Numerical modeling of multiphase compressible flows with the presence of shock waves using an interface-sharpening five-equation model

Abstract

An accurate shock- and interface-capturing method is introduced for simulations of compressible multiphase flows. First, an associated Godunov-type numerical scheme is established for a five-equation two-phase model obtained from a seven-equation model by assuming a single velocity and a single pressure between two phases. The computational finite-volume Riemann solver using the scheme and computing algorithms is presented. Next, an interface-sharpening technique (IST) is extended for the compressible two-phase model to improve numerical simulations and correct diffusion errors. The modified IST was applied as postprocessing to correct the numerical diffusion error in the solution of the discretization scheme while maintaining a sharp interface with a desired thickness after each time step. A mixture-consistent interface regularization approach of all conservative variables is combined with the IST to obtain consistent thermodynamic laws for the mixture, ensuring the consistency of the variables in the correction process. Several examples of fluid interface simulations including shock-tube, shock-bubble interactions, and underwater explosions were performed to demonstrate the accuracy and capability of the proposed method. Those compressible multiphase flow problems are complicated by the presence of both shock waves and the dynamics of interfaces. Comparisons of the numerical method with theoretical results and experimental data indicate that the present method can simulate interface dynamics with the presence of shock waves and large density differences.