论有限元素理论中SUPG方法与PG方法在解高速粘流时的等效性

对流场中含激波问题,若用有限元法来数值模拟,目前较有效的方法是SUPG方法和PG方法。本文讨论了这两种方法在数值求解N-S方程组时具有等效性,并对它们的应用前景作了简单的评估。

ON THE EQUIVALENCE OF THE SUPG AND THE PG METHOD IN FINITE ELEMENT THEORY FOR VISCOUS FLOWS AT HIGH SPEED

For the numerical simulation of flow fields and problems containing shocks, the stremline upwind/Petrov-Galerkin method (SUPG) and penalty-Galerkin method (PG) are the most effective finite element methods of all. In this paper, further elaboration on the general aspects of the above two methods is given here. And we prove that they are equivalent in solving unsteady N-S equations numerically. But as to PG, It is only applied to solving unsteady N-S. equations for transonic flows, and requires none of source terms. Therefore, at least presently, there is a great limitation for PG in applications. And it is difficult to extend further. SUPG has no these drawbacks. And in SUPG, the capturing technique of strong discontinuities can be developed. For these reasons, SUPG has good prospects for applications.