Adaptive Multi Scale modeling of groundwater flow and transport

Usually the permeability tensor is the most dominant parameter affecting groundwater flow and transport, while it is also the most heterogeneous parameter. Permeability can be measured on laboratory scale and subsequently a spatially correlated random field generator is often used to construct a field scale model. This procedure results in a very fine grid with discrete tensor coefficients for each cell. To reduce the number of unknowns in the flow model fine scale permeabilities have to be upscaled to coarse scale permeabilities that relate the spatial averaged pressure, flux and dissipation to each other. However exact values cannot be found in general and traditional upscaling methods depend heavily on the local boundary conditions chosen. This paper presents an operator based scaling technique that is applied for communication between scales in combination with adaptive mesh refinement that balances the loss in accuracy due to the averaging procedure. The technique is used to solve three dimensional groundwater flow and transport problems in partly saturated highly heterogeneous porous media. The subdomain collocation finite element method discretizes the flow and transport equation. Both sets of linearized equations are then solved sequentially in a number of multigrid cycles where mesh refinement is restricted to elements for which a local error criterion does not hold. Picard iterations resolve the non-linearities due to unsaturated flow and density and viscosity coupling. One example illustrates this adaptive multi scale technique by simulating flow and transport through a heterogeneous embankment. The application shows the reduction of computational work required to obtain the desired level of accuracy by refining the mesh only in regions of interest where high concentration fronts or high permeability contrast exist.