A Combined Approach to Model Reduction for Nonlinear Groundwater Flow and Solute Transport Simulations Using POD and DEIM.

Abstract:

Model reduction techniques using proper orthogonal decomposition (POD) have been very effective in applications to confined groundwater flow models. These techniques consist of performing a projection of the solution of the full model onto a reduced basis. POD combined with the snapshot approach has been successfully applied to highly discretized linear models. In many cases, the reduced model is orders of magnitude smaller than the full model and runs 1,000 times faster. For nonlinear models, such as the unconfined groundwater flow, direct application of POD requires additional calls to the full model to generate additional snapshots. This is time consuming and increases the dimension of the reduced model. The discrete empirical interpolation method (DEIM) is a technique that avoids the additional full model calls and captures the dynamics of the nonlinear term while reducing the dimensions.

Here, POD and DEIM are combined to reduce both the nonlinear unconfined groundwater flow and solute transport equations. To prove the concept, simple one-dimensional models are created for MODFLOW and MT3DMS separately. The dual approach is then tested on a density-dependent flow and transport simulation using the LMT package developed for MODFLOW. For each iteration of the nonlinear flow solver and the transport solver, the respective reduced models are solved instead. Numerical experiments show that significant reduction is obtainable before errors become too large. This method is well suited for a coastal aquifer seawater intrusion scenario, where nonlinearities only exist in small subregions of the model domain. A fine discretization can be utilized and POD will effectively eliminate unnecessary parameterization by projecting the full model system matrix onto a subspace with fewer column dimensions. DEIM can then reduce the row dimension of the original system by using only those state variable nodes with the most influence. This combined approach allows for full characterization of a groundwater basin in the simulation without the severe runtime limitations introduced by nonlinearities and growing dimensionality.