Second-order discontinuous Galerkin flood model: Comparison with industry-standard finite volume models

Abstract

Finite volume (FV) numerical solvers of the two-dimensional shallow water equations are core to industry-standard flood models. The second-order Discontinuous Galerkin (DG2) alternative, although a viable way forward to improve current FV-based flood models, is yet under-studied and rarely used to support flood modelling applications. This paper systematically explores and compares the predictive properties of a robust DG2 flood model to those of prominent FV-based industrial flood models. To identify the simplest and most efficient DG2 configuration suitable for flood inundation modelling, two variants – with and without local slope limiting – are considered. The numerical conservation properties of the DG2 variants are compared to those of a first-order FV (FV1) and a second-order FV (FV2) counterparts. The DG2 variants are then tested over five realistic flooding scenarios, recommended by the UK Environment Agency to validate 2D flood model capabilities, while comparing their performance against that of four FV-based commercial models (i.e. TUFLOW-FV1, TUFLOW-FV2, TUFLOW-HPC and Infoworks ICM). Results reveal that the DG2 variant without local limiting (DG2-NL) is capable to simulate shockless flood flows featured in a wide range of flood modelling applications. The DG2-NL shows closer predictions to commercial model outputs at twice-coarser spatial resolution, and can run twice faster to produce more informative hydrograph with small-scale transients over long-range simulations, even when the sampling is far away from the flooding source.