求解变系数对流扩散方程的高阶紧致差分格式

A High-order Compact Finite Difference Scheme for Solving the Variable Coefficient Convection Diffusion Equations

利用变量替换在对流扩散方程中消去对流项得到反应扩散方程组,采用Crank-Nicolson格式处理时间导数,构造新的二阶中心差分格式和四阶紧致差分格式处理空间导数。证明了2种新格式是无条件稳定的方法。数值试验结果表明:与标准二阶中心差分格式相比,这2种新方法具有更好的健壮性,并且可有效求解对流占优问题。

In this paper, the variable substitutions were used to eliminate the convection term in the nonlinear convection diffusion equations. Then, Crank-Nieolson scheme was used to process time de-rivative ; a new 2nd scheme and a fourth-order compact difference scheme were structured for the spa-tial derivative. Proofs of unconditional stability of these new schemes were given in the article. Com-pared with the standard central difference scheme, the new methods are more robust for the convection dominated problems.