Model order reduction strategies for weakly dispersive waves

TL;DR

This paper develops and compares two reduced order modeling strategies for weakly dispersive water wave equations, focusing on computational efficiency and robustness against parameter variations.

Contribution

It introduces a hybrid linear reduction (pdROM) and an empirical interpolation-based hyper-reduction (EIMROM) for dispersive wave models, enhancing efficiency and robustness.

Findings

Both methods significantly reduce computational cost.

pdROM offers superior robustness to parameter changes.

EIMROM achieves greater cost reduction.

Abstract

We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator. We propose two strategies to construct reduced order models for these problems, with the main focus being the control of the overhead related to the inversion of the elliptic operators, as well as the robustness with respect to variations of the flow parameters. In a first approach, only a linear reduction strategies is applied only to the elliptic component, while the computations of the nonlinear fluxes are still performed explicitly. This hybrid approach, referred to as pdROM, is compared to a hyper-reduction strategy based on the empirical interpolation method to reduce also the nonlinear fluxes. We evaluate the two approaches on a variety of benchmarks involving a generalized variant of the BBM-KdV model with a variable bottom, and a one-dimensional enhanced weakly dispersive shallow water system. The results show the potential of both approaches in terms of cost reduction, with a clear advantage for the pdROM in terms of robustness, and for the EIMROM in terms of cost reduction.