A discontinuous Galerkin finite element model for river bed evolution under shallow flows

Tassi, Pablo; Rhebergen, Sander; Vionnet, Carlos A.; Bokhove, Onno

doi:10.1016/j.cma.2008.01.023

Cited by 41 publications

(30 citation statements)

References 13 publications

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“…These authors propose a new WENO reconstruction technique that can be easily evaluated and differentiated at any point. In [34] a discontinuous Galerkin finite element for river bed evolution has also been presented. In this work, we present a new second order reconstruction operator for unstructured meshes of MUSCL type (see [1]).…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

́az

Fernández-Nieto

Ferreiro

et al. 2009

Computer Methods in Applied Mechanics and Engineering

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In this paper we study the numerical approximation of bedload sediment transport due to shallow layer flows. The hydrodynamical component is modeled by a 2D shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can be written as a nonconservative hyperbolic system. To discretize it, first we consider a Roe-type first order scheme as well as a variant based on the use of flux limiters. These first order schemes are then extended to second order accuracy by means of a new MUSCL-type reconstruction operator on unstructured meshes. Finally, some numerical tests are presented.Short title : Second order discretization of 2D sediment transport models.

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Section: Introductionmentioning

confidence: 99%

Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

́az

Fernández-Nieto

Ferreiro

et al. 2009

Computer Methods in Applied Mechanics and Engineering

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“…As in Kubatko et al [44], we observe that the bed experiences erosion in the converging part of the channel due to an increase in the flow velocity and the development of a mound in the diverging part of the channel. The results compare qualitatively well with those presented [44] and are the same as we obtained using space DGFEM in Tassi et al [73]. 3.3 Effect of the path in phase space on the numerical solution…”

Section: River Bed Evolution Under Shallow Flowssupporting

confidence: 80%

“…The mesh considered is given in Figure 3.12. In Tassi et al [73] we show results of this test case using space DGFEM and here we use space-time DGFEM. The physical time step is ∆t = 0.0001.…”

Section: River Bed Evolution Under Shallow Flowsmentioning

confidence: 99%

“…[72,73]). For one dimensional numerical examples solving (3.26) including convergence rates with space and space-time DGFEM we refer to Tassi et al [73].…”

Section: River Bed Evolution Under Shallow Flowsmentioning

confidence: 99%

“…Test case 11: hydraulic and sediment transport through a contraction Consider the non-dimensional form of the shallow water equations and the bed evolution equation (for details see Tassi et al [72,73]):…”

Section: River Bed Evolution Under Shallow Flowsmentioning

confidence: 99%

See 2 more Smart Citations

Discontinuous Galerkin finite element methods for (non)conservative partial differential equations

Rhebergen¹

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A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

Benkhaldoun

Sahmim

Seaı̈d

2010

Numerical Methods in Fluids

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SUMMARYWe discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.

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A discontinuous Galerkin finite element model for river bed evolution under shallow flows

Cited by 41 publications

References 13 publications

Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

Discontinuous Galerkin finite element methods for (non)conservative partial differential equations

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

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