Application of the Multiscale Finite Element Method to the numerical modeling of regional land subsidence

Abstract

For a regional land subsidence problem, there are difficulties for the traditional finite element method to solve the regional groundwater flow equation involved. A new finite element method - multiscale finite element method (MsFEM) applied to resolve three dimensional groundwater flow problem- is introduced. Three advantages make the MsFEM very useful for groundwater flow simulation in a large region with highly heterogeneous porous media. One advantage is that this method can significantly save computing efforts by coarse grid mesh. The variation of parameters in an element is brought to the multiscale base functions. Second one is that this method can to a large extent avoid large aspect ratios of elements by combining aquifers and aquitards in one element. The third advantage is that the hydraulic heads in different depths of aquitards or aquifers could be rather accurately interpolated using the multiscale base functions and the nodal heads of the element by MsFEM. The third advantage is useful for the subsidence modeling. A numerical example is done to verify the advantages of MsFEM. Finally, the MsFEM is applied to solve the regional land subsidence model of Shanghai, which includes a three-dimensional groundwater flow mathematical model and a one-dimensional subsidence model. The traditional two-step approach is followed in this study, with the hydrodynamics of the pumped multiaquifer system first simulated by a 3-D groundwater flow model and the subsidence then computed with a 1-D subsidence model with the pore pressure field specified as an external distributed source of strength within the porous medium. The simulation period is from March, 1986 to December, 1998. Using MsFEM, the aquifer system in Shanghai is divided into six layers, which means one aquifer and one aquitard are in one layer with an average thickness of about 50 meters. Every element in MsFEM is subdivided into 7 sub-layers in the vertical direction and every horizontal layer in an element is divided into 4 hexahedral elements. So each element is subdivided into 28 hexahedral sub-cells, which allows the heterogeneity of aquifers and aquitards to be considered by multiscale base functions. The aquifers system in total is discretized into 19,996 elements with a total of 25,000 nodes. The hydraulic heads in any depth of aquitards or aquifers could be interpolated using the multiscale base functions and the nodal heads of the element. It is very useful for the settlement calculation for the aquitards or aquifers after hydraulic heads at nodes of elements are obtained by MsFEM. The application of MsFEM significantly saves computing efforts, effectively decreases the aspect ratios of elements and obtains good results, which proves the MsFEM can be applied to solve the real regional 3D groundwater flow problems, and it is an effective numerical method for regional land subsidence modeling.