An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

Finaud-Guyot, Pascal; Delenne, Carole; Lhomme, Julien; Guinot, Vincent; Llovel, Cécile

doi:10.1002/fld.2066

Cited by 35 publications

(33 citation statements)

References 34 publications

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“…For shallow ows over natural topographies, the porosity is depth-dependent [1,5,6,39], while urban ood applications consider a depth-independent porosity [15,16,37,38]. A number of numerical solution techniques have been developed for the depthindependent SP equations [2,4,8,15,26]. Recently, a generalized source term has been proposed for the specic purposes of urban ood modelling [38].…”

Section: Introductionmentioning

confidence: 99%

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

Guinot

2017

Advances in Water Resources

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To cite this version:Vincent Guinot. A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations. Advances in Water Resources, Elsevier, 2017, 109, pp.133-157 AbstractThe validity of ux and source term formulae used in shallow water models with porosity for urban ood simulations is assessed by solving the two-dimensional shallow water equations over computational domains representing periodic building layouts. The models under assessment are the Single Porosity (SP), the Integral Porosity (IP) and the Dual Integral Porosity (DIP) models. 9 dierent geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are dened. This results in a set of 96 ne grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP ux and source term models outperform those of the SP and IP models when the Riemann problem is aligned with the main street directions, (ii) all models give erroneous ux closures when is the Riemann problem is not aligned with one of the main street directions or when the main street directions are not orthogonal, (iii) the solution of the Riemann problem is self-similar in space-time when the street directions are orthogonal and the Riemann problem is aligned with one of them, (iv) a momentum balance conrms the existence of the transient momentum dissipation model presented in the DIP model, (v) none of the source term models presented so far in the literature allows all ow congurations to be accounted for(vi) future laboratory experiments aiming at the validation of ux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and ow velocity elds.

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Section: Introductionmentioning

confidence: 99%

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

Guinot

2017

Advances in Water Resources

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“…Attempts to tackle the issue in a more theoretical way have also been made by many other researchers, e.g. Rogers et al 26, Lhomme andGuinot 27, Liang and Borthwick 28, Lee and Wright 29 and Finaud‐Guyot et al 30. Nonetheless, this review is far from complete due to the extensive research involved in this topic (useful reviews may be found in 2, 31, 32).…”

Section: Introductionmentioning

confidence: 96%

A conservative high‐order discontinuous Galerkin method for the shallow water equations with arbitrary topography

Kesserwani

Liang

2010

Numerical Meth Engineering

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SUMMARYA conservative high-order Godunov-type scheme is presented for solving the balance laws of the 1D shallow water equations (SWE). The scheme adopts a finite element Runge-Kutta (RK) discontinuous Galerkin (DG) framework. Based on an overall third-order accurate formulation, the model is referred to as RKDG3. Treatment of topographic source term is built in the DG approximation. Simplified formulae for initializing bed data at a discrete level are derived by assuming a local linear bed function to ease practical flow simulations. Owing to the adverse effects caused by using an uncontrolled global limiting process in an RKDG3 scheme (RKDG3-GL), a new conservative RKDG3 scheme with user-parameter-free local limiting method (RKDG3-LL) is designed to gain better accuracy and conservativeness. The advantages of the new RKDG3-LL model are demonstrated by applying to several steady and transient benchmark flow tests with irregular (either differentiable or non-differentiable) topography.

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“…Once the matrices R(U) and R −1 (U) are calculated the sign matrix can be easily updated according to (9).…”

Section: Determination Of the Sign Matrixmentioning

confidence: 99%

“…Similar free-surface flow models have been developed in [10,19] and the references therein. Applications of shallow water flows with porosity have also been studied in [7,9,11,13,14,22,23] among others. The governing equations form a two-dimensional nonlinear system of hyperbolic conservation laws with source terms.…”

Section: Introductionmentioning

confidence: 99%

“…However, for practical applications, this method may become computationally demanding due to its treatment of the source terms. Numerical methods based on approximate-state Riemann solvers have also been applied to shallow water equations with porosity in [9,11]. Unfortunately, most HLLC solvers that solves real models correctly are still very computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

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

Benkhaldoun

Elmahi

Moumna

et al. 2015

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. The purpose of the current research is to develop an accurate and efficient solver for shallow water flows in porous media. The hydraulics is modeled by the two-dimensional shallow water flows with variable horizontal porosity. The variation of porosity in the water flows can be attributed to the variation of bed properties of the water system. As an example of porous shallow water flows is the passage of water discharge over vegetated areas in a river. Driving force of the phase separation and the mixing is the gradient of the porosity. For the numerical solution procedure we propose a non-homogeneous Riemann solver in the finite volume framework. The proposed method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. The efficiency of the solver is evaluated by several test problems for shallow water flows in porous media. The numerical results demonstrate high resolution of the proposed non-homogeneous Riemann solver and confirm its capability to provide accurate simulations for porous shallow water equations under flow regimes with strong shocks.

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An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

Cited by 35 publications

References 34 publications

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

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

A conservative high‐order discontinuous Galerkin method for the shallow water equations with arbitrary topography

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

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