二维对流扩散方程的欧拉—拉格朗日分裂格式

本文在[1]基础上发展了一种有效的处理大P_e(R_e)数、非定常二维对流扩散方程的欧拉-拉格朗日(E-L)分裂格式,由于方法本质上与区域形状无关,且不需再分网格,因此是一种无网格的E-L方法,特别对于定常流动,E.-L.分裂格式可以导致比一阶迎风格式更精确的单调、无振荡格式,文中对于常系数、变系数和非线性的二维非定常和定常对流扩散方程的(初)边值问题进行了数值计算,数值结果与精确解的比较表明,本方法具有很好的精度,解是单调无振荡的,比通常一阶迎风格式具有较少的数值扩散,最大计算网格P-e(R-e)数可达100—500。

AN EULERIAN-LAGRANGIAN SPLITTING SCHEME FOR 2-D DIFFUSION CONVECTION EQUATIONS

An Eulerian-Lagrangian splitting scheme which is very efficient to deal with the 2-D diffusion-convection equations with high peclet number, has been developed in the present paper. The method esseatially does not relate to the form of domain and does not need to form the meshes (only needs the coordinates of nodes), so it is a free-grid E-L method. The steady E-L splitting schemes also are given in the paper. Five difficult examples including the constant coefficients, variable coefficients and nonlinear cases, are calculated. The comparisons between the numerical results and the exact solutions illustrate that the agreements are very good, even for the flow with initial grid peclet number 500. The E-L solutions show no oscillation and have only a little numerical diffusion.