A Dual Model-Reduction Approach to Groundwater Flow and Solute Transport Simulations.

Abstract:

Mathematical-model reduction using singular value decomposition (SVD) has been shown to be an effective method for reducing the computer runtime of linear and nonlinear groundwater-flow models without sacrificing accuracy. The discrete empirical interpolation method (DEIM) is an alternate method of model reduction better suited for nonlinear systems. In this research, both methods are applied simultaneously to reduce the dimensionality of a 3-D unconfined groundwater-flow model: SVD to reduce the column space and DEIM to reduce the row space. The results of the dimensional reduction can approach several orders of magnitude, resulting in significantly faster simulation runtimes. The implementation and benefit of SVD/DEIM model reduction is demonstrated through its application to a synthetic, groundwater-flow and solute-transport model with groundwater extraction wells that influence of seawater intrusion. The developed methodology identifies the dominant locations (i.e. the discrete points) of the model that have the most influence on the water levels and saltwater concentrations. The result is a reduced model constructed from fewer equations (row dimension) and is projected into a reduced subspace (column dimension). The methodology first independently constructs the reduced flow and transport models such that their errors are minimized for a flow-only model and transport-only model, respectively. Once the two reduced models have been established, a density-dependent flow simulation is preformed by iterating between the flow and transport models for each time step. Further analysis of the SVD/DEIM method illustrates the tradeoff between magnitude of the reduced dimension and corresponding errors in model output, with respect to the unreduced and independently reduced models. The application of this method shows that runtime can be significantly decreased for models of this type while still maintaining control of desired model accuracy.