Numerical Simulation of Low Mach Number Steady and Unsteady Flow Past a Circular Cylinder with Preconditioning Method

Abstract

Preconditioning techniques have become established as a useful technique for optimizing accuracy and efficiency of CFD solutions over a range of flow conditions. Specifically, at low Mach numbers, it is well known that the standard physical time derivatives lead to an ill-conditioned system due to the stiffness between the acoustic and particle wave speeds, which in turn results in degraded convergence and inaccurate discretization. With preconditioning, the pseudo-time derivatives scale the acoustic speeds so that they remain well conditioned at all Mach numbers. A low-diffusion preconditioning Roe scheme by using an adjustable parameter in preconditioning Roe scheme to control the numerical dissipation and the adjustable parameter value rules are proposed. Numerical results show the efficiency of the new scheme and the low Mach/Reynolds number steady and unsteady solutions of viscous flow past a circular cylinder are satisfied.