饱和—非饱和渗流三维数学模型及数值方法

3-D THEORETICAL MODEL AND NUMERICAL METHOD OF SATURATED-UNSATURATED SEEPAGE

建立了以总水头表示的统一形式的饱和—非饱和渗流三维控制方程,给出了主要耦合参数的计算方法,选取了合适的有限差分格式,分析了其截断误差和稳定性条件,针对实际算例获得了较为合理的模拟结果.所建立的饱和—非饱和渗流三维模型,避开了两者独立建模时潜水面边界上下波动带来的困难,避开了以压力水头表示的饱和—非饱和渗流模型求解时的数值振荡和弥散问题,有效解决了饱和—非饱和渗流的建模及求解难题.

A unified 3-D governing equation of saturated-unsaturated seepage expressed by total head was built,computed methods of main coupling parameters were given,appropriate difference schemes were selected,truncation error and stability condition were analyzed,and reasonable simulation results were got for a true example.The 3-D model of saturated-unsaturated seepage avoids the difficulty brought by water table fluctuation when saturated model and unsaturated seepage model are built independently,avoids the numerical oscillation and dispersion when the saturated-unsaturated seepage model is expressed by pressure head,and solves the difficult modeling and solving problem of saturated-unsaturated seepage effectively.