In this paper, an unsteady preconditioning formulation for multi-phase flows with arbitrary equation of state based on the approximated Riemann solver is developed for multi-phase flows at all speed. This paper considers a homogeneous two-phase multi-equation mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature-dependent hybrid equation of state. Benchmark test cases, including one-dimensional (1D) condensation shock in the cavitated nozzle and two-dimensional (2D) cavitated blunt body problem, demonstrate accurate capturing of interfaces, shock waves and cavitation zones.
International Journal of Computational Methods 13(4), 1641010(15 pages)