对流扩散方程的指数型高阶差分格式

High-Order Difference Schemes of Exponential Type for Convection Diffusion Equation with Source Term

提出了求解含源汇项非定常对流扩散方程的一类高精度格式.在离散子域内利用指数变换将对流扩散方程转化成扩散方程.结合已发展的含源扩散方程的一类紧致差分格式,建立了含源汇项非定常对流扩散方程的无条件稳定的、具有迎风效应的指数型四阶紧致差分格式.

A high order accuracy compact difference method is presented for soling unsteady convection equation with source term. First, the equation is linearied in the small domain discreted then ,the convection - diffusion equation is transferred to the diffusion equation based on a transformation function of exponential type. Finally, a class of non - condition stable and upwind type compact difference schemes which has fourth order is constructed by utilizing the high order compact finite - difference schemes proposed by author for the diffusion inhomogeneous equation.