An algorithm for low Mach number unsteady flows

An algorithm is proposed for the simulation of unsteady viscous compressible subsonic Rows at low Mach number. The method is second-order accurate both in space and time. To remove the stiffness of the numerical problem due to the large disparity between the Row and the acoustic wave speeds, an adaptation of the artificial compressibility method is proposed in order to preserve the possibility to simulate standard subsonic applications. After a detailed description of the method, the scheme is applied to the unsteady incompressible numerical benchmark of the Poiseuille-Benard channel flow in order to validate the possibility to simulate stratified Row without Boussinesq approximation. Next, the efficiency of the method, compared with Runge-Kutta (RK) scheme, is evaluated thanks to the advection of a Lamb vortex at reference Mach number, M-o, 0.8 and 0.001.