A simple finite volume method for the shallow water equations

Benkhaldoun, Fayssal; Seaı̈d, Mohammed

doi:10.1016/j.cam.2009.12.005

Cited by 48 publications

(39 citation statements)

References 17 publications

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“…A detailed analysis of convergence and stability has been presented in [8] for nonlinear scalar problems. Notice that this property is achieved by assuming a linear interpolation procedure in the predictor stage of the FVC method.…”

Section: Discretization Of the Source Termsmentioning

confidence: 99%

“…Note that several interpolation procedures can be applied in step 3. In the current study we have used a linear interpolation since for this type of interpolations the obtained solution remains monotone and the FVC method preserves the exact C-property at the machine precision, compare for example [8].…”

Section: Step 3 Compute the Approximationsmentioning

confidence: 99%

“…In the present work we propose a new finite volume method of characteristics (FVC) to solve the multi-layered shallow water equations. The method has been first introduced and analyzed in [8] for the standard single-layer shallow water equations. The proposed FVC method avoids the solution of Riemann problems and belongs to the predictor-corrector type methods.…”

Section: Introductionmentioning

confidence: 99%

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A fast finite volume solver for multi-layered shallow water flows with mass exchange

Audusse¹,

Benkhaldoun²,

Sari³

et al. 2014

Journal of Computational Physics

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(2014) 'A fast nite volume solver for multi-layered shallow water ows with mass exchange.', Journal of computational physics., 272 . pp. 23-45. Further information on publisher's website:http://dx.doi.org/10.1016/j.jcp.2014.04.026Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Journal of Computational Physics, 272, 2014Physics, 272, , 10.1016Physics, 272, /j.jcp.2014 Additional information: 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. AbstractA fast finite volume solver for hydrostatic multi-layered shallow water flows with mass exchange is investigated. In contrast to many models for multi-layered hydrostatic shallow water flows where the immiscible suppression is assumed, the present model allows for mass exchange between the layers. The multi-layered shallow water equations form a system of conservation laws with source terms for which the computation of the eigenvalues is not trivial. For most practical applications, complex eigenvalues may arise in the system and the multi-layered shallow water equations are not hyperbolic any more. This property makes the application of conventional finite volume methods difficult or even impossible for those methods which require in their formulation the explicit computation of the eigenvalues. In the current study, we propose a finite volume method that avoids the solution of Riemann problems. At each time step, the method consists of two stages to update the new solution. In the first stage, the multilayered shallow water equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed from the intermediate solutions in the first stage and used in the conservative form of the multi-layered shallow water equations. The proposed method is simple to implement, satisfies the conservation property and is suitable for multi-layered shallow water equations on non-flat topography. The proposed finite volume solver is verified against several benchmark tests and it shows good agreement with analytical solutions of the incompressible hydrostat...

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Section: Discretization Of the Source Termsmentioning

confidence: 99%

Section: Step 3 Compute the Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A fast finite volume solver for multi-layered shallow water flows with mass exchange

Audusse¹,

Benkhaldoun²,

Sari³

et al. 2014

Journal of Computational Physics

Self Cite

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show abstract

“…The internal cells are indicated by N 1, to N P. Based on Eq. 1 and applying both processes of line integration and integral averages of Φ , and lead us to the discrete conservative form of the conservation laws [13],…”

Section: Discrete Solution Based On the Godunov Schemementioning

confidence: 99%

Analysis of Wellbore Drilling Hydraulics Applying a Transient Godunov Scheme Considering Variations of Injected Flow Rates

Nicolás-López¹

2017

OGCE

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Abstract:A new application of the Godunov scheme to describe dynamic oil-well behavior is presented. The numerical model is able to capture discontinuities associated with surface flow-rate variations. The finite volume method and Riemann problems are utilized for building the unsteady discrete solution. Initial and boundary conditions are related to cases of static, steady and transient well condition. Well data used in simulation are taken from true operational conditions and well mechanical configuration. The results of Godunov's modeling describe the behavior of transient pressure and transient flow rate inside drill pipe and annulus. These profiles are commonly caused by turning on, adjusting mud flow rate and turning off the rig pumps. The evaluated rig indicators are: back pressure, pumping pressure, bottomhole pressure and injected flow rate. Calculated transient profiles are physically consistent and in good agreement with published well data. Therefore, engineering contribution is the application of first-order Godunov method to evaluate the transient hydraulics whereas variations of mud flow rate; also, the analysis and interpretation of the dynamic pressure behavior travelling inside the well. The Godunov scheme has robust engineering applications for modeling the transient drilling hydraulics, e.g., managed pressure drilling, hydraulics of pipe connections, and foam cementing, as well.

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“…This article deals with the development of a GPU implementation of a Finite Volume-Characteristics (FVC) method [1]. It is used to solve 2d multi-layered shallow water flows.…”

Section: Introductionmentioning

confidence: 99%

Gpu Implementation of Multi-Layered Shallow Water Model in Two Dimensions

Boubekeur¹,

Benkhaldoun²

2017

Topical Problems of Fluid Mechanics 2017

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This paper presents a new simulation method for a class of open channel flow problems. This method is used here for the resolution of multi-layered shallow water model in two dimensions. The numerical scheme is a hybrid finite volume-characteristics scheme (FVC). It is implemented on GPU. This method allows a faster resolution than on a CPU, and the FVC scheme is easily parallelizable. This implementation allows to show simulation results in real time, thanks to the absence of GPU and CPU communication. Numerical example, for comparisons, with simulations on CPU is presented to illustrate the interest of this approach.

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A simple finite volume method for the shallow water equations

Cited by 48 publications

References 17 publications

A fast finite volume solver for multi-layered shallow water flows with mass exchange

A fast finite volume solver for multi-layered shallow water flows with mass exchange

Analysis of Wellbore Drilling Hydraulics Applying a Transient Godunov Scheme Considering Variations of Injected Flow Rates

Gpu Implementation of Multi-Layered Shallow Water Model in Two Dimensions

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