Preconditioning algorithms for the computation of multi-phase mixture flows

Preconditioned time-marching algorithms are developed for a class of isothermal compressible multi-phase mixture flows, relevant to the modeling of sheet- and super-cavitating flows in hydrodynamic applications. Using the volume fraction and mass fraction forms of the multi-phase governing equations, three closely related but distinct preconditioning forms are derived. The resulting algorithm is incorporated within an existing multi-phase code and several representative solutions are obtained to demonstrate the capabilities of the method. Comparisons with measurement data suggest that the compressible formulation provides an improved description of the cavitation dynamics compared with previous incompressible computations.