期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 197, 期 51-52, 页码 4610-4625出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2008.06.005
关键词
Richards' equation; Finite element method; Multiscale stabilization; Local conservation
资金
- National Science Foundation [DMS 0411413]
Standard Galerkin finite element methods for variably saturated groundwater flow have several deficiencies. For instance, local oscillations can appear around sharp infiltration fronts without the use of mass-lumping, and velocity fields obtained from differentiation of pressure fields are discontinuous at element boundaries. Here, we consider conforming finite element discretizations based on a multiscale formulation along with recently developed, local postprocessing schemes. The resulting approach maintains the basic flexibility and appeal of traditional finite element methods, while controlling nonphysical oscillations and producing element-wise mass-conservative velocity fields. Accuracy and efficiency of the proposed schemes are evaluated through a series of steady-state and transient variably saturated groundwater flow problems in homogeneous as well as heterogeneous domains. The schemes are formulated for a generic nonlinear advection-diffusion equation and are thus applicable to many other flow models. (c) 2008 Elsevier B.V. All rights reserved.
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