Anti-dissipation pressure correction under low Mach numbers for Godunov-type schemes

Abstract

An effective and unified framework, termed anti-dissipation pressure correction, is established to overcome the deterioration in the accuracy observed in Godunov-type schemes in low-speed scenarios. Based on the scale analysis of the nonlinear characteristic line relation, the deteriorated-accuracy source term is associated with the speed of sound and velocity difference term. Subsequently, the anti-dissipation pressure correction term is constructed by using the scaling Mach number function to rescale the error source term to be of the magnitude of the convective velocity and ensure a satisfactory accuracy. This scaling function is a polynomial of the local Mach number and restrained by the shock indicator. Results of the asymptotic analysis demonstrate that the anti-dissipation pressure correction helps recover the correct Ma2 scaling of the pressure fluctuations and damps the checkerboard modes, and this aspect is verified considering low Mach number flows over the NACA0012 airfoil. This novel framework can remarkably enhance the low Mach number performance and is also applicable to scenarios involving moderate or high Mach numbers. The performance of the approach is validated through numerical investigations across a wide range of Mach numbers.