Abstract:
Coordinate transformation is often used in solving CFD problems on structured meshes, including curvilinear meshes and moving and deforming meshes, where the coordinate-transformation metrics and Jacobian are introduced. The differential forms of the metrics and Jacobian's discretization may cause different errors, which may lead to wrong flow distribution. The investigation of geometric conservation law (GCL) is needed to reduce or eliminate such errors. In this paper, we discuss the GCL for finite difference method(FDM), and draw a conclusion that the main error source is the inaccurate identities derived from coordinate transformation under different discrete operation. The GCL is satisfied under following conditions:the governing equations of discretized grid meshes with identities as source term is equal to that of uniform grids; and the discrete operators of the flux term and source term are the same. In view of the aforementioned facts, we present a new algorithm to satisfy the GCL based on the discrete and equivalent equations. The new algorithm is verified by an example of uniform flow with the numerical flux schemes of AUSM, HLLC, Roe, and VanLeer, and the simulation result has shown that it can eliminate errors caused by the GCL errors effectively either for FDS or FVS.