The Experts below are selected from a list of 36 Experts worldwide ranked by ideXlab platform
Laxminarayan L Raja - One of the best experts on this subject based on the ideXlab platform.
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a matrix free implicit scheme for solution of resistive magneto hydrodynamics equations on unstructured grids
Journal of Computational Physics, 2013Co-Authors: Hariswaran Sitaraman, Laxminarayan L RajaAbstract:The resistive magneto-hydrodynamics (MHD) governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in an electrically conducting fluid, typically a plasma. A matrix free implicit method is developed to solve the conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective Flux Jacobian is derived on a general unstructured mesh and used in a Lower-Upper Symmetric Gauss Seidel (LU-SGS) technique developed as part of the implicit scheme. A grid coloring technique is also developed to create data parallelism in the algorithm. The computational efficiency of the matrix free method is compared with two common approaches: a global matrix solve technique that uses the GMRES (Generalized minimum residual) algorithm and an explicit method. The matrix-free method is observed to be overall computationally faster than the global matrix solve method and demonstrates excellent parallel scaling on multiple cores. The computational effort and memory requirements for the matrix free approach is comparable to the explicit approach which in turn is much lower than the global solve implicit approach. Both the matrix free and global solve implicit techniques exhibit superior steady state convergence compared to the explicit method.
T Tanaka - One of the best experts on this subject based on the ideXlab platform.
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finite volume tvd scheme on an unstructured grid system for three dimensional mhd simulation of inhomogeneous systems including strong background potential fields
Journal of Computational Physics, 1994Co-Authors: T TanakaAbstract:Abstract A three-dimensional (3D) high-resolution MHD simulation scheme on an unstructured grid system is developed for inhomogeneous systems, including strong background potential fields. The scheme is based on the finite volume method (FVM) with an upwinding numerical Flux by the linearized Riemann solver. Upwindings on an unstructured grid system are realized from the fact that the MHD equations are symmetric with the rotation of the space. The equation system is modified to avoid direct inclusions of the background potential field as a dependent variable, through the use of changed dependent variables. Despite such a change of the equation system, the eigenvectors in the mode-synthesis matrix that are necessary for the evaluation of the upwinding numerical Flux vectors can still be written analytically. The eigenvalues of the MHD Flux Jacobian matrix that are also necessary for the upwinding calculations are derived from the well-known Alfven, fast and slow, velocities. The calculations of the eigen vectors is done with special care when the wave propagations become parallel or perpendicular to the ambient magnetic field, because degeneration of the eigenvalues occurs in these cases. To obtain a higher order of accuracy, the upwinding Flux is extended to the second-order TVD numerical Flux in the calculation of FVM, through the MUSCL approach and Van Leer's differentiable limiter. In order to show the efficiency of the above scheme, a numerical example is given for the interaction process of high-β supersonic plasma flow with the region of a strong dipole field, including magnetized low-β plasma.
Hariswaran Sitaraman - One of the best experts on this subject based on the ideXlab platform.
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a matrix free implicit scheme for solution of resistive magneto hydrodynamics equations on unstructured grids
Journal of Computational Physics, 2013Co-Authors: Hariswaran Sitaraman, Laxminarayan L RajaAbstract:The resistive magneto-hydrodynamics (MHD) governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in an electrically conducting fluid, typically a plasma. A matrix free implicit method is developed to solve the conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective Flux Jacobian is derived on a general unstructured mesh and used in a Lower-Upper Symmetric Gauss Seidel (LU-SGS) technique developed as part of the implicit scheme. A grid coloring technique is also developed to create data parallelism in the algorithm. The computational efficiency of the matrix free method is compared with two common approaches: a global matrix solve technique that uses the GMRES (Generalized minimum residual) algorithm and an explicit method. The matrix-free method is observed to be overall computationally faster than the global matrix solve method and demonstrates excellent parallel scaling on multiple cores. The computational effort and memory requirements for the matrix free approach is comparable to the explicit approach which in turn is much lower than the global solve implicit approach. Both the matrix free and global solve implicit techniques exhibit superior steady state convergence compared to the explicit method.
John D Pryce - One of the best experts on this subject based on the ideXlab platform.
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ad tools and prospects for optimal ad in cfd Flux Jacobian calculations
Automatic differentiation of algorithms, 2000Co-Authors: Mohamed Tadjouddine, Shaun A Forth, John D PryceAbstract:We consider the problem of linearising the short (approximately 100 lines of ) code that defines the numerical Fluxes of mass, energy and momentum across a cell face in a finite volume compressible flow calculation. Typical of such formulations is the numerical Flux due to Roe, widely used in the numerical approximation of flow fields containing moderate to strong shocks. Roe's Flux takes as input 10 variables describing the flow either side of a cell face and returns as output the 5 variables for the numerical Flux. We present results concerning the efficiency of derivative calculations for Roe's Flux using several currently available AD tools. We also present preliminary work on deriving near optimal differentiated code using the node elimination approach. We show that such techniques, within a source transformation approach, will yield substantial gains for application code such as the Roe Flux.
Charles Merkle - One of the best experts on this subject based on the ideXlab platform.
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a strong conservative riemann solver for the solution of the coupled maxwell and navier stokes equations
Journal of Computational Physics, 2014Co-Authors: Richard J Thompson, Andrew Wilson, Trevor Moeller, Charles MerkleAbstract:The coupled system of the Navier-Stokes and Maxwell equations are recast into a strong conservative form, which allows the fluid coupling to the Maxwell system to be written in terms of Flux divergence rather than explicit source terms. This effectively removes source terms from the Navier-Stokes equations, although retaining an exact coupling to the electromagnetics. While this relieves the stiff source terms and potentially stabilizes the system, it introduces a much more complicated eigenstructure to the governing equations. The Flux Jacobian and eigenvectors for this strong conservative system are presented in the current paper for the first time. An approximate Riemann solver based upon these eigenvectors is then introduced and tested. The solver is implemented in a preconditioned, dual-time implicit form. Validations for classic one- and two-dimensional problems are presented, and the performances of the new formulation and the traditional source-coupled formulation are compared.