High-resolution TVD schemes in finite volume method for hydraulic shock wave modeling

Abstract

High-resolution total variation diminishing (TVD) schemes in the framework of the finite volume method are presented and evaluated for hydraulic shock wave modeling. Three approximate Riemann solvers, namely the FVS, Roe and Osher schemes, are extended to high-resolution TVD schemes based on the direct MUSCL-Hancock (DMH) slope limiter approach. The TVD schemes are then used to develop numerical models to compute water depth and velocity. The numerical models developed are then verified through simulations of the dam-break flows, the oblique hydraulic jump, and the shock-on-shock interaction. The numerical models with TVD schemes are capable of capturing discontinuous shock waves without any spurious oscillation. A comparison of numerical efficiency shows that the Osher-DMH scheme coupled with van Leer limiter performs the best among the proposed TVD schemes. Applications of the Osher-DMH scheme to flows of partial dam-break experiments have shown that the simulated water depths agree well with the measured data.