Nonlinear model reduction of solute transport models

Computer simulations of groundwater flow and solute transport are often burdened by long runtimes. The simulations are necessarily complex to capture the system dynamics and finely discretized spatial and temporal domains are often needed for solution accuracy and stability. Model reduction allows for the approximation of system state by solving equations in a reduced dimensional space. Proper orthogonal decomposition (POD) is an effective way to reduce the dimensionality of systems of differential equations that are discretized by finite difference or finite element methods. If the problems are nonlinear in nature, the discrete empirical interpolation method (DEIM) has been shown to supplement POD by further reducing the dimension of nonlinear calculations. Here, the combined POD-DEIM approach is shown to work on a problem of 2-dimensional groundwater flow with solute transport exhibiting nonlinear sorption. The application is restricted to largely dispersive problems (low Peclet number). Results show areas of high concentration are effectively identified with mean errors less than 2% of the full model.