Local-uniform-grid refinement and transport in heterogeneous porous media

Abstract

The application of an adaptive-grid method to a mathematical model for unsteady flow, coupled with transport of solute in heterogeneous porous media, is discussed. When the concentration of solute is large, the solute-concentration profile in transport problems can show locally large gradients in space and in time. For this type of problem, an adaptive-grid method can be greatly beneficial. We consider a method based on local-uniform-grid refinement, where integration takes place on a series of nested, local-uniform finer and finer subgrids. These subgrids are created up to a level of refinement where sufficient spatial accuracy is reached, and their location and shape are adjusted after each time step. The space domain is considered to be a rectangle, and all grids in use are uniform and cartesian. The interfaces, demarking the inhomogeneities, are assumed to coincide with cell edges in the numerical approximation. Special conditions are applied here, connecting the solutions on both sides of the interface. These interface conditions involve continuity of fluxes across the interfaces. The mesh-refinement process and the variable-time stepsizes are controlled by heuristic error monitors.