSc-based fluid modeling equations solver for simulating gas discharges is developed. Fluid modeling equations include: the neutral species continuity equation, the charged species continuity equation with drift-diffusion approximation for mass fluxes, the electron energy density equation, and Poisson's equation for electrostatic potential. Except for Poisson's equation, all model equations are discretized by the fully implicit backward Euler method as a time integrator, and finite differences with the Scharfetter-Gummel scheme for mass fluxes on the spatial domain. At each time step, the resulting large sparse algebraic nonlinear system is solved by the Newton-Krylov-Schwarz algorithm. A 2D-GEC RF discharge is used as a benchmark to validate our solver by comparing the numerical results with both the published experimental data and the theoretical prediction. The parallel performance of the solver is investigated.
Wavelet-based Poisson Solver for use in Particle-In-CellSimulations
Terzic, B.; Mihalcea, D.; Bohn, C.L.; Pogorelov, I.V.
2005-05-13
We report on a successful implementation of a wavelet based Poisson solver for use in 3D particle-in-cell (PIC) simulations. One new aspect of our algorithm is its ability to treat the general(inhomogeneous) Dirichlet boundary conditions (BCs). The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modeling of the Fermilab/NICADD and AES/JLab photoinjectors.
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
NASA Technical Reports Server (NTRS)
Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.
Parallel performance investigations of an unstructured mesh Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
2000-01-01
A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.
Flutter and Forced Response Analyses of Cascades using a Two-Dimensional Linearized Euler Solver
NASA Technical Reports Server (NTRS)
Reddy, T. S. R.; Srivastava, R.; Mehmed, O.
1999-01-01
Flutter and forced response analyses for a cascade of blades in subsonic and transonic flow is presented. The structural model for each blade is a typical section with bending and torsion degrees of freedom. The unsteady aerodynamic forces due to bending and torsion motions. and due to a vortical gust disturbance are obtained by solving unsteady linearized Euler equations. The unsteady linearized equations are obtained by linearizing the unsteady nonlinear equations about the steady flow. The predicted unsteady aerodynamic forces include the effect of steady aerodynamic loading due to airfoil shape, thickness and angle of attack. The aeroelastic equations are solved in the frequency domain by coupling the un- steady aerodynamic forces to the aeroelastic solver MISER. The present unsteady aerodynamic solver showed good correlation with published results for both flutter and forced response predictions. Further improvements are required to use the unsteady aerodynamic solver in a design cycle.
A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations
Adelmann, A. Arbenz, P. Ineichen, Y.
2010-06-20
We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or 'mildly' nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our iterative solver with an FFT-based solver that is more commonly used for applications in beam dynamics.
Gao, Hao; Phan, Lan; Lin, Yuting
2012-09-01
A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/.
Nonlinear vector eigen-solver and parallel reassembly processing for structural nonlinear vibration
NASA Astrophysics Data System (ADS)
Xue, D. Y.; Mei, Chuh
1993-12-01
In the frequency domain solution of large amplitude nonlinear vibration, two operations are computationally costly. They are: (1) the iterative eigen-solution and (2) the iterative nonlinear matrix reassembly. This study introduces a nonlinear eigen-solver which greatly speeds up the solution procedure by using a combination of vector iteration and nonlinear matrix updating. A feature of this new method is that it avoids repeatedly using a costly eigen-solver or equation solver. This solution procedure has also been engaged in parallel processing to further speed up the computation. Parallel nonlinear matrix reassembly is the main interest in this parallel processing. Force Macro is used in the parallel program on a CRAY-2S supercomputer.
Prediction of ship resistance in head waves using RANS based solver
NASA Astrophysics Data System (ADS)
Islam, Hafizul; Akimoto, Hiromichi
2016-07-01
Maneuverability prediction of ships using CFD has gained high popularity over the years because of its improving accuracy and economics. This paper discusses the estimation of calm water and added resistance properties of a KVLCC2 model using a light and economical RaNS based solver, called SHIP_Motion. The solver solves overset structured mesh using finite volume method. In the calm water test, total drag coefficient, sinkage and trim values were predicted together with mesh dependency analysis and compared with experimental data. For added resistance in head sea, short wave cases were simulated and compared with experimental and other simulation data. Overall the results were well predicted and showed good agreement with comparative data. The paper concludes that it is well possible to predict ship maneuverability characteristics using the present solver, with reasonable accuracy utilizing minimum computational resources and within acceptable time.
dugksFoam: An open source OpenFOAM solver for the Boltzmann model equation
NASA Astrophysics Data System (ADS)
Zhu, Lianhua; Chen, Songze; Guo, Zhaoli
2017-04-01
A deterministic Boltzmann model equation solver called dugksFoam has been developed in the framework of the open source CFD toolbox OpenFOAM. The solver adopts the discrete unified gas kinetic scheme (Guo et al., 2015) with the Shakhov collision model. It has been validated by simulating several test cases covering different flow regimes including the one dimensional shock tube problem, a two dimensional thermal induced flow and the three dimensional lid-driven cavity flow. The solver features a parallel computing ability based on the velocity space decomposition, which is different from the physical space decomposition based approach provided by the OpenFOAM framework. The two decomposition approaches have been compared in both two and three dimensional cases. The parallel performance improves significantly using the newly implemented approach. A speed up by two orders of magnitudes has been observed using 256 cores on a small cluster.
Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver
Shonibare, Olabanji Y.; Wardle, Kent E.
2015-01-01
A novel hybrid multiphase flow solver has been used to conduct simulations of a vertical plunging liquid jet. This solver combines a multifluid methodology with selective interface sharpening to enable simulation of both the initial jet impingement and the long-time entrained bubble plume phenomena. Models are implemented for variable bubble size capturing and dynamic switching of interface sharpened regions to capture transitions between the initially fully segregated flow types into the dispersed bubbly flow regime. It was found that the solver was able to capture the salient features of the flow phenomena under study and areas for quantitative improvement havemore » been explored and identified. In particular, a population balance approach is employed and detailed calibration of the underlying models with experimental data is required to enable quantitative prediction of bubble size and distribution to capture the transition between segregated and dispersed flow types with greater fidelity.« less
Plasma wave simulation based on versatile FEM solver on Alcator C-mod
Shiraiwa, S.; Meneghini, O.; Parker, R.; Wallace, G.; Wilson, J.
2009-11-26
The finite element method (FEM) has the potential of simulating plasma waves seamlessly from the core to the vacuum and antenna regions. We explored the possibility of using a versatile FEM solver package, COMSOL, for lower hybrid (LH) wave simulation. Special care was paid to boundary conditions to satisfy toroidal symmetry. The non-trivial issue of introducing hot plasma effects was addressed by an iterative algorithm. These techniques are verified both analytically and numerically. In the lower hybrid (LH) grill antenna coupling problem, the FEM solver successfully reproduced the solution that was obtained analytically. Propagation of LH waves on the Alcator C and Alcator C-MOD plasmas was compared with a ray-tracing code, showing good consistency. The approach based on the FEM is computationally less intensive compared to spectral domain solvers, and more suitable for the simulation of larger device such as ITER.
