数值求解非线性Burgers方程的有限分析混合格式

本文采用有限分析混合格式对非线性Burgers方程进行数值模拟,通过定常和非定常算例表明,在连续特征线法离散的非线性对流算子所生成的非均匀网格上,采用有限分析法耦合离散扩散算子,对处理大Re数和大Pe数问题行之有效,数值结果是令人满意的。

A Finite Analytic Splitting Numerical Scheme for Nonlinear Burgers Equation

This paper presents a scheme based on the methods of continuous characteristics and finite analysis for solving the Burgers equation. The related operator is first splitted into the convection and diffusion operators. Then with the characteristics method. the convection equation is turned into an ODE one in the direction of charcteristics and the numerical solution is used as the initial conditions for the diffusion equation, while the letter is solved with the finite analysis method and nonuniform mesh generated in the proceess of convection. In this way, two kinds of operators are properly and effectively coupled. Three numerical examples on the problems with large Reynolds number and Peclet number are given. The results indicate the satisfactory agreement with the known results and exact solutions.