An algorithm for low Mach number unsteady flows

An algorithm is proposed for the simulation of unsteady viscous stratified compressible flows. The advantage of the method is its capability to deal w ith a broad range of subsonic Mach numbers, including nearly incompressible flows, with a single modelling, based on the fully compressible Navier-Sto kes 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 appro ximate Newton method, based on artificial compressibility, is used. After a detailed description of the method, the accuracy of the algorithm is check ed by computing compressible and incompressible benchmark test cases. Resul ts of flows over a backward facing step with or without stratification effe cts for a Reynolds number of 800 are compared with the steady solution of i ncompressible methods, The computation of a compressible natural convection allows to evaluate the accuracy of the method for flow including significa nt compressibility effects, whereas numerical results of a Poiseuille-Benar d channel flow for a Reynolds number of 10 demonstrate the efficiency of th e present algorithm to compute unsteady hows. (C) 2000 Elsevier Science Ltd . All rights reserved.