  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.

Numerical Analysis;Numerical Analysis