A finite-volume Euler solver for computing rotary-wing aerodynamics on unstructured meshes
NASA Technical Reports Server (NTRS)
Strawn, Roger C.; Barth, Timothy J.
1992-01-01
An unstructured-grid solver for the unsteady Euler equations has been developed for predicting the aerodynamics of helicopter rotor blades. This flow solver is a finite-volume scheme that computes flow quantities at the vertices of the mesh. Special treatments are used for the flux differencing and boundary conditions in order to compute rotary-wing flowfields, and these are detailed in the paper. The unstructured-grid solver permits adaptive grid refinement in order to improve the resolution of flow features such as shocks, rotor wakes and acoustic waves. These capabilities are demonstrated in the paper. Example calculations are presented for two hovering rotors. In both cases, adaptive-grid refinement is used to resolve high gradients near the rotor surface and also to capture the vortical regions in the rotor wake. The computed results show good agreement with experimental results for surface airloads and wake geometry.
Phan, Lan; Lin, Yuting
2012-01-01
Abstract. A graphics processing unit–based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/. PMID:23085905
Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru; Guruswamy, Guru P.
1995-01-01
New capabilities have been developed for a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is based on a combination of the lower-upper factored symmetric Gauss-Seidel implicit method and the modified Harten-Lax-van Leer-Einfeldt upwind scheme. A numerically stable and efficient pseudo-time-marching method is also developed for computing steady flows over flexible wings. Results are demonstrated for transonic flows over rigid and flexible wings.
A weakly compressible SPH method based on a low-dissipation Riemann solver
NASA Astrophysics Data System (ADS)
Zhang, C.; Hu, X. Y.; Adams, N. A.
2017-04-01
We present a low-dissipation weakly-compressible SPH method for modeling free-surface flows exhibiting violent events such as impact and breaking. The key idea is to modify a Riemann solver which determines the interaction between particles by a simple limiter to decrease the intrinsic numerical dissipation. The modified Riemann solver is also extended for imposing wall boundary conditions. Numerical tests show that the method resolves free-surface flows accurately and produces smooth, accurate pressure fields. The method is compatible with the hydrostatic solution and exhibits considerably less numerical damping of the mechanical energy than previous methods.
NASA Technical Reports Server (NTRS)
Martin, E. D.; Lomax, H.
1977-01-01
Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.
A second-order Grad-Shafranov solver with accurate derivative computation
NASA Astrophysics Data System (ADS)
Eshghi, Iraj; Ricketson, Lee; Cerfon, Antoine
2016-10-01
We present progress on a fast Grad-Shafranov and Poisson solver that uses the finite element method with linear elements to find equilibria of the electro-magnetic potentials inside tokamaks. The code converges with second-order errors, and we introduce a module which can take derivatives of the potential at no increase in error. Thus, this code can be much faster than most higher-order finite element solvers, while still retaining a sufficiently small error margin in the physically relevant quantities.
Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics
NASA Technical Reports Server (NTRS)
Martin, E. D.
1977-01-01
Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
NASA Technical Reports Server (NTRS)
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles
NASA Astrophysics Data System (ADS)
Moffitt, Nicholas J.
This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate
An accurate predictor-corrector HOC solver for the two dimensional Riemann problem of gas dynamics
NASA Astrophysics Data System (ADS)
Gogoi, Bidyut B.
2016-10-01
The work in the present manuscript is concerned with the simulation of twodimensional (2D) Riemann problem of gas dynamics. We extend our recently developed higher order compact (HOC) method from one-dimensional (1D) to 2D solver and simulate the problem on a square geometry with different initial conditions. The method is fourth order accurate in space and second order accurate in time. We then compare our results with the available benchmark results. The comparison shows an excellent agreement of our results with the existing ones in the literature. Being a finite difference solver, it is quite straight-forward and simple.
NASA Astrophysics Data System (ADS)
Shippee, N. J.; Atkinson, D. E.
2014-12-01
The idea of considering the "end user perspective" regarding storm activity and objective tracking methods used to compile information on their behaviour is particularly important in the Alaskan region. Annually, coastal regions in the North are exposed to stormy conditions, though most impacts occur during periods where multiple storms track over the same area in a short period of time (serial cyclones) or where strong storms occur without the presence of a protective sea ice buffer. From a fixed perspective (i.e. Eulerian), a storm may be identified more by the impacts that it generates at that location (winds, sea state, erosion). From a Lagrangian (tracking) view, the intensity, duration, and characteristics of the synoptic environment may prove more relevant for understanding. The overall "effectiveness" of an objective tracking method depends on the intended use of the provided information. While pitting different methods against each other is not necessarily a fruitful exercise (Mesquita et al. 2009), the reality is that one method may better reflect the reality of storm activity and impacts to those experiencing the weather first hand. One of the more subtle points in extra-tropical cyclone tracking and comparison work is the method by which a storm is defined. Most cyclones are analyzed on MSLP fields; others define a cyclone by relative vorticity (ζ) maxima at 850 hPa (NH) and minima (SH). Storms can also be defined by wind events, or even impacts, at a location. Using counts of strong wind events at a grid point or location can account for pressure gradients both associated with storms and absent of a synoptic event. Three separate tracking algorithms are analyzed to determine the method most likely to produce a long-term homogeneous dataset that can be used to train a statistical seasonal prediction method. These methods include the Serreze algorithm, Hodges TRACK algorithm, and Atkinson algorithm. Both the Serreze and Hodges methods provide a tracking
Kastanya, Doddy Yozef Febrian; Turinsky, Paul J.
2005-05-15
A Newton-Krylov iterative solver has been developed to reduce the CPU execution time of boiling water reactor (BWR) core simulators implemented in the core simulator part of the Fuel Optimization for Reloads Multiple Objectives by Simulated Annealing for BWR (FORMOSA-B) code, which is an in-core fuel management optimization code for BWRs. This new solver utilizes Newton's method to explicitly treat strong nonlinearities in the problem, replacing the traditionally used nested iterative approach. Newton's method provides the solver with a higher-than-linear convergence rate, assuming that good initial estimates of the unknowns are provided. Within each Newton iteration, an appropriately preconditioned Krylov solver is utilized for solving the linearized system of equations. Taking advantage of the higher convergence rate provided by Newton's method and utilizing an efficient preconditioned Krylov solver, we have developed a Newton-Krylov solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator. Numerical tests on the new solver have shown that speedups ranging from 1.6 to 2.1, with reference to the traditional approach of employing nested iterations to treat the nonlinear feedbacks, can be achieved. However, if a preconditioned Krylov solver is employed to complete the inner iterations of the traditional approach, negligible CPU time differences are noted between the Newton-Krylov and traditional (Krylov) approaches.
NASA Technical Reports Server (NTRS)
Carmichael, G. R.; Peters, L. K.
