在控制方程为双曲型的问题中SUPG方法与Galerkin方法的比较

常规Galerkin方法只适用于离散椭圆型方程,而在许多流动和传热问题中控制方程的类型会发生转变,由于对流项占优而成为双曲型,这时Galerkin方法的结果将产生失真振荡。采用流线迎风Petrov-Galerkin方法可以提前抑制与流动方向相垂直的扩散,从而大大提高了求解的精度。文中计算了两个问题:Oldroyd-B流体绕圆管内一球的流动和非等温搅拌流动。结果证实了当W_i数或Pe数较大时,Galerki方法得到失真振荡的解,而nSUPG方法可以得到较好的结果。

THE ADVANTAGE OF STREAMLINE-UPWINDPETROV-GALERKIN FINITE ELEMENTMETHOD FOR HYPERBOLIC SYSTEMS

The conventional Glalerkin finite element metbod is only applicable to discretizing elliptic equations. In many flow or heat-transfer problems, the governing equations may change type; they become hyperbolic because convection is dominating. The solutions are often corrupted by node-to-node oscillations or 'wiggles' the Streamline-Upwind Petrov-Galerkin finite element method can inbibit the crosswind. diffusion and improve the computational accuracy. Two aumerical exarnples are given: the flow of Oldroyd-B fluid around a sphere in a tube and the nonisothermal agitating flow When the Weissenberg number or the Peclet umber is high , the Ga]erlkin method produces ,wiggles' while SUPG method yields good results.