Forms of Convection and Quadratic Conservative Finite Difference Schemes for Low-Mach Number Compressible Flow Simulations

Abstract

After studying forms of convection in governing equations for compressible fluid flow, a new and useful skew-symmetric form was proposed. This leads to quadratic conservative schemes of convection for low-Mach number compressible fluid flow simulations. Then, commutable divergence, advection and skew-symmetric forms of convection were indicated for standard finite difference method in regular and staggered grid systems. Also, convection schemes for compact finite difference method in regular and staggered grid systems were indicated. In order to check the quadratic conservation property of the schemes, a numerical test was done on a three-dimensional periodic inviscid flow. The computational results have shown that the commutable convection schemes for standard finite difference method have quite good conservative property. For compact finite difference method, only the schemes with the proposed skew-symmetric form have acceptable conservative property.