1984-01-01
A three-dimensional, time dependent Eulerian atmospheric SO2 and sulfate transport/transformation/removal model is described and applied to the eastern U.S. The model was developed in anticipation of increased input to the atmospheric sulfur content by coal-burning power plants in the near future and is intended as an aid in identifying sources of SO2. The Eulerian transport model incorporates functions for chemical transformations, dry deposition, spatial topographical variations, spatial and temporal variations of mixing layer heights, the wind field, eddy diffusivities, deposition velocities, and temperature and water concentration profiles. Attention is also given to the SO2 photochemical oxidation mechanism and rates. Results from a 72-hr simulation of SO(x) transport over the eastern U.S., using actual 1974 meteorological data, illustrate the model's capability to depict interactions between emissions, transport, chemistry and removal. Concentration distributions are demonstrated to have significant spatial and temporal variations.
Mastin, Larry G.; Randall, Michael J.; Schwaiger, Hans F.; Denlinger, Roger P.
2013-01-01
Ash3d is a three-dimensional Eulerian atmospheric model for tephra transport, dispersal, and deposition, written by the authors to study and forecast hazards of volcanic ash clouds and tephra fall. In this report, we explain how to set up simulations using both a web interface and an ASCII input file, and how to view and interpret model output. We also summarize the architecture of the model and some of its properties.
Ganshin, A; Oda, T; Saito, M; Maksyutov, S; Valsala, V; Andres, Robert Joseph; Fischer, R; Lowry, D; Lukyanov, A; Matsueda, H; Nisbet, E; Rigby, M; Sawa, Y; Toumi, R; Tsuboi, K; Varlagin, A; Zhuravlev, R
2012-01-01
Abstract. We designed a method to simulate atmospheric CO2 concentrations at several continuous observation sites around the globe using surface fluxes at a very high spatial resolution. The simulations presented in this study were performed using the Global Eulerian-Lagrangian Coupled Atmospheric model (GELCA), comprising a Lagrangian particle dispersion model coupled to a global atmospheric tracer transport model with prescribed global surface CO2 flux maps at a 1 1 km resolution. The surface fluxes used in the simulations were prepared by assembling the individual components of terrestrial, oceanic and fossil fuel CO2 fluxes. This experimental setup (i.e. a transport model running at a medium resolution, coupled to a high-resolution Lagrangian particle dispersion model together with global surface fluxes at a very high resolution), which was designed to represent high-frequency variations in atmospheric CO2 concentration, has not been reported at a global scale previously. Two sensitivity experiments were performed: (a) using the global transport model without coupling to the Lagrangian dispersion model, and (b) using the coupled model with a reduced resolution of surface fluxes, in order to evaluate the performance of Eulerian-Lagrangian coupling and the role of high-resolution fluxes in simulating high-frequency variations in atmospheric CO2 concentrations. A correlation analysis between observed and simulated atmospheric CO2 concentrations at selected locations revealed that the inclusion of both Eulerian-Lagrangian coupling and highresolution fluxes improves the high-frequency simulations of the model. The results highlight the potential of a coupled Eulerian-Lagrangian model in simulating high-frequency atmospheric CO2 concentrations at many locations worldwide. The model performs well in representing observations of atmospheric CO2 concentrations at high spatial and temporal resolutions, especially for coastal sites and sites located close to sources of
Short, Mark; Aslam, Tariq D
2010-01-01
The detonation structure in many insensitive high explosives consists of two temporally disparate zones of heat release. In PBX 9502, there is a fast reaction zone ({approx} 25 ns) during which reactants are converted to gaseous products and small carbon clusters, followed by a slower regime ({approx} 250 ns) of carbon coagulation. A hybrid approach for determining the propagation of two-stage heat release detonations has been developed that utilizes a detonation shock dynamics (DSD) based strategy for the fast reaction zone with a direct hydrodynamic simulation of the flow in the slow zone. Unlike a standard DSD/programmed bum formulation, the evolution of the fast zone DSD-like surface is coupled to the flow in the slow reaction zone. We have termed this formulation flow integrated detonation shock dynamics (FIDSD). The purpose of the present paper is to show how the FIDSD formulation can be applied to detonation propagation on an Eulerian grid using an algorithm based on level set interface tracking and a ghost fluid approach.
Saenz, Juan A.; Chen, Qingshan; Ringler, Todd
2015-05-19
Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWA framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, we verify our analysis by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.
Saenz, Juan A.; Chen, Qingshan; Ringler, Todd
2015-05-19
Recent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWAmore » framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, we verify our analysis by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.« less
NASA Astrophysics Data System (ADS)
Adesemowo, Morakinyo; Shelton, John
2016-11-01
Previous experimental and numerical investigations involving lid-driven cavity flows with particle suspensions have primarily focused on particle tracking and the visualization of complex three-dimensional structures that compose the flow field. However, these particle suspensions and their resulting particle-particle interactions could also be viewed as a system of time-dependent perturbation equations to the steady-state Navier-Stokes equations and could affect both the stability and steady-state characteristics of the two-dimensional lid-driven cavity system. In this investigation, an Eulerian-Lagrangian approach to modeling particle suspensions in the lid-driven cavity is utilized in FV-CFD simulations to investigate the effect particle density, area fraction, and Reynolds number have on the two-dimensional flow characteristics of a laminar fluid. Observations have indicated that the development of the primary vortex in the lid-driven cavity varies according to the area fraction of particle suspensions in the system; transitioning from development via an adverse pressure gradient at the top-right corner of the cavity towards particle-laden behavior where particle-particle interactions dominate the development of the primary vortex. Dynamic responses were also observed for particle systems of less dense particles. Finally, a comparison between flows perturbed using disturbance velocities and from particle interactions was performed.
Efficient simulation of 2+2-D multi-species plasmas waves using an Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Banks, Jeffrey; Berger, Richard; Chapman, Thomas; Hittinger, Jeffrey; Bruner, Stephan
2013-10-01
We discuss multi-species aspects of the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space (Banks et al., Phys. Plasmas 18, 052102 (2011)). In order to control the inherent cost associated with phase-space simulation, our approach uses a minimally diffuse, fourth-order-accurate finite-volume discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198-2207). The scheme is discretely conservative and controls unphysical oscillations. The details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of 2D simulations of propagating ion acoustic waves (IAWs) created using an external driving potential. The evolution of the plasma wave field and associated self-consistent distribution of trapped electrons and ions is studied after the external drive is turned off. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Research and Development Program at LLNL under project tracking code 12-ERD-061.
Briere, E.; Larrauri, D.; Olive, J.
1995-09-01
For about four years, Electricite de France has been developing a 3-D computer code for the Eulerian simulation of two-phase flows. This code, named ASTRID, is based on the six-equation two-fluid model. Boiling water flows, such as those encountered in nuclear reactors, are among the main applications of ASTRID. In order to provide ASTRID with closure laws and boundary conditions suitable for boiling flows, a boiling model has been developed by EDF and the Institut de Mecanique des Fluides de Toulouse. In the fluid, the heat and mass transfer between a bubble and the liquid is being modelled. At the heating wall, the incipient boiling point is determined according to Hsu`s criterion and the boiling heat flux is split into three additive terms: a convective term, a quenching term and a vaporisation term. This model uses several correlations. EDF`s program in boiling two-phase flows also includes experimental studies, some of which are performed in collaboration with other laboratories. Refrigerant subcooled boiling both in tubular (DEBORA experiment, CEN Grenoble) and in annular geometry (Arizona State University Experiment) have been computed with ASTRID. The simulations show the satisfactory results already obtained on void fraction and liquid temperature. Ways of improvement of the model are drawn especially on the dynamical part.
