A Projection Method for Compressible Generic Two-Fluid Model

A new projection method for a generic two-fluid model is presented in this work. To be specific, it is shown that the projection method for solving single-phase variable density incompressible flows or compressible flows can be extended to the case of viscous compressible two-fluid flows. The idea relies on the property that the single pressure $p$ can be uniquely determined by the products of volume fractions and densities $\phi_k \rho_k$ of the two fluids, respectively. Moreover, a suitable assignment of the intermediate step variables is necessary to maintain the stability. The energy stability for the proposed numerical scheme is proved and the first order convergence in time is justified by three numerical tests.