Computation of multiphase mixture flows with compressibility effects

A time-marching computational fluid dynamics method is developed and applied to the computation of multiphase mixture flows. The model accounts for finite acoustic speeds in the constituent phases, which typically lead to transonic/supersonic flow and associated compressibility phenomena such as shock formation in the mixture region. Preconditioning or artificial compressibility methods are devised using perturbation theory to insure that the method retains efficiency and accuracy in both the incompressible and compressible flow regimes. The resulting algorithm is incorporated within an existing multiphase code, and several representative applications are used to demonstrate the capabilities of the method. In particular, our results suggest that the present compressible formulation provides an improved description of cavitation dynamics compared with previous incompressible computations.