A totally Eulerian finite volume solver for multi-material fluid flows III: The low Mach number case

We build an extension of the FVCF-ENIP multi-material solver for the computation of low Mach number fluid flows. The loss of accuracy generally noticed for Godunov type solvers when the Mach number goes to zero is handled through the renormalization of the viscosity matrix of the numerical flux. An implicit scheme is proposed in order to achieve numerical stability with reasonable CFL numbers. Its linear unconditional stability is proved in the case of a one-dimensional isentropic Euler system. Various numerical tests attest the efficiency of the method.