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 (FV2) solver 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 submeter 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. The estimation of the spatial distribution of horizontal velocity fields is useful to analyze the design of hydraulic and flood-defense structures undergoing shallow water flow processes. Examples include flooding through a residential area with piered buildings where recirculation flow eddies occur within side cavities, past building blocks, and across of street junctions. This paper demonstrates the utility of a relatively new hydraulic simulation tool, the second-order discontinuous Galerkin (DG2) solver, as an alternative to existing finite-volume solvers featured in popular tools such as HEC-RAS 2D, Rubar20, Iber, and TUFLOW-HPC. The DG2 solver is open source, as part of the LISFLOOD-FP 8.0 software suite, and particularly excels in the estimation of velocity fields that are more informative of the flow processes within a few minutes of simulation time. The proposed simulation tool is limited to modeling problems where the depth-integrated assumption of the shallow water equations is appropriate.