求解对流-扩散-反应问题的改进有限积分法

将求解偏微分方程的有限积分法应用于对流-扩散-反应问题，发现对于非对流占优的对流扩散问题，有限积分法的精度比QUICK法高一个数量级，比传统的有限体积法高两个数量级.处理对流占优的对流-扩散-反应问题时，对流项的离散时引进加权参数，通过调节该参数反映输运的方向性.结果表明这种改进的有限积分法的精度比传统的有限体积法至少高四个数量级，同时明显改进了原来的有限积分法的精度和稳定性.对于对流占优的对流-扩散-反应问题，即使采用粗网格，计算结果也未出现非物理振荡现象，表明改进的有限积分法具有很好的稳定性.

A Modified Finite Integration Method for Convection-Diffusion-Reaction Problems

Finite integration method is employed to solve convection-diffusion equations. For diffusion-dominated convection-diffusion problems, numerical results show that finite integration method is more than one and two orders of magnitude better in accuracy than QUICK scheme and central differencing scheme, respectively. We find that finite integration method can be improved by introducing a weighting parameter in numerical quadrature. By appropriately adjusting the parameter, modified finite integration method is at least more than four orders of magnitude better in accuracy than traditional finite volume method for convection-dominated flows. Furthermore, even coarse grids are utilized to divide flow domain modified finite integration method has not lead to unphysical oscillations in convection-dominated convection-diffusion problem, which demonstrates a good stability of the method.