NASA Astrophysics Data System (ADS)
Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song
2015-09-01
An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.
Park, Byoung Yoon; Leavy, Richard Brian; Niederhaus, John Henry J.
2013-03-01
The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the Eulerian frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by less than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.
NASA Astrophysics Data System (ADS)
Wang, C. Y.
This paper describes fluid-structure-interaction and structure response analyses of a reactor vessel subjected to loadings associated with postulated accidents, using the hybrid Lagrangian-Eulerian code ALICE-II. This code has been improved recently to accommodate many features associated with innovative designs of reactor vessels. Calculational capabilities have been developed to treat water in the reactor cavity outside the vessel, internal shield structures and internal thin shells. The objective of the present analyses is to study the cover response and potential for missile generation in response to a fuel-coolant interaction in the core region. Three calculations were performed using the cover weight as a parameter. To study the effect of the cavity water, vessel response calculations for both wet- and dry-cavity designs are compared. Results indicate that for all cases studied and for the design parameters assumed, the calculated cover displacements are all smaller than the bolts' ultimate displacement and no missile generation of the closure head is predicted. Also, solutions reveal that the cavity water of the wet-cavity design plays an important role of restraining the downward displacement of the bottom head. Based on these studies, the analyses predict that the structure integrity is maintained throughout the postulated accident for the wet-cavity design.
A Comparison of the Intellectual Abilities of Good and Poor Problem Solvers: An Exploratory Study.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
This study examined a selected sample of fourth-grade students who had been previously identified as good or poor problem solvers. The pupils were compared on variables considered as "reference tests" for Verbal, Induction, Numerical, Word Fluency, Memory, Spatial Visualization, and Perceptual Speed abilities. The data were compiled to…
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Das, Raja; Saltz, Joel; Vermeland, R. E.
1992-01-01
An efficient three dimensional unstructured Euler solver is parallelized on a Cray Y-MP C90 shared memory computer and on an Intel Touchstone Delta distributed memory computer. This paper relates the experiences gained and describes the software tools and hardware used in this study. Performance comparisons between two differing architectures are made.
NASA Technical Reports Server (NTRS)
Jameson, A.
1975-01-01
The use of a fast elliptic solver in combination with relaxation is presented as an effective way to accelerate the convergence of transonic flow calculations, particularly when a marching scheme can be used to treat the supersonic zone in the relaxation process.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Flowfield Comparisons from Three Navier-Stokes Solvers for an Axisymmetric Separate Flow Jet
NASA Technical Reports Server (NTRS)
Koch, L. Danielle; Bridges, James; Khavaran, Abbas
2002-01-01
To meet new noise reduction goals, many concepts to enhance mixing in the exhaust jets of turbofan engines are being studied. Accurate steady state flowfield predictions from state-of-the-art computational fluid dynamics (CFD) solvers are needed as input to the latest noise prediction codes. The main intent of this paper was to ascertain that similar Navier-Stokes solvers run at different sites would yield comparable results for an axisymmetric two-stream nozzle case. Predictions from the WIND and the NPARC codes are compared to previously reported experimental data and results from the CRAFT Navier-Stokes solver. Similar k-epsilon turbulence models were employed in each solver, and identical computational grids were used. Agreement between experimental data and predictions from each code was generally good for mean values. All three codes underpredict the maximum value of turbulent kinetic energy. The predicted locations of the maximum turbulent kinetic energy were farther downstream than seen in the data. A grid study was conducted using the WIND code, and comments about convergence criteria and grid requirements for CFD solutions to be used as input for noise prediction computations are given. Additionally, noise predictions from the MGBK code, using the CFD results from the CRAFT code, NPARC, and WIND as input are compared to data.
A Riemann solver based on a global existence proof for the Riemann problem
NASA Technical Reports Server (NTRS)
Dutt, P.
1986-01-01
Godunov's method and several other methods for computing solutions to the equations of gas dynamics use Riemann solvers to resolve discontinuities at the interface between cells. A new method is proposed here for solving the Riemann problem based on a global existence proof for the solution to the Riemann problem. The method is found to be very reliable and computationally efficient.
MLTE: An LTE Solver for Diatomic Molecules and Atoms above 6,000 Degrees K
2007-11-02
Bresmann, " SOLGASMIX - PV , A Computer Program to Calculate Equilibrium Relationships in Complex Chemical Systems", Oak Ridge National Laboratory Report...34 equilibria solvers for use on mainframe computers have emerged, among them are SOLGASMIX [Ref.l] and CHEMKIN [Ref.6]. To evaluate the free energy of a
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.
2005-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.
Jia, Jingfei
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. PMID:26345531
VDJSeq-Solver: In Silico V(D)J Recombination Detection Tool
Paciello, Giulia; Acquaviva, Andrea; Pighi, Chiara; Ferrarini, Alberto; Macii, Enrico; Zamo’, Alberto; Ficarra, Elisa
2015-01-01
In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(D)J rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/. PMID:25799103
Parallel FFT-based Poisson Solver for Isolated Three-dimensional Systems
Budiardja, Reuben D; Cardall, Christian Y
2011-01-01
We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel computer. Test results to demonstrate the convergence and scaling properties of the implementation are presented. The solver is offered to interested users as the library PSPFFT.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Fisicaro, G. Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less
Fast Time Domain Integral Equation Solvers for Large-Scale Electromagnetic Analysis
2004-10-01
separable and non-separable source expansions. The separable representations will rely on divergence-conforming Nedelec elements defined on geometrically...the work of Ha-Duong/Aboud/ Nedelec , such solvers, when carefully implemented, are stable. Their implementation however is very difficult; moreover
LEOPARD: A grid-based dispersion relation solver for arbitrary gyrotropic distributions
NASA Astrophysics Data System (ADS)
Astfalk, Patrick; Jenko, Frank
2017-01-01
Particle velocity distributions measured in collisionless space plasmas often show strong deviations from idealized model distributions. Despite this observational evidence, linear wave analysis in space plasma environments such as the solar wind or Earth's magnetosphere is still mainly carried out using dispersion relation solvers based on Maxwellians or other parametric models. To enable a more realistic analysis, we present the new grid-based kinetic dispersion relation solver LEOPARD (Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally-symmetric Distributions) which no longer requires prescribed model distributions but allows for arbitrary gyrotropic distribution functions. In this work, we discuss the underlying numerical scheme of the code and we show a few exemplary benchmarks. Furthermore, we demonstrate a first application of LEOPARD to ion distribution data obtained from hybrid simulations. In particular, we show that in the saturation stage of the parallel fire hose instability, the deformation of the initial bi-Maxwellian distribution invalidates the use of standard dispersion relation solvers. A linear solver based on bi-Maxwellians predicts further growth even after saturation, while LEOPARD correctly indicates vanishing growth rates. We also discuss how this complies with former studies on the validity of quasilinear theory for the resonant fire hose. In the end, we briefly comment on the role of LEOPARD in directly analyzing spacecraft data, and we refer to an upcoming paper which demonstrates a first application of that kind.
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
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.
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
ERIC Educational Resources Information Center
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
A fast parallel solver for the forward problem in electrical impedance tomography.
Jehl, Markus; Dedner, Andreas; Betcke, Timo; Aristovich, Kirill; Klöfkorn, Robert; Holder, David
2015-01-01
Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and the resulting surface voltages are measured. It has the potential to distinguish between ischaemic and haemorrhagic stroke with a portable and inexpensive device. The image reconstruction relies on an accurate forward model of the experimental setup. Because of the relatively small signal in stroke EIT, the finite-element modeling requires meshes of more than 10 million elements. To study the requirements in the forward modeling in EIT and also to reduce the time for experimental image acquisition, it is necessary to reduce the run time of the forward computation. We show the implementation of a parallel forward solver for EIT using the Dune-Fem C++ library and demonstrate its performance on many CPU's of a computer cluster. For a typical EIT application a direct solver was significantly slower and not an alternative to iterative solvers with multigrid preconditioning. With this new solver, we can compute the forward solutions and the Jacobian matrix of a typical EIT application with 30 electrodes on a 15-million element mesh in less than 15 min. This makes it a valuable tool for simulation studies and EIT applications with high precision requirements. It is freely available for download.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines
NASA Technical Reports Server (NTRS)
Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.
1994-01-01
The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).
Jia, Jingfei; Kim, Hyun K; Hielscher, Andreas H
2015-12-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.
Large Eddy and Detached Eddy Simulations Using an Unstructured Multigrid Solver
2001-08-01
SOLVER DIMITRI J. MAVRIPLIS ICASE NASA Langley Research Center, Hampton, VA, USA JUAN PELAEZ Department of Aerospace Engineering Old Dominion University...computations for 3D high-lift analysis. AIAA Journal of Aircraft, 36(6):987-998, 1999. [2] J. Pelaez , D. J. Mavriplis, and 0. Kandil. Unsteady analysis of
VDJSeq-Solver: in silico V(D)J recombination detection tool.
Paciello, Giulia; Acquaviva, Andrea; Pighi, Chiara; Ferrarini, Alberto; Macii, Enrico; Zamo', Alberto; Ficarra, Elisa
2015-01-01
In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(D)J rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/.
Determining the Optimal Values of Exponential Smoothing Constants--Does Solver Really Work?
ERIC Educational Resources Information Center
Ravinder, Handanhal V.
2013-01-01
A key issue in exponential smoothing is the choice of the values of the smoothing constants used. One approach that is becoming increasingly popular in introductory management science and operations management textbooks is the use of Solver, an Excel-based non-linear optimizer, to identify values of the smoothing constants that minimize a measure…
A Tensor-Train accelerated solver for integral equations in complex geometries
NASA Astrophysics Data System (ADS)
Corona, Eduardo; Rahimian, Abtin; Zorin, Denis
2017-04-01
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log N) and once the inverse is computed, it can be applied in O (Nlog N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.
Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Frink, N. T.; Mavriplis, D. J.; Rausch, R. D.; Milholen, W. E.
2004-01-01
A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not
AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation
Koehl, Patrice; Delarue, Marc
2010-01-01
The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on
Large-scale 3D EM modeling with a Block Low-Rank multifrontal direct solver
NASA Astrophysics Data System (ADS)
Shantsev, Daniil V.; Jaysaval, Piyoosh; de la Kethulle de Ryhove, Sébastien; Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves; Mary, Theo
2017-03-01
We put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10%, 30% and 40% of their full rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O( {{N^2}} ) for the full-rank solver to O( {{N^m}} ) with m = 1.4 - 1.6 . The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3D CSEM Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.
NASA Astrophysics Data System (ADS)
Aricò, Costanza; Lo Re, Carlo
2016-12-01
We extend a recently proposed 2D depth-integrated Finite Volume solver for the nonlinear shallow water equations with non-hydrostatic pressure distribution. The proposed model is aimed at simulating both nonlinear and dispersive shallow water processes. We split the total pressure into its hydrostatic and dynamic components and solve a hydrostatic problem and a non-hydrostatic problem sequentially, in the framework of a fractional time step procedure. The dispersive properties are achieved by incorporating the non-hydrostatic pressure component in the governing equations. The governing equations are the depth-integrated continuity equation and the depth-integrated momentum equations along the x, y and z directions. Unlike the previous non-hydrostatic shallow water solver, in the z momentum equation, we retain both the vertical local and convective acceleration terms. In the former solver, we keep only the local vertical acceleration term. In this paper, we investigate the effects of these convective terms and the possible improvements of the computed solution when these terms are not neglected in the governing equations, especially in strongly nonlinear processes. The presence of the convective terms in the vertical momentum equation leads to a numerical solution procedure, which is quite different from the one of the previous solver, in both the hydrostatic and dynamic steps. We discretize the spatial domain using unstructured triangular meshes satisfying the Generalized Delaunay property. The numerical solver is shock capturing and easily addresses wetting/drying problems, without any additional equation to solve at wet/dry interfaces. We present several numerical applications for challenging flooding processes encountered in practical aspects over irregular topography, including a new set of experiments carried out at the Hydraulics Laboratory of the University of Palermo.
NASA Astrophysics Data System (ADS)
Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike
The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under
NASA Astrophysics Data System (ADS)
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
Suk, Heejun
2016-07-01
MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes.
Miniati, Francesco
2014-02-10
We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z = 0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h {sup –1} kpc across the virial volume. The probability density functions of various velocity-derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within the R {sub vir}/3 region and 40% beyond that. We compute second- and third-order longitudinal and transverse structure functions for both solenoidal and compressional components in the cluster core, virial region, and beyond. The structure functions exhibit a well-defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases toward the outskirts. Within R {sub vir}/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers's; the flow is mostly solenoidal and statistically rigorously, which is consistent with fully developed homogeneous and isotropic turbulence. Small-scale anisotropy appears due to numerical artifact. Toward the virial region, the flow becomes increasingly compressional, the structure functions become flatter, and modest genuine anisotropy appear particularly close to the injection scale. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution leads to a lack of turbulent power on a small scales, an excess thereof on large scales, and
Neutrino transport in type II supernovae: Boltzmann solver vs. Monte Carlo method
NASA Astrophysics Data System (ADS)
Yamada, Shoichi; Janka, Hans-Thomas; Suzuki, Hideyuki
1999-04-01
We have coded a Boltzmann solver based on a finite difference scheme (S_N method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find good overall agreement between the two methods. This gives credibility to both methods which are based on completely different formulations. In particular, the number and energy fluxes and the mean energies of the neutrinos show remarkably good agreement, because these quantities are determined in a region where the angular distribution of the neutrinos is nearly isotropic and they are essentially frozen in later on. On the other hand, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to slightly underestimate the flux factor and the Eddington factor outside the (mean) ``neutrinosphere'' where the angular distribution of the neutrinos becomes highly anisotropic. As a result, the neutrino number (and energy) density is somewhat overestimated in this region. This fact suggests that the Boltzmann solver should be applied to calculations of the neutrino heating in the hot-bubble region with some caution because there might be a tendency to overestimate the energy deposition rate in disadvantageous situations. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. Employing three different flux limiters, we find that all of them lead to a significant
Simulation of vortex-induced vibrations of a cylinder using ANSYS CFX rigid body solver
NASA Astrophysics Data System (ADS)
Izhar, Abubakar; Qureshi, Arshad Hussain; Khushnood, Shahab
2017-03-01
This article simulates the vortex-induced oscillations of a rigid circular cylinder with elastic support using the new ANSYS CFX rigid body solver. This solver requires no solid mesh to setup FSI (Fluid Structure Interaction) simulation. The two-way case was setup in CFX only. Specific mass of the cylinder and flow conditions were similar to previous experimental data with mass damping parameter equal to 0.04, specific mass of 1 and Reynolds number of 3800. Two dimensional simulations were setup. Both one-degree-of-freedom and two-degree-of-freedom cases were run and results were obtained for both cases with reasonable accuracy as compared with experimental results. Eight-figure XY trajectory and lock-in behavior were clearly captured. The obtained results were satisfactory.
