An improved technique for solving two-dimensional shallow water problems

Guillou, Sylvain; Nguyen, Kim Dan

doi:10.1002/(sici)1097-0363(19990228)29:4<465::aid-fld797>3.0.co;2-h

Cited by 21 publications

(14 citation statements)

References 23 publications

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“…Each numerical scheme has some kinds of advantage in 38 certain flow problems but may not perform satisfactorily in a different situation. As a result, 39 the combined or mixed solution schemes have been developed to deal with more complicated 40 issues, such as the FEM-based FVM, FVM-based FEM and hybrid FDM/FVM methods 41 (Guillou and Nguyen, 1999;Du, 2000;Casulli and Zanolli, 2002 The following 2-D shallow water equations (SWEs), sediment transport and bed deformation 71 equations are used for the water-sediment mixture flows as 72 Here it should be noted that the above water flow equations (1) -(2) are not influenced by 85 any sediment transport parameters in equation (3) -(4), and thus they are represented in the 86 uncoupled form, which is in contrast to those used by Cao et al (2011). This is based on the 87 rational that the suspended load is not the dominant sediment transport mode in the present 88 field case studies and the flow structure is not significantly modified by the existence of the 89 sediment mixture.…”

Section: Introduction 1mentioning

confidence: 99%

Water–sediment flow modeling for field case studies in Southwest China

2015

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The paper presents a highly robust numerical model to simulate water-sediment mixture flows in practical field studies. The model is composed of an integrated algorithm combining the finite element characteristic splitting method and finite volume Godunov scheme. The former maintains the generality and stability of the numerical algorithm while the latter ensures the conservation and accuracy of the model. The proposed model is first tested by three benchmark flow problems including flood flow in a pool, dam break over a mobile bed and morphological process of a dam removal. Then the model is applied to two practical field case studies to demonstrate its potential engineering values. The first case study is related to the damage of the Polo Hydropower Plant by a sediment flooding event. The second one is the investigation of a well-known 2013 dam break flooding that happened in the Tangjiashan Mountain. It is shown that the simulated water and sediment flows are in good agreement with the documented laboratory and field data and the numerical model is capable of providing useful information on the flow predictions thus making further engineering measures to mitigate these disasters.

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Section: Introduction 1mentioning

confidence: 99%

Water–sediment flow modeling for field case studies in Southwest China

2015

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“…In the second and the most important remark, we now need to discretize an elliptic equation with a general symmetric matrix K.x/ and not a harmonic averaging of an isotropic tensor (K.x/ D .x/I, where I is the identity matrix) as in (1). In this case, there is no direct way to calculate the numerical flux in terms of the cell-centered values.…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

“…D´C h H ; (2) where H D hCÁ is the total depth with h.x ; y / being the still depth and Á.x ; y ; t / the surface display; and´D OE h; Á is the vertical coordinate in the physical domain that has the origin´D 0 on the still level (see Figure 1). The Poisson equation (1) that is constructed in the Cartesian coordinate has to be modified in the transformed computational domain. Using the principle of chain differentiation, the partial differentiation of a variable in the physical domain is transformed as follows:…”

Section: Introductionmentioning

confidence: 99%

An unstructured finite volume technique for the 3D Poisson equation on arbitrary geometry using a σ‐coordinate system

Zapata

Bang

Nguyen

2014

Numerical Methods in Fluids

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SUMMARYWe present a solver for a three‐dimensional Poisson equation issued from the Navier–Stokes equations applied to model rivers, estuaries, and coastal flows. The three‐dimensional physical domain is composed of an arbitrary domain in the horizontal direction and is bounded by an irregular free surface and bottom in the vertical direction. The equations are transformed vertically to the σ‐coordinate system to obtain an accurate representation of top and bottom topographies. The method is based on a second‐order finite volume technique on prisms consisting of triangular grids in the horizontal direction. The algorithm is accompanied by an analysis of different linear system solvers in order to achieve fast solutions. Numerical experiments are conducted to test the numerical accuracy and the computational efficiency of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

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“…The free surface flow in a single lhranch of a river network can be described by the so-called Saint-Venant equations [1][2][3] under the assumption of a hydrostatic pressure and an uniform distribution of the velocity along the vertical axis.…”

Section: Equations For a Single River Bradchmentioning

confidence: 99%

“…The flow can be simulated by one-or two-dimensional mathematical models [1][2][3], depending on the study purpose. However, two-dimensional models are expensive for large river deltas.…”

Section: Introductionmentioning

confidence: 99%

On an one- and quasi-two dimensional linking hydraulic model for the complex river network-validation and application

2002

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ABSTRACT. This paper describes an approach to construct an one-and quasi-two dimensional hydraulic model for the complex river network, including various hydraulic structures. The model is based on the numerical solution of the Saint-Venant equations for river branches, the continuity equation for storages, the equation for junction conditions of the confluences, tributaries, the equation for hydraulic structures between rivers and storage cells. Cross sections are modeled as a combination of main and flood plain parts to simulate better the flow pattern. The calculating program has been ~eveloped, validated by test cases, proposed by European big hydraulic research laboratories and then applied to build a hydraulic model for the complicated Red-Thai Binh river network.

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An improved technique for solving two-dimensional shallow water problems

Cited by 21 publications

References 23 publications

Water–sediment flow modeling for field case studies in Southwest China

Water–sediment flow modeling for field case studies in Southwest China

An unstructured finite volume technique for the 3D Poisson equation on arbitrary geometry using a σ‐coordinate system

On an one- and quasi-two dimensional linking hydraulic model for the complex river network-validation and application

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