复杂边界数学模型数值解析的求法及在渗流计算中的应用

The Numerical Analytic Solution To Mathematical Model of Complex Boundary And the Application in Seepage Flow Calculation

由于地质体和地质过程相当复杂,其相应的数学模型也较复杂,模型的求解只能采用数值法近似得到,结果误差大,精度低。要想得到较高的精度,需大大地增加运算量。本文介绍一种新的数值解析解,是基于有限元方法,通过变化单元的划分,消除系统误差,来推出高精度的解。此法方便易行,使用于各种复杂的数学模型,尤其适用于精度较高的计算问题。文中给出一个渗流算例,结果令人满意。

Because geologic bodys and geologic processes are rather complicated,their mathemadcal models are very complex. The solutions to the model is only approximate value by numerical method, so these solutions have comparatively big error and lower precision. In order to get a comparatively high precision solution, the amount of calculation must be greatly increased. Based on finite element and a change of unit dissection, a new kind of numerical analytic solution is developed in this paper and it can eliminate system errors and extrapolate a highly precise solution. This method is simple and convenient, so it can be used in all kinds of compb'cated mathematical models, especially in high precision problem. A calculation example for seepage flow is shown in this paper and the result is satisfied.