An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Erickson, Larry L.
1994-01-01
A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.
Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases
NASA Astrophysics Data System (ADS)
Zengler, Christoph; Küchlin, Wolfgang
We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2005-01-01
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
NASA Technical Reports Server (NTRS)
Yarrow, Maurice; Vastano, John A.; Lomax, Harvard
1992-01-01
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
Linear optical response of finite systems using multishift linear system solvers
Hübener, Hannes; Giustino, Feliciano
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Multitasking domain decomposition fast Poisson solvers on the Cray Y-MP
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Fatoohi, Rod A.
1990-01-01
The results of multitasking implementation of a domain decomposition fast Poisson solver on eight processors of the Cray Y-MP are presented. The object of this research is to study the performance of domain decomposition methods on a Cray supercomputer and to analyze the performance of different multitasking techniques using highly parallel algorithms. Two implementations of multitasking are considered: macrotasking (parallelism at the subroutine level) and microtasking (parallelism at the do-loop level). A conventional FFT-based fast Poisson solver is also multitasked. The results of different implementations are compared and analyzed. A speedup of over 7.4 on the Cray Y-MP running in a dedicated environment is achieved for all cases.
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
O. Kononenko
2015-02-17
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
Analysis, tuning and comparison of two general sparse solvers for distributed memory computers
Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.; Li, X.S.
2000-06-30
We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differences in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.
Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew
2010-01-01
A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole to local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. PMID:20532187
An unstructured-grid, parallel, projection solver for computing low-speed flows
Christon, M.A.; Carroll, D.E.
1998-08-01
This paper presents an overview of the issues associated with applying a domain-decomposition message-passing paradigm to the parallel implementation of both explicit and semi-implicit projection algorithms. The use of an element-based domain decomposition with an efficient solution strategy for the pressure field is shown to yield a scalable, parallel solution method capable of treating complex flow problems where high-resolution grids are required. In addition, the use of an SSOR or Jacobi preconditioned conjugate gradient solver with an A-conjugate projection reduces the computational time for the solution of the pressure field, and yields parallel efficiencies above 80% for computations with O(250) elements per processor. The parallel projection solver is verified using a series of 2-D and 3-D benchmarks designed to evaluate time-accurate flow solution methods. Finally, the extension of the projection algorithm to reacting flows is demonstrated for a time-dependent vortex-shedding problem.
A GPU-enabled Finite Volume solver for global magnetospheric simulations on unstructured grids
NASA Astrophysics Data System (ADS)
Lani, Andrea; Yalim, Mehmet Sarp; Poedts, Stefaan
2014-10-01
This paper describes an ideal Magnetohydrodynamics (MHD) solver for global magnetospheric simulations based on a B1 +B0 splitting approach, which has been implemented within the COOLFluiD platform and adapted to run on modern heterogeneous architectures featuring General Purpose Graphical Processing Units (GPGPUs). The code is based on a state-of-the-art Finite Volume discretization for unstructured grids and either explicit or implicit time integration, suitable for both steady and time accurate problems. Innovative object-oriented design and coding techniques mixing C++ and CUDA are discussed. Performance results of the modified code on single and multiple processors are presented and compared with those provided by the original solver.
Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai
2014-10-20
We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.
An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.
1994-01-01
An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.
Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Pandyna, Mohagna J.; Frink, Neal T.; Noack, Ralph W.
2005-01-01
A static and dynamic Chimera overset-grid capability is added to an established NASA tetrahedral unstructured parallel Navier-Stokes flow solver, USM3D. Modifications to the solver primarily consist of a few strategic calls to the Donor interpolation Receptor Transaction library (DiRTlib) to facilitate communication of solution information between various grids. The assembly of multiple overlapping grids into a single-zone composite grid is performed by the Structured, Unstructured and Generalized Grid AssembleR (SUGGAR) code. Several test cases are presented to verify the implementation, assess overset-grid solution accuracy and convergence relative to single-grid solutions, and demonstrate the prescribed relative grid motion capability.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K.
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1987-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
Navier-Stokes cascade analysis with a stiff k-epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1988-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
NASA Astrophysics Data System (ADS)
Zhang, Chenglong; Gamba, Irene M.
2016-11-01
We propose a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with Poisson equation. Through time-splitting scheme, a Vlasov-Poisson (collisionless) problem and a homogeneous Landau (collisional) problem are obtained. These two subproblems can be treated separately. We use operator splitting where the transport dynamics for Runge-Kutta Discontinuous Galerkin (RK-DG) method and the collisional dynamics for homogeneous conservative spectral method are adopted respectively. Since two different numerical schemes are applied separately, we have designed a new conservation correction process such that, after projecting the conservative spectral solution onto the DG mesh, there is no loss of moment consvervation. Parallelization is readily implemented. To verify our solver, numerical experiments on linear and nonlinear Landau damping are provided.
SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
Li, Xiaoye S.; Demmel, James W.
2002-03-27
In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.
Duan, Nan; Dimitrovski, Aleksandar D; Simunovic, Srdjan; Sun, Kai
2016-01-01
The development of high-performance computing techniques and platforms has provided many opportunities for real-time or even faster-than-real-time implementation of power system simulations. One approach uses the Parareal in time framework. The Parareal algorithm has shown promising theoretical simulation speedups by temporal decomposing a simulation run into a coarse simulation on the entire simulation interval and fine simulations on sequential sub-intervals linked through the coarse simulation. However, it has been found that the time cost of the coarse solver needs to be reduced to fully exploit the potentials of the Parareal algorithm. This paper studies a Parareal implementation using reduced generator models for the coarse solver and reports the testing results on the IEEE 39-bus system and a 327-generator 2383-bus Polish system model.
