Semianalytical series solutions for three-dimensional groundwater-surface water interaction

A semianalytical grid-free series solution method is presented for modeling 3-D steady state free boundary groundwater-surface water exchange in geometrically complex stratified aquifers. Continuous solutions for pressure in the subsurface are determined semianalytically, as is the location of the water table surface. Mass balance is satisfied exactly over the entire domain except along boundaries and interfaces between layers, where errors are shown to be acceptable. The solutions are derived and demonstrated on a number of test cases and the errors are assessed and discussed. This accurate and grid-free scheme can also be a helpful tool for providing insight into lake-aquifer and stream-aquifer interactions. Here it is used to assess the impact of lake sediment geometry and properties on lake-aquifer interactions. Various combinations of lake sediment are considered and the appropriateness of the Dupuit-Forchheimer approximation for simulating lake bottom flux distribution is investigated. In addition, the method is applied to a test problem of surface seepage flows from a complex topographic surface; this test case demonstrated the method's efficacy for simulating physically realistic domains.