Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow (Advances in Applied Mathematics and Mechanics, 2018)
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-layernested meshes are used including velocity mesh and pressure mesh, and velocity meshcan be obtained by globally refining pressure mesh. We use hierarchy geometry treeto store the nested meshes. This data structure provides convenience for adaptive meshmethod and the construction of multigrid preconditioning. Several numerical problemsare used to show the effect of moving mesh.