求解非均质多孔介质中非饱和水流问题的一种自适应多尺度有限元方法——Ⅰ数值格式

为了有效地模拟跨越多个尺度的非均质多孔介质中的非饱和水流问题，本文提出一种自适应多尺度有限元方法。该方法能在一个粗尺度网格上精确而有效地获得具有非均质系数的非饱和水流方程的粗尺度解。其基本思路是使用修改的皮卡迭代格式来处理方程中的非线性性和构造一种自适应多尺度基函数来捕捉方程系数中的时空变异性。本文详细地描述了构造这一方法的原理并且给出了一种相应的算法。

Adaptive multi scale finite element method for unsaturated flow in heterogeneous porous media I. Numerical scheme

For effectively simulating unsaturated flow in heterogeneous porous media spanning over many scales, an adaptive multi scale FEM was proposed. The purpose of this method is to obtain the large scale solution of unsaturated water flow equation with heterogeneous coefficients accurately and efficiently in a coarse scale mesh. The basic idea is to use the modified Picard iteration scheme to address the nonlinear characteristics of the equation, and to construct an adaptive multi scale basic function to account for the spatial temporal variability in the coefficients of the equation. The principle for constructing this method is given and the algorithm for implementation is also presented.