This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-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 the regions containing rapid variation of the solutions.In each moving mesh step,the solutions 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 a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.
Phase-field models provide a way to model fluid interfaces as having finitethickness;the interface between two immiscible fluids is treated as a thin mixing layeracross which physical properties vary steeply but continuously. One of the main chal-lenges of this approach is in resolving the sharp gradients at the interface. In this paper,moving finite-element methods are used to simulate interfacial dynamics of two-phaseviscoelastic flows. The finite-element scheme can easily accommodates complex flowgeometry and the moving mesh strategy can cluster more grid points near the thin in-terfacial areas where the solutions have large gradients. A diffused monitor function isused to ensure high quality meshes near the interface. Several numerical experimentsare carried out to demonstrate the effectiveness of the moving mesh strategy.
