跨声速三维 Euler 方程的显式/隐式格式有限元解法

A Finite Element Method for Solving 3 D Euler Equations with Explicit/Implicit Schemes in Transonic Flow

本文采用有限体积Ｇａｌｅｒｋｉｎ法和非结构网格数值求解了跨声速三维Ｅｕｌｅｒ方程。通量的求解采用ＶａｎＬｅｅｒ一阶逆风矢通量分裂方法，并通过外插使其上升为二阶精度，分别采用了显式及隐式两种格式求解。

Two finite volume Galerlkin solutions of the transonic three dimensional Euler equations are presented.The upwind Vanleer scheme is used to calculate the fluxes which are developed from first order accuracy to second order accuracy by extrapolation.First,a two step explicit scheme is developed by combining the finite volume Galerkin method with the Richtmyer two step explicit time marching scheme.And then,in order to obtain a higher rate of convergence,an implicit scheme relying on a linearization of fluxes is developed.Both solutions are obtained on the three dimentional unstructured meshes.