Hybrid flux-splitting finite-volume scheme for the shallow water flow simulations with source terms

The extension of the hybrid flux-splitting finite-volume (HFF) scheme to the shallow water equations with source terms is presented. Based on the monotonic upstream schemes for conservation laws (MUSCL) method, the scheme is second-order-accurate both in space and time. An accurate and efficient surface gradient method (SGM), in conjunction with the HFF scheme, is adopted for the discretization of source terms, including the bed slopes and friction slopes. The resulting scheme has several desirable properties: ease of implementation, satisfaction of entropy condition, sharp shock resolution and preservation of well-balancing. The HFF scheme with SGM is verified through the simulations of steady transcritical flow over a hump and steady flow over an irregular bed. Besides, the effects of the limiter functions, the grid sizes and the Manning roughness coefficients on the simulated results are investigated for the steady transcritical flow problems. Using the laboratory measurements, the scheme is also applied to the dam-break flows: with an adverse slope, with a triangular hump, and with a constriction. Furthermore, the HFF scheme is employed in the simulation of typhoon flood flow with natural-irregular river topography to demonstrate the practical engineering application. The results show good agreements compared with the exact solutions, the experimental data and the field measurements.