The High Order Accuracy Numerical Method For The Simulation Of Low-Density Or Low-Pressure Flows

In the numerical simulations of the multi-medium flow such as blast waves, the negative density or pressure may occur due to the numerical errors of the high-order scheme in the low density and pressure domain. Failure of preserving positivity of the density or pressure can cause blow-ups of the numerical algorithm. In this paper, based on the idea of Zhang for ideal gas, the limiter is modified and extended to the simulation of multi-medium flow. The obtained method is cost effective and keeps the property of the positivity-preserving limiter. The real Ghost Fluid method is coupled to treat the interface. Several one-dimensional cases and two-dimensional cases are given to test robustness and efficiency of the algorithm. Numerical results show that the obtained method can maintain the positivity of pressure and density and can capture the discontinuities accurately.