Analysis on physical-constraint-preserving high-order discontinuous Galerkin method for solving Kapila's five-equation model

Abstract

This work focuses on the analysis and development of a high-order physical-constraint-preserving discontinuous Galerkin (DG) method for compressible two-fluid flows by solving Kapila's five-equation model with the ideal gas equation of state. The proposed method is proved to possess the following two attractive advantages: first, the high-order DG discretization intrinsically satisfies the mechanical equilibrium criterion around an isolated material interface, and the numerical oscillations due to the use of high-order approximations are well suppressed by using a cell-based characteristic-wise weighted essentially non-oscillatory (WENO) limiter without destroying the mechanical equilibrium criterion; second, it maintains the physical-constraint-preserving property, including the bound-preserving property of volume fractions and positivity-preserving property of partial densities and internal energy. A thorough analysis on the sufficient condition is given to achieve the physical-constraint-preserving property. Several benchmark test cases are examined to validate the accuracy and robustness of the proposed method. Further discussion on the application of the physical-constraint-preserving DG method for solving Kapila's five-equation model with the stiffened gas equation of state is also presented.