Dual integral porosity shallow water model for urban flood modelling

Abstract

International audienceWith CPU times 2 to 3 orders of magnitude smaller than classical shallow water-based models , the shallow water equations with porosity are a promising tool for large-scale modelling of urban floods. In this paper, a new model formulation called the Dual Integral Porosity (DIP) model is presented and examined analytically and computationally with a series of benchmark tests. The DIP model is established from an integral mass and momentum balance whereby both porosity and flow variables are defined separately for control volumes and boundaries, and a closure scheme is introduced to link control volume-and boundary-based flow variables. Previously developed Integral Porosity (IP) models were limited to a single set of flow variables. A new transient momentum dissipation model is also introduced to account for the effects of sub-grid scale wave action on porosity model solutions, effects which are validated by fine-grid solutions of the classical shallow-water equations and shown to be important for achieving self-similarity in dam-break solutions. One-dimensional numerical test cases show that the proposed DIP model outperforms the IP model, with signicantly improved wave propagation speeds, water depths and discharge calculations. A two-dimensional field scale test case shows that the DIP model performs better than the IP model in mapping the floods extent and is slightly better in reproducing the anisotropy of the flow field when momentum dissipation parameters are calibrated

Evaluating the Effects of Low Impact Development Practices on Urban Flooding under Different Rainfall Intensities

“…A large number of studies have shown that the selected indices are positively related to flood evaluation. Therefore, all indices are used in Equation (2) to normalize x ij to X ij .…”

“…Along with significant changes in global climate and the considerably increasing disturbance caused by human activities, flood disasters in urban areas have become more serious, substantially restricting social and economic development and posing a threat to the safety of human lives and properties [1,2]. In recent years, urban flooding has caused many casualties and property losses in Japan, Singapore, The Netherlands, Britain and other countries [3][4][5][6].…”

A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations

“…In [14], the concept of closure is introduced. It stems from the consideration that the dual nature of the porosity (storage vs. porosity) should result in a dual denition of the ow variables (domain-based vs. boundary-based).…”

“…The IP model can be obtained as a particular case of the DIP formalism, by assuming a very specic closure. The IP closure yields inaccurate mass and momentum uxes [14]. Correcting this with the DIP closure and introducing a transient momentum dissipation model derived from [11] results in substantially improved model performance.…”

“…The Dual Integral Porosity (DIP) model [14] is a generalization of the IP model. In [14], the concept of closure is introduced.…”