A Moving Mesh Method for Kinetic/Hydrodynamic Coupling (Advances in Applied Mathematics and Mechanics, 2021)
This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, thedomain is dynamically decomposed into three parts: kinetic regions where fluidsare far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. TheBoltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to theregions containing rapid variation of the solutions. In each moving mesh step, thesolutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such aframework, the evolution of the hybrid model and the moving mesh procedure canbe implemented independently, therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.