Generalized dual porosity: A numerical method for representing spatially variable sub-grid scale processes

A generalized dual porosity method (GDPM) has been developed to incorporate sub-grid scale heterogeneity into large-scale flow and transport simulations. The method is spatially variable in the sense that the method can be applied with different levels of resolution for different spatial nodes in the simulation. The method utilizes the nodal connectivity structure and linear equation solvers of unstructured grids like those used in the finite element method, and can be applied to any problem without externally modifying the numerical grid. The algorithm scales linearly in CPU time and storage with the number of GDPM nodes. We demonstrate the utility and computational efficiency of the technique with two verification problems and an example problem of a field site.