Shallow-flow velocity predictions using discontinuous Galerkin solutions

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.