A New Well-Balanced Reconstruction Technique for the Numerical Simulation of Shallow Water Flows with Wet/Dry Fronts and Complex Topography

Abstract

This study develops a new well-balanced scheme for the one-dimensional shallow water system over irregular bed topographies with wet/dry fronts, in a Godunov-type finite volume framework. A new reconstruction technique that includes flooded cells and partially flooded cells and preserves the non-negative values of water depth is proposed. For the wet cell, a modified revised surface gradient method is presented assuming that the bed topography is irregular in the cell. For the case that the cell is partially flooded, this paper proposes a special reconstruction of flow variables that assumes that the bottom function is linear in the cell. The Harten⁻Lax⁻van Leer approximate Riemann solver is applied to evaluate the flux at cell faces. The numerical results show good agreement with analytical solutions to a set of test cases and experimental results.

Keywords

• finite volume method
• shallow water flow
• well-balanced scheme
• reconstruction technique
• flooded and partially flooded cells