An algorithm for low Mach number unsteady flows

Abstract

An algorithm is proposed for the simulation of unsteady viscous stratified compressible flows. The advantage of the method is its capability to deal with a broad range of subsonic Mach numbers, including nearly incompressible flows, with a single modelling, based on the fully compressible Navier–Stokes equations. 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 flow and the acoustic wave speeds at low Mach number, an approximate Newton method, based on artificial compressibility, is used. After a detailed description of the method, the accuracy of the algorithm is checked by computing compressible and incompressible benchmark test cases. Results of flows over a backward facing step with or without stratification effects for a Reynolds number of 800 are compared with the steady solution of incompressible methods. The computation of a compressible natural convection allows to evaluate the accuracy of the method for flow including significant compressibility effects, whereas numerical results of a Poiseuille–Bénard channel flow for a Reynolds number of 10 demonstrate the efficiency of the present algorithm to compute unsteady flows.