On handling smoothly continuous and singular parameter fields in finite element models of flow and transport

Most finite element methods (FEMs) for simulating groundwater flow and solute transport rely upon a discrete representation of the specified independent parameters. In flow models, hydraulic conductivity and storage coefficients are specified as uniform within each element. Likewise, in solute transport models, velocity, dispersion tensor components, and porosity are typically treated as piecewise-constant. For both flow and transport, source distributions are typically nodal, linearly distributed along sides, or element-averaged. Recent work by the author has addressed the integration of finite element flow and transport models with analytic element method (AEM) flow solutions. When AEM flow solutions are used as input to a transport model, the independent parameters are characterized by generally smooth and continuous fields with sharp discontinuities and singularities, requiring revised techniques for evaluating system residuals. These approaches are currently being extended to develop hybrid AEM / FEM flow simulation methods that rely upon superposition of discrete and analytical solutions, where AEM is used to simulate regional trends and the FEM is used to resolve local detail. Notably, such an approach would remove the requirements of excessive discretization near wells or surface water features and enable the development of simulation models that are more accurate at both regional and local scales. The revised methods can also be used to more accurately simulate flow and transport through kriged or otherwise interpolated parameter fields. Some intermediate results of investigations into the handling and behavior of the resultant system integrals are addressed and discussed within the context of integrated or hybrid AEM / FEM solution methods.