Predictions of a Supersonic Jet-in-Crossflow: Comparisons Among CFD Solvers and with Experiment
2014-09-01
data was oriented with the nozzle at y = 0. Hence, the comparisons with CFD results are presented with nozzle on the bottom wall and the jet plume ...The AMRDEC CFD model includes the full Navier-Stokes (FNS) equation set providing an aero-thermo- chemical plume / airframe predictions for unsteady...Predictions of a Supersonic Jet-in-Crossflow: Comparisons Among CFD Solvers and with Experiment by James DeSpirito, Kevin D Kennedy, Clark
Cummings, Julian C.
2013-05-15
This project was a collaboration between researchers at the California Institute of Technology and the University of California, Irvine to investigate the utility of a global field-aligned mesh and gyrokinetic field solver for simulations of the tokamak plasma edge region. Mesh generation software from UC Irvine was tested with specific tokamak edge magnetic geometry scenarios and the quality of the meshes and the solutions to the gyrokinetic Poisson equation were evaluated.
A semi-direct solver for compressible 3-dimensional rotational flow
NASA Technical Reports Server (NTRS)
Chang, S. C.; Adamczyk, J. J.
1983-01-01
An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.
A semi-direct solver for compressible three-dimensional rotational flow
NASA Technical Reports Server (NTRS)
Chang, S.-C.; Adamczyk, J. J.
1983-01-01
An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.
An Efficient Solver of Elasto-plastic Problems in Mechanics Based on TFETI Domain Decomposition
NASA Astrophysics Data System (ADS)
Čermák, M.; Kozubek, T.; Markopoulos, A.
2011-09-01
This paper illustrates how to implement efficiently solvers for elasto-plastic problems. We consider the time step problems formulated by nonlinear variational equations in terms of displacements. To treat nonlinearity and nonsmoothnes we use semismooth Newton method. In each Newton iteration we have to solve linear system of algebraic equations and for its numerical solution we use TFETI domain decomposition method. In our benchmark we demonstrate our approach on von Mises plasticity with isotropic hardening using the return mapping concept.
A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae
Reynolds, D R; Swesty, F D; Woodward, C S
2008-06-12
This paper describes an implicit approach and nonlinear solver for solution of radiation-hydrodynamic problems in the context of supernovae and proto-neutron star cooling. The robust approach applies Newton-Krylov methods and overcomes the difficulties of discontinuous limiters in the discretized equations and scaling of the equations over wide ranges of physical behavior. We discuss these difficulties, our approach for overcoming them, and numerical results demonstrating accuracy and efficiency of the method.
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
NASA Astrophysics Data System (ADS)
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
NASA Astrophysics Data System (ADS)
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
Hybrid MPI+OpenMP Programming of an Overset CFD Solver and Performance Investigations
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Jin, Haoqiang H.; Biegel, Bryan (Technical Monitor)
2002-01-01
This report describes a two level parallelization of a Computational Fluid Dynamic (CFD) solver with multi-zone overset structured grids. The approach is based on a hybrid MPI+OpenMP programming model suitable for shared memory and clusters of shared memory machines. The performance investigations of the hybrid application on an SGI Origin2000 (O2K) machine is reported using medium and large scale test problems.
Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique
NASA Astrophysics Data System (ADS)
Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi
2013-09-01
According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.
NASA Technical Reports Server (NTRS)
Eidson, T. M.; Erlebacher, G.
1994-01-01
While parallel computers offer significant computational performance, it is generally necessary to evaluate several programming strategies. Two programming strategies for a fairly common problem - a periodic tridiagonal solver - are developed and evaluated. Simple model calculations as well as timing results are presented to evaluate the various strategies. The particular tridiagonal solver evaluated is used in many computational fluid dynamic simulation codes. The feature that makes this algorithm unique is that these simulation codes usually require simultaneous solutions for multiple right-hand-sides (RHS) of the system of equations. Each RHS solutions is independent and thus can be computed in parallel. Thus a Gaussian elimination type algorithm can be used in a parallel computation and the more complicated approaches such as cyclic reduction are not required. The two strategies are a transpose strategy and a distributed solver strategy. For the transpose strategy, the data is moved so that a subset of all the RHS problems is solved on each of the several processors. This usually requires significant data movement between processor memories across a network. The second strategy attempts to have the algorithm allow the data across processor boundaries in a chained manner. This usually requires significantly less data movement. An approach to accomplish this second strategy in a near-perfect load-balanced manner is developed. In addition, an algorithm will be shown to directly transform a sequential Gaussian elimination type algorithm into the parallel chained, load-balanced algorithm.
Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain.
Dragna, Didier; Blanc-Benon, Philippe; Poisson, Franck
2013-06-01
The current work aims at developing a linearized Euler equations solver in curvilinear coordinates to account for the effects of topography on sound propagation. In applications for transportation noise, the propagation environment as well as the description of acoustic sources is complex, and time-domain methods have proved their capability to deal with both atmospheric and ground effects. First, equations in curvilinear coordinates are examined. Then time-domain boundary conditions initially proposed for a Cartesian coordinate system are implemented in the curvilinear solver. Two test cases dealing with acoustic scattering by an impedance cylinder in a two-dimensional geometry and by an impedance sphere in a three-dimensional geometry are considered to validate the boundary conditions. Accurate solutions are obtained for both rigid and impedance surfaces. Finally, the solver is used to examine a typical outdoor sound propagation problem. It is shown that it is well-suited to study coupled effects of topography, mixed impedance ground and meteorological conditions.
Parallel satellite orbital situational problems solver for space missions design and control
NASA Astrophysics Data System (ADS)
Atanassov, Atanas Marinov
2016-11-01
Solving different scientific problems for space applications demands implementation of observations, measurements or realization of active experiments during time intervals in which specific geometric and physical conditions are fulfilled. The solving of situational problems for determination of these time intervals when the satellite instruments work optimally is a very important part of all activities on every stage of preparation and realization of space missions. The elaboration of universal, flexible and robust approach for situation analysis, which is easily portable toward new satellite missions, is significant for reduction of missions' preparation times and costs. Every situation problem could be based on one or more situation conditions. Simultaneously solving different kinds of situation problems based on different number and types of situational conditions, each one of them satisfied on different segments of satellite orbit requires irregular calculations. Three formal approaches are presented. First one is related to situation problems description that allows achieving flexibility in situation problem assembling and presentation in computer memory. The second formal approach is connected with developing of situation problem solver organized as processor that executes specific code for every particular situational condition. The third formal approach is related to solver parallelization utilizing threads and dynamic scheduling based on "pool of threads" abstraction and ensures a good load balance. The developed situation problems solver is intended for incorporation in the frames of multi-physics multi-satellite space mission's design and simulation tools.
AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL
NASA Astrophysics Data System (ADS)
Cercos-Pita, J. L.
