求解对流扩散反应方程的四阶混合紧致差分方法

A Fourth-order Hybrid Compact Finite Difference Method for 1D Convection-Diffusion-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,以及一阶导数的四阶Padé公式,发展了一种高效求解对流扩散反应方程的混合型四阶紧致差分格式.数值实验结果验证了格式对于边界层问题或大雷诺数或大Pelect数的大梯度问题的求解的高精度和鲁棒性的优点.

A fourth-order hybrid compact finite difference method,based on the exponential high order compact finite difference scheme of the convection diffusion equation with constant coefficients,combined with the classical fourth-order Pad e scheme for first and second-order derivatives,is proposed for the one-dimension（1D） convection-diffusion-reaction equation.Numerical experiments,mostly with boundary layer where sharp gradients may appear due to high Peclet or Reynolds numbers,are conducted to verify the robustness and the high accuracy of this new method.