不可压Navier—Stokes方程组的SUPG有限元数值解

本文从定常不可压NaVier-Stokes方程组出发,构造了SUPG加权剩余公式。为保证数值解的精度,本文对速度取八节点插值,保留了摄动项中的二阶导数项。从用本文方法所做的算例来看,计算结果是令人满意的。

SUPG FINITE ELEMENT NUMERICAL METHOD OF INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

In this paper, numerical examples of a simple one-dimen-sinal model problem are used to show that Galerkin solutions are often underdiffuse and demonstrate the superiority of the Streamline-Upwind/ Petrov-Galerkin (SUPG) methods over Galerkin methods. And then the SUPG weighted residual formulation is developed in the light of the steady incompressible Navier-Stokes Equations. Due to accuracy considerations, we employ the same element geometry where all eight nodes are associated with velocities and only corner nodes with pressures. Therefore, the streamline upwind contribution affects the weighting of the stress divergence terms. Numerical results obtained with the present algorithm are completely satisfactory in all test cases, and the algorithm is shown to be efficient and robust.