A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations
A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations
Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A fast, matrix-free implicity method for compressible flows on unstructured grids
Journal of Computational Physics
A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
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This paper reports the performance of our parallel implicit finite volume solver for compressible flows. The Jacobian-free Generalized Minimal Residual method (GMRES) is used to solve the linear system resulting from the discretization. Furthermore, the matrix-free Lower-Upper Symmetric Gauss Seidel (LU-SGS) method is employed as a preconditioning technique to the GMRES solver. A new slope limiting procedure is designed to suppress the unphysical overshoots and undershoots of the numerical solution while not hampering the convergence of the steady-state simulation. The solver is also parallelized using mesh partitioning and Message Passing Interface (MPI) functions. The Cray X1 is used to measure the performance of the flow solver. A few 2D and 3D numerical examples are presented to demonstrate the performance of the present solver.