Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids

作者：Vincent Guinot, Sandra Soares Frazão · 发表于：International Journal for Numerical Methods in Fluids · 年份：2005 · DOI：10.1002/fld.1059 · 被引用次数：134 · 研究领域：Flood Risk Assessment and Management、Computational Fluid Dynamics and Aerodynamics、Meteorological Phenomena and Simulations

Two-dimensional shallow water models with porosity appear as an interesting path for the large-scale modelling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. This paper presents a discretization of the modified fluxes using a modified HLL Riemann solver on unstructured grids. The source term arising from the gradients in the topography and in the porosity is treated in an upwind fashion so as to enhance the stability of the solution. The Riemann solver is tested against new analytical solutions with variable porosity. A new formulation is proposed for the macroscopic head loss in urban areas. An application example is presented, where the large scale model with porosity is compared to a refined flow model containing obstacles that represent a schematic urban area. The quality of the results illustrates the potential usefulness of porosity-based shallow water models for large scale floodplain simulations. Copyright © 2005 John Wiley & Sons, Ltd.