Preconditioning of explicit finite volume compressible flow solvers to compute low Mach number flows

Abstract

Finite volume methods have been used to compute transonic flows by numerically solving the equations for a compressible fluid. The eigenvalues of this system of equations, however, renders the system stiff at low speed flows because the ratio of convective speed to the speed of sound is much reduced as compared to the case of transonic flows. Stiffness in the system hampers the speed of convergence to the final steady-state solution of the iteration process, thereby destroying the computational efficiency of the numerical scheme at low Mach numbers. In order to overcome this stiffness issue, the time evolution of the equations can be altered by way of pre-conditioning methods without changing the steady-state behaviour of the original system of equations. Consequently, the resulting wave speeds in the solution domain become compatible with one another in magnitude and hence overcomes any disparity between the convective and acoustic speeds which would otherwise generate stiffness in the system.