Shallow-flow velocity predictions using discontinuous Galerkin solutions

TL;DR

This paper demonstrates that a second-order discontinuous Galerkin (DG2) solver provides more accurate shallow-flow velocity predictions at coarser resolutions compared to finite volume methods, especially in smooth flow regions.

Contribution

The study introduces the use of a second-order discontinuous Galerkin solver for shallow water flow velocity predictions, showing its advantages over traditional finite volume methods.

Findings

DG2 reduces error dissipation and improves accuracy at coarser resolutions.

DG2 outperforms FV2 and FV3 in predicting velocity magnitude and direction.

DG2 is a computationally efficient alternative for smooth shallow flow simulations.

Abstract

Numerical solvers of the two-dimensional (2D) shallow water equations (2D-SWE) can be an efficient option to predict spatial distribution of velocity fields in quasi-steady flows past or throughout hydraulic engineering structures. A second-order finite volume solver (FV2) spuriously elongates small-scale recirculating eddies within its predictions, unless sustained by an artificial eddy viscosity, while a third-order finite volume (FV3) solver can distort the eddies within its predictions. The extra complexity in a second-order discontinuous Galerkin (DG2) solver leads to significantly reduced error dissipation and improved predictions at a coarser resolution, making it a viable contender to acquire velocity predictions in shallow flows. This paper analyses this predictive capability for a grid-based, open source DG2 solver with reference to FV2 or FV3 solvers for simulating velocity magnitude and direction at the sub-meter scale. The simulated predictions are assessed against measured velocity data for four experimental test cases. The results consistently indicate that the DG2 solver is a competitive choice to efficiently produce more accurate velocity distributions for the simulations dominated by smooth flow regions.