Applicability of Higher-Order TVD Method to Low Mach Number Compressible Flows.

Abstract

Steep gradients of fluid density are the influential factor of spurious oscillation in numerical solutions of low Mach number (M«1) compressible flows. The total variation diminishing (TVD) scheme is a promising remedy to overcome this problem and obtain accurate solutions. TVD schemes for high-speed flows are, however, not compatible with commonly used methods in low Mach number flows using pressure-based formulation. In the present study a higher-order TVD scheme is constructed on a modified form of each individual scalar equation of primitive variables. It is thus clarified that the concept of TVD is applicable to low Mach number flows within the framework of the existing numerical method. Results of test problems of the moving interface of two-component gases with the density ratio g4, demonstrate the accurate and robust (wiggle-free) profile of the scheme.