Combination of intrusive POD-based reduced-order models and augmented Riemann solvers applied to unsteady 2D shallow water equations

The shallow water equations (SWEs) can be used to model the spatio-temporal evolution of free surface flows. The numerical resolution of realistic problems based on the 2D SWEs by means of augmented Roe-based (ARoe) methods requires the inclusion of certain numerical corrections to avoid non-physical results in presence of irregular topography and wet dry fronts. Besides that, their complex and transient nature involves high computational costs. In this direction, intrusive reduced-order models (ROMs) based on the proper orthogonal decomposition (POD) are presented as alternative to speed up computational calculations without compromising the accuracy of the solutions. The main objective of this article is to study whether the inclusion of numerical corrections in the ROM strategy of the 2D SWEs for non trivial situations is necessary to obtain accurate solutions or not, and, if necessary, to present their reduced version. In addition to this, it is proposed to solve problems with Dirichlet-type boundary conditions (BCs) by means of ROMs using a technique whereby the BCs are directly integrated into the on-line phase of ROM solving. The efficiency of the ARoe-based ROM has been tested with respect to the full-order model by comparing their computational cost and the accuracy of their solutions in different numerical cases.