The Adaptive Mesh Technique For The Simulation Of Multi-medium Flow

Adaptive mesh refinement technique has been widely used in computational fluid dynamics, in this method the numerical solution can be obtained with high resolution at the discontinuity and computational cost can be saved. It behaves well for single-medium but the extension to multi-medium flow is not straightforward due to the different medium on both sides of the interface. In this paper a numerical algorithm is presented for the multi-medium flow by coupling the rGFM and the AMR technique.The Riemann problems are constructed at the interface and solved to define the interface boundary conditions for fluid on both sides of the interface respectively, so the computation of multi-medium flow can be carried out as if in the single medium, and AMR method for single-medium flow is then employed for each medium. As the adaptive mesh refinement method works only in the local domain where large-gradient change happens, it increases the computational efficiency besides the improvement of flow field resolution. Several numerical experiments are conducted to demonstrate robustness and efficiency of the current method. They include several 1D and 2D gas–water flow problems, involving a large density gradient at the material interface and strong shock-interface interactions. The results show that our algorithm can capture the shock waves and the material interface accurately, and is stable and robust even for solutions with large density and pressure gradients.