2015-07-01
In this paper, AQUAgpusph, a new free Smoothed Particle Hydrodynamics (SPH) software accelerated with OpenCL, is described. The main differences and progress with respect to other existing alternatives are considered. These are the use of the Open Computing Language (OpenCL) framework instead of the Compute Unified Device Architecture (CUDA), the implementation of the most popular boundary conditions, the easy customization of the code to different problems, the extensibility with regard to Python scripts, and the runtime output which allows the tracking of simulations in real time, or a higher frequency in saving some results without a significant performance lost. These modifications are shown to improve the solver speed, the results quality, and allow for a wider areas of application. AQUAgpusph has been designed trying to provide researchers and engineers with a valuable tool to test and apply the SPH method. Three practical applications are discussed in detail. The evolution of a dam break is used to quantify and compare the computational performance and modeling accuracy with the most popular SPH Graphics Processing Unit (GPU) accelerated alternatives. The dynamics of a coupled system, a Tuned Liquid Damper (TLD), is discussed in order to show the integration capabilities of the solver with external dynamics. Finally, the sloshing flow inside a nuclear reactor is simulated in order to show the capabilities of the solver to treat 3-D problems with complex geometries and of industrial interest.
Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems
NASA Astrophysics Data System (ADS)
Puzyrev, Vladimir; Koric, Seid; Wilkin, Scott
2016-04-01
High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.
Optimum plane selection for transport-of-intensity-equation-based solvers.
Martinez-Carranza, J; Falaggis, K; Kozacki, T
2014-10-20
Deterministic single beam phase retrieval techniques based on the transport of intensity equation (TIE) use the axial intensity derivative obtained from a series of intensities recorded along the propagation axis as an input to the TIE-based solver. The common belief is that, when reducing the error present in the axial intensity derivative, there will be minimal error in the retrieved phase. Thus, reported optimization schemes of measurement condition focuses on the minimization of error in the axial intensity derivative. As it is shown in this contribution, this assumption is not correct and leads to underestimating the value of plane separation, which increases the phase retrieval errors and sensitivity to noise of the TIE-based measurement system. Therefore, in this paper, a detailed analysis that shows the existence of an optimal separation that minimizes the error in the retrieved phase for a given TIE-based solver is carried out. The developed model is used to derive analytical expressions that provide an optimal plane separation for a given number of planes and level of noise for the case of equidistant plane separation. The obtained results are derived for the widely used Fourier-transform-based TIE solver, but it is shown that they can also be applied to multigrid-based techniques.
Software design of a multi-block, multi-zone, Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Vogels, M. E. S.
A multi-block flow solver technique broadens the applicability of structured grid approaches to stationary flows about complex geometries. For instance, the compuational flow domain about a wing-section with extended flap and slat cannot be covered by a single structured grid. It can, however, be subdivided into a number of blocks (topologically a cube), and per block a structured grid can be generated. In a multi-zone flow solver, the flow domain is subdivided into zones in which models (and sometimes algorithms) can be chosen. Thus, one has the option to trade off accuracy versus efficiency by choosing the Euler equations in the far field zones and the Navier-Stokes equations in the near-geometry zones. In the present multi-block, multi-zone flow solver (SOLEQS) both techniques have been combined: a zone is the union of one or more blocks. In addition, in a zone not only a model can be chosen, but also a numerical integration scheme.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Pei, J. C.; Fann, George I; Harrison, Robert J; Nazarewicz, W.; Hill, Judith C; Galindo, Diego A; Jia, Jun
2012-01-01
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems
Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...
2012-01-01
Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less
NASA Astrophysics Data System (ADS)
Xiao, Cheng-Nian; Denner, Fabian; van Wachem, Berend
2015-11-01
A pressure-based Navier-Stokes solver which is applicable to fluid flow problems of a wide range of speeds is presented. The novel solver is based on collocated variable arrangement and uses a modified Rhie-Chow interpolation method to assure implicit pressure-velocity coupling. A Mach number biased modification to the continuity equation as well as coupling of flow and thermodynamic variables via an energy equation and equation of state enable the simulation of compressible flows belonging to transonic or supersonic Mach number regimes. The flow equation systems are all solved simultaneously, thus guaranteeing strong coupling between pressure and velocity at each iteration step. Shock-capturing is accomplished via nonlinear spatial discretisation schemes which adaptively apply an appropriate blending of first-order upwind and second-order central schemes depending on the local smoothness of the flow field. A selection of standard test problems will be presented to demonstrate the solver's capability of handling incompressible as well as compressible flow fields of vastly different speed regimes on structured as well as unstructured meshes. The authors are grateful for the financial support of Shell.
Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection.
Pimentel, Eduardo da Cruz Gouveia; Sargolzaei, Mehdi; Simianer, Henner; Schenkel, Flávio Schramm; Liu, Zengting; Fries, Luiz Alberto; de Queiroz, Sandra Aidar
2010-01-01
The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use.
Simulating underwater propulsion using an immersed boundary method based open-source solver
NASA Astrophysics Data System (ADS)
Senturk, Utku; Hemmati, Arman; Smits, Alexander J.
2016-11-01
The performance of a newly developed Immersed Boundary Method (IBM) incorporated into a finite volume solver is examined using foam-extend-3.2. IBM uses a discrete forcing approach based on the weighted least squares interpolation to preserve the sharpness of the boundary, which decreases the computational complexity of the problem. Initially, four case studies with gradually increasing complexities are considered to verify the accuracy of the IBM approach. These include the flow past 2D stationary and transversely oscillating cylinders and 3D wake of stationary and pitching flat plates with aspect ratio 1.0 at Re=2000. The primary objective of this study, which is pursued by an ongoing simulation of the wake formed behind a pitching deformable 3D flat plate, is to investigate the underwater locomotion of a fish at Re=10000. The results of the IBM based solver are compared to the experimental results, which suggest that the force computations are accurate in general. Spurious oscillations in the forces are observed for problems with moving bodies which change based on spatial and temporal grid resolutions. Although it still has the full advantage of the main code features, the IBM-based solver in foam-extend-3.2 requires further development to be exploited for complex grids. The work was supported by ONR under MURI Grant N00014-14-1-0533.
An asynchronous solver for systems of ODEs linked by a directed tree structure
NASA Astrophysics Data System (ADS)
Small, Scott J.; Jay, Laurent O.; Mantilla, Ricardo; Curtu, Rodica; Cunha, Luciana K.; Fonley, Morgan; Krajewski, Witold F.
2013-03-01
This paper documents our development and evaluation of a numerical solver for systems of sparsely linked ordinary differential equations in which the connectivity between equations is determined by a directed tree. These types of systems arise in distributed hydrological models. The numerical solver is based on dense output Runge-Kutta methods that allow for asynchronous integration. A partition of the system is used to distribute the workload among different processes, enabling a parallel implementation that capitalizes on a distributed memory system. Communication between processes is performed asynchronously. We illustrate the solver capabilities by integrating flow transport equations for a ˜17,000 km2 river basin subdivided into 305,000 sub-watersheds that are interconnected by the river network. Numerical experiments for a few models are performed and the runtimes and scalability on our parallel computer are presented. Efficient numerical integrators such as the one demonstrated here bring closer to reality the goal of implementing fully distributed real-time flood forecasting systems supported by physics based hydrological models and high-quality/high-resolution rainfall products.