A non-homogeneous Riemann solver for shallow water equations in porous media

Sanders

Schubert

2017

137

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

Section: Introductionmentioning

confidence: 99%

Dual integral porosity shallow water model for urban flood modelling

Sanders

Schubert

2017

137

“…In the Single Porosity (SP) approach, a single porosity is used to account for both the storage and the connectivity properties of the subgrid-scale geometry. While early developments [1,13] used a depth-dependent SP eld, most of the developments and applications of the SP approach presented to date have focused on depth-independent SP versions of the shallow water equations [2,8,15,17,21,25,38,42,47]. This restriction of the original approach is easily justied by the fact that these models were developed for urban ood modelling purposes, where the buildings are assumed not to be submerged by the ood in practice.…”

Section: Introductionmentioning

confidence: 99%

Flux closures and source term models for shallow water models with depth-dependent integral porosity

Delenne

Rousseau

et al. 2018

A two-dimensional shallow water model with depth-dependent porosity is presented. The purpose is the coarse grid simulation of shallow ows over complex topographies and geometries. Two ux closures are examined: the Integral Porosity (IP) and Dual Integral Porosity (DIP) closures. Energy losses are described using a subgrid scale model that accounts for bottom and wall friction, transient momentum dissipation and energy losses induced by obstacle submersion. A complete wave propagation property analysis is provided for the IP and DIP closures, yielding more accurate numerical stability constraints than published previously. Five computational examples are presented, including transients in compound and meandering channels, urban dambreak problems with building submersion and runo over variable microtopography. The ability of the model to deal with subgrid-scale features is conrmed. The DIP ux is shown to be superior to the IP closure. The transient dissipation term is essential in reproducing the eect of obstacles and microtopography. Distinguishing between the building wall-and building roof-induced friction is seen to be essential. The model is validated successfully against a scale model experimental dataset for the submersion of a coastal urban area by a tsunami wave.

“…Originally, these models incorporated only one type of porosity and were formulated in dierential form [5,11,13]. Most developments so far have focused on this isotropic, Single Porosity (SP) version [1,2,6,21]. The methods proposed to address the anisotropy of the urban medium use several types of porosity instead of a single one.…”

Section: Introductionmentioning

confidence: 99%

Consistency and bicharacteristic analysis of integral porosity shallow water models. Explaining model oversensitivity to mesh design

2017

International audienceThe Integral Porosity and Dual Integral Porosity two-dimensional shallow water models have been proposed recently as ecient upscaled models for urban oods. Very little is known so far about their consistency and wave propagation properties. Simple numerical experiments show that both models are unusually sensitive to the computational grid. In the present paper, a two-dimensional consistency and characteristic analysis is carried out for these two models. The following results are obtained: (i) the models are almost insensitive to grid design when the porosity is isotropic, (ii) anisotropic porosity elds induce an articial polarization of the mass/momentum uxes along preferential directions when triangular meshes are used and (iii) extra rst-order derivatives appear in the governing equations when regular, quadran-gular cells are used. The hyperbolic system is thus mesh-dependent, and with it the wave propagation properties of the model solutions. Criteria are derived to make the solution less mesh-dependent, but it is not certain that these criteria can be satised at all computational points when real-world situations are dealt with