非饱和土壤水流方程的CN广义差分法

首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便.

A CN GENERALIZED DIFFERENCE FORMULATION FOR UNSATURATED SOIL WATER EQUATION

In this paper, based on Crank-Nicolson (CN) technique, a semi-discrete formulation with respect to time second-order accuracy for two-dimensional unsaturated soil water flow equation is established firstly. And then, a fully discrete CN generalized difference formulation with fully second-order accuracy is directly found from a semi-discrete formulation with respect to time second-order accuracy and the error estimates of its solutions are provided. Finally, a numerical example is presented to show the advantage of the fully discrete CN generalized difference formulation. The approach here improves time discrete accuracy so that the number of iterative step is greatly lessened and the accumulation of truncation errors in practical calculation is reduced, and the calculation accuracy and computational efficiency are improved. And it avoids the discussion of the semi-discrete formulation with respect to spatial variable so that its theory analysis is very simple.