Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

Accurate modelling of groundwater ow and transport with sharp moving fronts often involves high computational cost, when a xed=uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial di erential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial di erential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear in ltration in soil, and the coupling of density dependent ow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and e ciently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement