A GPU-accelerated DOT scheme for the coupled 2D shallow water and Exner equations

In this work, a novel numerical model to solve the coupled system of two-dimensional (2D) shallow water and Exner equations for simulating hydro-morphodynamical processes is presented. A finite-volume first-order scheme based on the path-conservative Dumbser-Osher-Toro (DOT) solver is adopted, thus representing one of the first attempts at 2D extension of this method. Moreover, a modified treatment of partially submerged and emerging topography is proposed to satisfy the C-property and mitigate the occurrence of negative water depths. The computational efficiency of the model is ensured thanks to a parallel implementation that exploits the capabilities of Graphic Processing Units (GPU) and guarantees good scalability with increasing grid resolutions. The validation is performed considering different analytical and experimental test cases involving bedload sediment transport. Results show that the model can preserve water-at-rest conditions, simulate dam-break flows over erodible beds, and predict the main erosion processes. An example of real application is finally reported to verify the computational performance of the code for practical case studies: thanks to the GPU acceleration, the ratio of physical to computational time is in the order of 40–300, depending on the grid size. This confirms the feasibility of field-scale simulations with competitive runtimes using the proposed model.