Well-resolved velocity fields using discontinuous Galerkin shallow water solutions

TL;DR

This paper demonstrates that a second-order discontinuous Galerkin (DG2) solver provides more accurate and efficient predictions of small-scale velocity transients in shallow water models compared to traditional finite volume methods.

Contribution

It introduces a specific DG2 solver configuration that improves the resolution and convergence of velocity fields in shallow water simulations.

Findings

DG2 solver reduces numerical diffusion compared to FV2.

DG2 achieves faster convergence rates in velocity field predictions.

Identified optimal DG2 settings for detailed wave-structure interaction modeling.

Abstract

Computational models based on the depth-averaged shallow water equations (SWE) offer an efficient choice to analyse velocity fields around hydraulic structures. Second-order finite volume (FV2) solvers have often been used for this purpose subject to adding an eddy viscosity term at sub-meter resolution, but have been shown to fall short of capturing small-scale field transients emerging from wave-structure interactions. The second-order discontinuous Galerkin (DG2) alternative is significantly more resistant to the growth of numerical diffusion and leads to faster convergence rates. These properties make the DG2 solver a promising modelling tool for detailed velocity field predictions. This paper focuses on exploring this DG2 capability with reference to an FV2 counterpart for a selection of test cases that require well-resolved velocity field predictions. The findings of this work lead to identifying a particular setting for the DG2 solver that allows for obtaining more accurate and efficient depth-averaged velocity fields incorporating small-scale transients.