An artificial compressibility approach to solve low Mach number flows in closed domains

Abstract

An artificial compressibility approach is proposed to compute the solution of the compressible equations in the low Mach number limit, in closed domain with moving boundaries. The low Mach number stiffness is reduced by introducing an artificial sound speed, much lower than the physical one. This allows to avoid both the acoustic time step restriction and the loss of accuracy of classical compressible solvers, without solving a Poisson equation for the pressure or using the time-implicit discretization of the Turkel-type preconditioning technique. Moreover the proposed formulation involves the conservative variables plus the dynamic pressure, which facilitates the implementation of the approach in classical CFD codes for compressible flows. The numerical experiments presented show that the approach is both accurate and CPU efficient.