N-S方程SUPG有限元解法

Streamline-Upwind Petrov-Galerkin Finite Element Method for Navier-Stokes Equations in the Stream Function-Vorticity Formulations

SUPG是八十年代初期发展的一种先进的有限元算法,该法既具有迎风算法的长处,又抑制了迎风法造成的虚假扩散问题,具有较好的稳定性和精度,是一种很有前途的新算法。本文从非定常二维不可压Navier-Stokes方程组出发,选用流函数-涡做为方程变量,构造了SUPG有限元离散化变分方程组,并采用预估—多步校正算法解方程组,在具体算例的计算中,数值生成了卡门涡街现象。

SUPG (Streamline-Upwind Petrov-Galerkin) is a new finite element formulation developed from earlier 1980s. This method has two advantages, (1)the streamline upwind concept precludes the possibility excessive crosswind diffusion, (2) the petrov-galerkin weighted residual formulation eliminates the artificial diffusion which plagues many classical upwind Schemes. SUPG finite element procedures for unsteady two dimensional, incompressible Navier-Stokes equations in the streamfunction-vorticity formulation have been implemented, and the equations are solved with the semi-implicit predicior/multicorrector algorithm. The effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.