Numerical Approximation of Compressible Two-Phase Six-Equation Model Using CE/SE and RKDG Schemes

Abstract

In this article, two-phase compressible six equation flow model is numerically investigated. The six-equation model consists of velocity, pressure equations, and also relaxation terms. An extra seventh equation is included describing the total energy of the mixture to ensure the correct treatment of the sharp discontinuities. The model is hyperbolic and poses numerous difficulties for numerical schemes. An efficient and well-balanced scheme can handle the numerical difficulties related to this model. The second order space-time CE/SE scheme is extended to solve the model. This scheme offers an effective numerical method for several continuum mechanics problems. The suggested scheme suppresses the numerical oscillations and dissipation effects. Several numerical test cases have been carried out to reveal the efficiency and performance of the proposed approach. The results are compared with the exact solution and also with Runge-Kutta Discontinuous Galerkin (RKDG) and central (NT) schemes.