在控制方程为双曲型的问题中SUPG方法与Galerkin方法的比较  

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

作　　者：王立刚[1] 华律[1] 

机构地区：[1]浙江大学

出　　处：《应用科学学报》1997年第1期96-100,共5页Journal of Applied Sciences

基　　金：国家自然科学基金;中科院化学所高分子物理实验室开放基金

摘　　要：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，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 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.

关 键 词：加辽金法 控制方程 双曲型方程 SUPG法 

分 类 号：O241.82[理学—计算数学]