University of California Water Resources Center

Mathematical models of the transport and fate of dissolved chemicals in groundwater are becoming increasingly important tools in understanding, managing, and remediating groundwater contamination. The success of such models is dependent on: 1) how well the relevant physical, chemical, and microbiological processes controlling subsurface transport are represented with mathematical equations, and 2) how accurately and efficiently the equations are solved with numerical methods that discretize the equations over space and time. The computational burden associated with multidimensional, multicomponent, numerical solute transport models can be prohibitive. In this project, we have implemented and extended a local adaptive grid refinement (LAGR) method of Berger and Oliger (1984) to solve CPU-intensive transport problems efficiently and accurately. The method tracks error-prone regions of the solution domain and supplies high-resolution subgrids where they are locally needed while maintaining relatively few nodes elsewhere on a coarse base grid. Novel features include a unique method for detecting a priori where the numerical error is unacceptable, variable time step control which allows smaller time steps on subgrids than on the base grid, and a modular framework which allows easy exchange of partial differential equation solvers to accommodate different problem formulations.

We use simulations for uniform and nonuniform flow fields and for single, nonreactive species and multiple, reactive species to demonstrate and evaluate the LAGR method. The cost and accuracy of LAGR simulations depends on design parameters controlling where subgrids are created, how frequently they are created, and how large they are once they are created. For any particular problem there is a trade-off between cost and accuracy, depending on how the design parameters are chosen. Although the optimal set of design parameters is nonunique, we have been able to provide important insight into the choice of parameters for a desired solution accuracy. Using this insight, solutions with accuracies comparable to those achieved with a uniform fine grid are obtained at between 15 and 30% of the computational cost.