Assessment of Friction Upscaling Methods in Dual-Mesh Shallow Water Simulations

This study investigates the challenge of accurately upscaling the friction source term of two-dimensional (2D) shallow water equations (SWEs) in computational simulations using nested meshes (also known as dual-meshes) for large-scale flood inundation problems. This work employs a recently developed dual-meshes sub-grid (SG) model, which performs runtime computations on a coarse computational mesh while incorporating high-resolution information from a fine mesh at the preprocessing stage. Four approaches proposed in the literature to approximate the friction source term are compared. They are formulated based on assumptions such as constant friction slope and constant water depth over a computational cell. The models are evaluated using two one-dimensional (1D) idealized test cases covering a wide range of flow regimes, water depths, and discharges, and two large-scale 2D real-world test cases. Methods that upscale the solution to compute frictional effects on a coarse-resolution mesh deliver 2–5x speedup relative to approaches performing friction computations on a fine-scale mesh. However, the speedup varies depending on the specific case. The approach delivering the best trade-off between accuracy and computational performance upscales friction by assuming a constant flow direction over each coarse cell. A detailed discussion is provided on the impact of various assumptions in the approximation of the friction source term on solution accuracy, and the limitations of the approach are explained.