High Accurate Numerical Simulation For The Multi-medium Spheric-symmetrical(axisymmetrical) And Cavitation Flow

The numerical simulation of high-pressure bubble is of important applications in many fields such as the explosion in air and under the water. These problems are generally spheric-symmetric or axisymmeric and can be transformed into one-dimensional or two-dimensional problems by using the coordinate transform, which can greatly reduce the computation cost. In this work a numerical simulation method is presented for the spheric-symmetric or axisymmeric multi-medium flow by coupling the RGFM to RKDG method. In the RGFM, the simulation for multi-medium flow can be carried out as in a single medium flow by defining the interface conditions for each medium with the fluid states from the Riemann solver at the interface, a level set equarion is solved to trace the interface, such that the high-order RKDG method can be directly applied to discretize the control equation for each medium. The one-fluid cavitation model is used to treat cavitations which may occur under the water. The finite differential schemes, which are compatible with the original Euler equations, are given to remove the instability due to the singularity at the origin. Several high-pressure explosion problems are tested and the numerical results show that the presented algorithm can capture all the physical phenomena accurately and cost efficiently.