Adaptive multi-scale finite element method for unsaturated flow in heterogeneous porous media II.Numerical results
HE Xin-guang · Journal of Hydraulic Engineering · 2009
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 provide good agreement with the reference fine-scale solutions.The adaptive method can efficiently capture the largescale structure of the fine-scale solution on a coarse-scale mesh,and only about 1/6 of the multi-scale base function is necessary to be recomputed at each time step under Dirichlet and Neuman infiltration top boundary conditions.Besides,the convergence of the adaptive coarse grid method and the comparability of the reconstructed fine-scale solution were also discussed.The numerical results show that the coarse-scale solution converges to the reference fine-scale solution as the coarse mesh is refined,and the reconstructed fine-scale solution can excellently approximate to the reference fine-scale solution.