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In this study, we introduce a numerical method to reduce the solute transport equation into a reduced form that can replicate the behavior of the model described by the original equation. The basic idea is to collect an ensemble of data of state variables (say, solute concentration), called snapshots, by running the original model, and then use the proper orthogonal decomposition (POD) techniques (or the Karhunen-Loeve decomposition) to create a set of basis functions that span the snapshot collection. The snapshots can be reconstructed using these basis functions. The solute concentration at any time and location in the domain is expressed as a linear combination of these basis functions, and a Galerkin procedure is applied to the original model to obtain a set of ordinary differential equations for the coefficients in the linear representation. The accuracy and computational efficiency of the reduced model have been demonstrated using several one-dimensional and two-dimensional example

Simulating Solute Transport in Porous Media Using Model Reduction Techniques