Discontinuous Galerkin flood model formulation: Luxury or necessity?

Abstract

The finite volume Godunov-type flood model formulation is the most comprehensive amongst those currently employed for flood risk modeling. The local Discontinuous Galerkin method constitutes a more complex, rigorous, and extended local Godunov-type formulation. However, the practical merit associated with such an increase in the level of complexity of the formulation is yet to be decided. This work makes the case for a second-order Runge-Kutta Discontinuous Galerkin (RKDG2) formulation and contrasts it with the equivalently accurate finite volume (MUSCL) formulation, both of which solve the Shallow Water Equations (SWE) in two space dimensions. The numerical complexity of both formulations are presented and their capabilities are explored for wide-ranging diagnostic and real-scale tests, incorporating all challenging features relevant to flood inundation modeling. Our findings reveal that the extra complexity associated with the RKDG2 model pays off by providing higher-quality solution behavior on very coarse meshes and improved velocity predictions. The practical implication of this is that improved accuracy for flood modeling simulations will result when terrain data are limited or of a low resolution.