Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow

Abstract

In this paper, we use moving mesh finite element method based upon $4P_1− P_1$ element to solve the time-dependent Navier-Stokes equations in 2D. Two-layer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure provides convenience for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.