The High-order Positivity-preserving Numerical Method For Multi-media Flow

In the problems such as high-velocity jets or blast waves, low density or low internal energy may occur. The loss of positivity of the numerical algorithm may lead to nonlinear stability or blow-ups of the algorithm for those problems. In this work, a positivity preserving high order RKDG method is presented for the simulation of multi-medium flow. The RFGM is used to treat the interface, the fluid states at the interface are obtained by solving the double shock approximate Riemann problem, which can preserve the positivity of the physically positivity such as density or internal energy. The obtained states are used define the interface boundary conditions such that the simulation of multi-medium flow can be carried out as single medium flow. Some numerical results show that the obtained algorithm can compute the fluid states and capture the interface and other discontinuity accurately.