Reduction of Large-Scale Groundwater Flow Models Via the Galerkin Projection

Abstract

In this paper we describe a reduced model structure that describes the hydraulic head h for ground water flow models as a linear combination of a set of spatial patterns P with time-varying coefficients r. We discuss a data-driven technique to extract patterns P (EOFs) that span a subspace of model results that captures most of the relevant information of the original model. We make use of the patterns to obtain a reduced dynamic model for the time-varying coeffecients via a Galerkin Projection. This technique substitutes h within the PDE for groundwater now by the reduced model structure PTr. We acquire a dynamic reduced model for dr/dt by multiplying the outcome with PT. The vector dimension of r is often small compared to the original dimension of h, and a model which operates within a lower dimension requires less computational time. The method has heen evaluated for a realistic case, whereby we achieved a maximal reduction in computational time of ≈ 80. The reduced model has a promising prospect as its efficiency increases whenever the number of grid cells increases and the parameterization of the original model grows in complexity.