A hybrid shallow water solver for overland flow modelling in rural and urban areas

This study aims to present an accurate and efficient finite volume approach for overland flow modelling in rural and urban areas through solving the two-dimensional shallow water equations. The proposed approach introduces a hybrid procedure that utilizes the sharpness of discontinuity to identify flow conditions in the entire computational domain, and then a low-accuracy/high-efficiency scheme (the Rusanov scheme) is used in regular flows, whereas a high-accuracy/low-efficiency scheme (the HLLC scheme) is adopted in strong discontinuous flows. Regions that simultaneously adopt the two schemes are artificially specified to diminish numerical unbalances between the two schemes. Model calibration is carried out through three strong discontinuous flow cases with the exact solutions. Model verification is next described by three benchmark cases, including rainfall-runoff around buildings, flash floods towards buildings, and street junction flows. Model efficiency assessment is also conducted to present the numerical efficiency improvement of the proposed approach for various flow conditions. Technical attention is devoted to the numerical performances on local accuracy and global efficiency of the proposed approach. The simulated results indicate that the proposed approach can simulate as accurate as the HLLC scheme with significant reduction on its computational time. How efficient the proposed hybrid approach can reach depends on flow conditions involved. It is more efficient than the HLLC scheme as the portion of strong discontinuous flows in the computational domain is relatively smaller. The proposed approach has proved its accuracy and efficiency for overland flow modeling, and it can also be used together with other speed-up techniques, such as local time stepping and parallelization, to improve its efficiency. Other finite volume schemes can also be utilized to improve the efficiency and accuracy of the proposed approach. Therefore, the solver has considerable potentials as a useful tool in flood inundation simulations.