对流扩散方程的一种新间断有限元解法

A Novel Discontinuous Galerkin Method for the Convection-Diffusion Equations

该文采用标准迎风格式离散对流项,结合Bassi和Rebay提出的高效格式离散拉普拉斯算子,构建了求解对流扩散方程的一种新的间断有限元方法。数值计算的结果表明:该方法对网格类型的依赖度较小并且精度比较高,可以使用高阶插值函数得到比较精确的结果;该方法数值耗散较小,对于强对流和强间断性的问题,可以得到很好的结果。

A novel Discontinuous Galerkin Method is developed to solve the convection-diffusion equations. In this method, the convection term is discreted by standard upwind scheme, and the Laplace term is discreted by an effective scheme proposed by Bassi and Rebay. Numerical results show that, this Discontinuous Galerkin Method is insensitive to the element type, and can achieve high accuracy by using high order shape function. Especially, this method has less numerical dissipation than other traditional methods, which is suited to solve the convection dominated problems with strong discontinuity.