A kinetic energy and entropy preserving (KEEP) finite volume scheme on unstructured meshes for compressible flows

Abstract

A kinetic energy and entropy preserving (KEEP) finite-volume scheme on unstructured meshes is proposed for non-dissipative and stable compressible flow computations. The KEEP finite volume scheme proposed in the present study is based on the existing KEEP schemes developed for finite difference methods. The KEEP schemes have shown superior numerical robustness without numerical dissipation in previous studies. The KEEP schemes are discretized such that the numerical fluxes discretely replicate the key analytical relations that the governing equations hold, leading to preservation of kinetic energy and a superior entropy preservation property in the incompressible and inviscid limits. This study proposes using cell-vertex discretization for the proposed KEEP finite volume scheme in order to maintain this characteristic property of the KEEP scheme and achieve second-order accuracy in space on simplex meshes and arbitrary meshes that are not highly irregular. In the numerical tests performed in this study, the proposed KEEP finite volume scheme successfully performs long-time stable computations on various unstructured meshes. Also, the proposed KEEP scheme shows much better numerical stability and spatial accuracy than the KEEP scheme with cell-centered discretization.