A numerical model for the flooding and drying of irregular domains

TLDR

The study focuses on unsteady flow problems in complex geometries. The paper presents a numerical technique for modelling shallow water flow in one and two dimensions applied to unsteady flows in complex geometries. The method uses a cell‑centred finite volume scheme with Roe’s Riemann solver, upwind bed‑slope discretization, and a special front‑tracking procedure to handle adverse dry beds in complex domains. The modification accurately reproduces still‑water steady states on steep bed variations, and numerical results agree with experiments in the presented tests. © 2002 John Wiley & Sons, Ltd.

Abstract

Abstract A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell‐centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd.