A finite volume multi-moment method with boundary variation diminishing principle for Euler equation on three-dimensional hybrid unstructured grids

Abstract

Abstract In this work, we have developed a novel numerical model for Euler equations on 3D hybrid unstructured grids including tetrahedral, hexahedral, prismatic and pyramidal elements. The model integrates the VPM (Volume integrated average and Point value based Multi-moment) spatial discretization scheme, the limiting projection with BVD (Boundary Variation Diminishing) manipulation and the Roe Riemann solver for unstructured grids. Distinguished from conventional finite volume method, both the volume-integrated average (VIA) and the point values (PV) at the cell vertices are memorized as prognostic variables and updated in time simultaneously. The VIA is computed by a finite volume formulation of flux form while the PV is point-wisely updated using the differential formulation, where the Roe solver is used to compute both conventional and differential Riemann problems. A special technique is introduced to the limiting projection that effectively suppresses both numerical oscillation and dissipation. The resulting numerical model provides remarkably improved numerical accuracy and robustness with a moderate increase in algorithmic complexity and computational cost, which makes it of practical significance for real-case applications. The numerical results of benchmark tests are presented to demonstrate the appealing solution quality of the present model in comparison with other existing methods.