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——Ⅱ.数值结果

Adaptive multi-scale finite element method for unsaturated flow in heterogeneous porous media Ⅱ.Numerical results

为了验证作者在本文第Ⅰ部分所提出的自适应多尺度有限元方法的有效性与精确性,在第Ⅱ部分对水力参数是随机生成的呈对数正态分布的非饱和水流问题进行了数值试验。数值算例分别考虑了具有各向同性和各向异性相关结构的水力参数场。计算结果表明:自适应多尺度有限元方法的粗尺度解与参考的细尺度解之间具有很好的一致性:在Dirichlet和Neumann入渗上边界条件下,在粗网格中该方法能够有效地抓住细尺度解的大尺度结构,而且,在每一时间步,只有大约1/6的多尺度基函数需要重新计算。此外,还进一步地讨论了自适应粗网格方法的收敛性和重构细尺度解的可比性。数值结果表明:随着粗网格被细分,粗尺度解将收敛到细尺度的参考解,而重构的细尺度解可以很好地近似参考的细尺度解。

Numerical experiments were carried out for unsaturated flow equation with randomly generated lognormal hydraulic parameters to demonstrate the efficiency and accuracy of the adaptive multi-scale FEM proposed by the authors.The hydraulic parameter fields with isotropic and anisotropic correlation structure were considered in the numerical examples respectively.The computational results show that the coarse-scale solutions obtained by the adaptive multi-scale method described in the part Ⅰ of this paper provi...