求解变系数对流扩散反应方程的指数型高精度紧致差分方法

发布时间：2018-06-16 14:33

本文选题：对流扩散反应方程 + 指数型有限差分格式　；参考：《工程数学学报》2017年03期

【摘要】：本文给出了一种数值求解变系数对流扩散反应方程的指数型高精度紧致差分方法.我们首先将模型方程变形,借助常系数对流扩散方程的指数型高精度紧致差分格式,采用残量修正法得到变系数对流扩散反应方程的指数型高精度紧致差分格式;并从理论上分析了当Pelect数很大时,本文格式达到四阶计算精度时网格步长的限制条件;离散得到的代数方程组可采用追赶法直接求解.数值实验结果与理论分析完全吻合,表明了本文格式对于边界层问题或大梯度变化的物理量求解问题具有的高精度和鲁棒性的优点.
[Abstract]:In this paper, an exponential compact difference method with high accuracy for solving convection-diffusion reaction equations with variable coefficients is presented. First, we deform the model equation and obtain the exponential high precision compact difference scheme of the variable coefficient convection-diffusion reaction equation by means of the exponential compact difference scheme of constant coefficient convection-diffusion equation and the residual correction method. The constraints of grid step size for the fourth order accuracy of the scheme are analyzed when the elect number is large, and the discrete algebraic equations can be directly solved by the catch-up method. The numerical results are in good agreement with the theoretical analysis, which shows that the proposed scheme has the advantages of high accuracy and robustness to the boundary layer problem or the physical quantity problem with large gradient variation.
【作者单位】：宁夏大学数学统计学院;
【基金】：宁夏大学自然科学基金(ZR15014)~~
【分类号】：O241.82

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