Generic five-equation model for compressible multi-material flows and its corresponding high-fidelity numerical algorithms

The five-equation model is widely used to simulate compressible multi-material flows. However, disunity and anomalous phenomena exist in both the model and corresponding numerical simulations. In this study, we first derived a unified formulation for the five-equation model, establishing a generic five-equation model. This model can not only recover existing typical five-equation models and generate new models but also provide a flexible framework for numerically simulating compressible multi-material flow problems in a consistent manner. Based on these properties, we constructed a suite of high-fidelity numerical algorithms, including a consistent algorithm for equations of volume fractions, technique for avoiding potential Mach number oscillation, and technique for restoring the non-monotonic sound speed if it is indeed physically possible. The proposed model and its corresponding high-fidelity numerical algorithms are verified on one-, two-, and three-dimensional problems, including artificial mixtures for separating pure or nearly pure fluids and physical fluid mixtures, and materials modeled as an ideal gas, stiffened gas, and Mie-Grüneisen-type equation of state. The numerical results validate our conclusions and confirm the broad applicability of the proposed model and its corresponding algorithm.