High performance computing of compressible flows

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 XI 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.