Application of level set method for groundwater flow with moving boundary

A potential of level set methods for the numerical modeling of moving boundaries and interfaces in groundwater flow problems is shown by the application for a particular model of the flow with moving water table (the phreatic surface). The main ingredients of the level set methods like the advection of level set function, the computation of signed distance function and the extrapolation of missing data are explained for a class of possible applications. The numerical solution of the groundwater flow problem is proposed using the flux-based level set method and the immersed interface method that are based on a finite volume discretization on any fixed (unstructured) grid. Presented examples show good properties of the method concerning a small mass balance error and a good grid convergence even for an example with merging boundaries. An example with seepage boundary is computed using the locally adapted grids by refining and coarsening the mesh according to the position of moving water table.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Model of groundwater flow with moving boundary, the phreatic surface. ► Compact level set formulation on a fixed domain. ► Finite volume discretization using immersed interface method. ► Examples with exact solution or exact mass balance. ► Examples with merging interfaces, local adaptivity, seepage boundary.