Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Abstract

This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model’s results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

Keywords

• finite volume method
• slope source term treatment
• shallow water flows
• two-dimensional models
• well-balanced scheme