求解对流扩散反应方程的高阶指数型组合紧致差分格式

A High-Order Exponential Combination Compact Finite Difference Scheme for Convection-Diffusiom-Reaction Equation

针对一维对流扩散反应方程,基于对流扩散方程的四阶指数型紧致差分格式,采用四阶混合差分逼近算子和Padé公式,间接地构造了两种求解一维对流扩散反应方程的四阶指数型组合紧致差分格式;针对二维对流扩散反应方程,采用降维法,结合高阶混合差分逼近算子和Padé公式构造了求解二维对流扩散反应方程的四阶指数型组合紧致差分格式.本文所提差分格式较经典四阶格式和文献中的组合型格式具有更低的耗散性,因此对于对流占优等边界层问题的求解计算精度更高.最后给出数值算例验证了本文格式的精度.

For the one-dimensional convection diffusion reaction equation,based on the fourth-order exponential compact difference scheme of convection diffusion equation,two fourth-order exponential combined compact difference lattices for solving one-dimensional convection diffusion reaction equation are constructed indirectly by using fourth-order mixed difference approximation operator and Padéformula;For the two-dimensional convection diffusion reaction equation,a fourth-order exponential combined compact difference scheme for solving the two-dimensional convection diffusion reaction equation is constructed by using the dimension reduction method,combining the high-order mixed difference approximation operator and Padéformula.The difference scheme proposed in this paper is less dissipative than the classical fourth-order scheme and the combined scheme in the literature,so it has higher accuracy for solving the convection dominated boundary layer problems.Finally,a numerical example is given to verify the accuracy of the proposed scheme.