高雷诺数流动的加罚有限元数值分析

Penalty Finite Element Numerical Analyses for High Reynolds Number Flows

在传统的伽辽金变分有限元数值逼近思想的基础上,本文采用改进的加罚有限元方法对粘性不可压缩紊流流动进行数值计算。在高雷诺数流动时,为避免对流效应过强产生的数值计算的振荡,对标准权函数引入迎风修正项,同时采用雷诺数加载法,保证数值解的收敛性。在有限元方程离散过程中,采用有效的隐式压力-显式速度方式,以准确的速度场确保获得压力场的稳定性。速度压力项选用不同阶次的插值函数。实践证明:当控制方程中对流项假扩散被降至最小时,压力项的振荡亦被较大程度的削弱。紊流计算仍使用标准K-ε紊流模型。通过对二维后掠台阶和三维弯曲管道内高雷诺数紊流流动算例的分析,表明本文方法对高雷诺数流动的数值计算是有效的。

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 k ε 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.