Penalty Finite Element Numerical Analyses for High
Reynolds Number Flows
Liu Xiaomin  Wang Shangjin  Xi Guang
(School of Energy and Power Engineering, Xi'an Jiaotong University, 710049)

Abstract: A modified penalty finite element method is presented for solving steady viscous incompressible flow problems. According to the characters of hgih Reynolds number flow, a streamline upwind perturbation term is introduced in order to avoid numerical oscillation caused by convection-dominated. At the same time the method of loading Reynolds number is used. In the course of discretization of finite element equations, the interpolation function for velocity is quadratic velocity along with linear discontinuous pressure and the implicit pressure/explicit velocity scheme is selected to ensure the solution of pressure to be stable by obtaining the correct velocity. The result shows that spurious pressure is alleviated while the false diffusion of convection is simultaneously weakened to great extent. The turbulent flow field is simulated with standard turbulent model.Through analyzing the two-dimensional flow over a backward facing step and the three-dimensional flow in a strongly curved bend at high Reynolds number, it indicated that the scheme is efficient for high Reynolds number flows.
Keywords: finite element method, viscous incompressible flow, numerical simulation, modified weight function.