TENSOR UNIVERSAL SERENDIPITY ELEMENTS AND UNSTEADY TAYLOR-GALERKIN FINITE ELEMENT METHOD

摘要

A new kind of Universal Serendipity Element (USE)—the TensorUniversal Serendipity Element (TUSE) is constructed by using both tensor force fi-nite elements and the basic idea of USE. The formulation of shape functions and theirderivatives for TUSE is presented. TUSE can be used to study steady and unsteadytransonic flow fields when combined with Taylor-Galerkin Finite Element Methods,the NND scheme in FDM, and four-stage Runge-Kutta methods. As numerical ex-amples the transonic flow in cascades and one kind of complex unsteady transonicaxisymmetric flow in engineering are studied. It is shown that the algorithm presentedin this paper is efficient and robust.