Effects of reconstruction of variables on the accuracy and computational performance of upscaling solutions of the shallow water equations

This paper presents a new sub-grid flood inundation model obtained by upscaling the shallow water equations (SWE) to enhance the model efficiency in large-scale problems. The model discretizes study domains using two nested meshes. The equations are solved at the coarse mesh by a second-order accurate in space (i.e. piecewise linear reconstruction of variables) Godunov-type finite volume (FV) method, while the fine mesh is used to incorporate high-resolution topography and roughness into the solution. The accuracy and performance of the model were compared against a first-order version of the model recently proposed by the authors and a second-order conventional FV model using artificial and real-world test problems. Results showed that improved accuracy is delivered by the proposed model, and that at low-resolution meshes, the spatial reconstruction of variables of the numerical scheme plays a major role in the solution's accuracy.