A Finite Volume Method Based on WENO Reconstruction for Compressible Flows on Hybrid Grids

A cell-centered finite volume method based on a WENO reconstruction, termed WENO(P0P1) in this paper, is presented for solving the compressible Navier-Stokes equations on 3D hybrid grids. This new WENO(P0P1) method is designed not only to achieve high-order accuracy but also to ensure non-linear stability of the finite volume method. The discretization of the viscous and heat fluxes is carried out using a modified averaging of gradients. The spatially discretized governing equations are integrated in time using a linearized implicit scheme. A fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The parallelization of the WENO(P0P1) method is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model using Message-Passing-Interface (MPI) programming paradigm for distributed memory parallel computing architectures. The developed WENO(P0P1) method is used to compute a variety of flow problems on hybrid grids to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical experiments indicate that this WENO(P0P1) method is able to maintain high accuracy for smooth flows and obtain oscillation-free solutions in the vicinity of discontinuities, and outperforms a van Albada limiter-based finite volume method.