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Nonlinear Model Reduction for Groundwater Flow and Solute Transport


Groundwater flow and solute transport models are necessary for understanding the quantity and quality of water in the subsurface. As these models get increasingly complex, their computational runtimes often increase. Reduced models can be developed to approximate the full complex model with reasonable accuracy and shorter runtimes. In this research, proper orthogonal decomposition (POD) is used to identify a lower dimensional subspace that captures most of the information contained in the full model system. Then, because of the nonlinearities present in many flow and transport models, a discrete empirical interpolation method (DEIM) is used to identify an additional lower dimensional subspace that captures the nonlinear dynamics. The reduced modeling framework is implemented within the MODFLOW and MT3DMS software families for groundwater flow and solute transport, respectively. The combined POD-DEIM approach is first applied to an unconfined groundwater flow model where dimensions were reduced by two and three orders of magnitude. The same approach is then applied to a solute transport model simulating nonlinear sorption where dimensions were also reduced by two and three orders of magnitude. The reduced models performed with sufficient accuracy and faster runtimes. The faster runtimes could allow for the reduced models to be embedded into an optimization or uncertainty analysis where thousands to millions of model runs could be required. With the developed POD-DEIM approach, reduced modeling is now viable for any existing MODFLOW or MT3DMS model.

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