Stabilized Reduced-Order Modeling of Reactive Transport
In this work, we consider the use of model order reduction in solving the advection-dispersion-reaction equation. Equations of this form appear in a wide range of application areas, but we focus on the study of reactive transport in groundwater systems. In cases where transport is dominated by advective forces, numerical models often suffer from instability which may pose a serious computational challenge by producing non-physical oscillations in the approximations. We aim to reduce the burden of the computational challenges in this setting through model order reduction, employing the method of snapshots and the singular value decomposition to construct a reduced basis via proper orthogonal decomposition (POD). We study the incorporation of Streamline Upwind Petrov-Galerkin (SUPG) methods to lend stability to full- and reduced-order transport models in 2d, considering advection-dominated transport and nonlinear reactive transport.