Element-Free Galerkin method for dynamic boundary flow problems

This paper focuses on the study of dynamic boundary flow problems based on the Element-Free Galerkin method. First, Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction, respectively. The penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. However, irregular changes in boundary conditions are often encountered in practical fluid problems. For example, the motion of flapping-foil is not uniform relative to the flow. In this paper, numerical experiments are carried out for the flow problems with non-uniform boundary motions. The problem which a plate with non-uniform drag movement above a rectangular tank filled with water is studied with the EFG method. The feasibility of the proposed algorithm is verified by comparison with the FEM method. Then, the procession of the water in the tank is stimulated. In the end, the influence of different calculation time steps on the accuracy of the solution is discussed.