Multilevel finite-difference model for three-dimensional hydrodynamic circulation

Shankar, N. Jothi; Cheong, Hin‐Fatt; Sankaranarayanan, S.

doi:10.1016/s0029-8018(96)00036-4

Cited by 28 publications

(28 citation statements)

References 6 publications

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“…We first examine the conservation property of the FVC scheme and then we compare the obtained results for a dambreak problem to those obtained using the three-dimensional Navier-Stokes equations. We also solve a class of wind-driven circulation problems in closed water channels and the obtained velocity profiles are compared to those analytically calculated [27]. The FVC results are also compared to numerical results obtained using the kinetic scheme developed in [7] to solve the multi-layer shallow water equations.…”

Section: Numerical Results and Examplesmentioning

confidence: 99%

“…with n b being the Manning roughness coefficient at the bed, w is the wind velocity at 10 m above the water surface and C w is the wind friction coefficient defined as [27] …”

Section: Multi-layered Shallow Water Equationsmentioning

confidence: 99%

“…Note that other interpolation procedures such as Spline or Hermite interpolation methods or interpolation techniques based on radial basis functions can also be applied in (27). It is worth mentioning that the proposed finite volume method is fully conservative by construction and the non-conservative system (15) is used only to compute the intermediate states for the numerical fluxes in (11).…”

Section: −Humentioning

confidence: 99%

“…Our final test example is a class of wind-driven circulation flows proposed in [27]. This type of test examples has widely served as a prototype to verify the performance of multi-layer shallow water flows, see for example [7,29].…”

Section: Wind-driven Circulation Flowmentioning

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: Numerical Results and Examplesmentioning

confidence: 99%

“…with n b being the Manning roughness coefficient at the bed, w is the wind velocity at 10 m above the water surface and C w is the wind friction coefficient defined as [27] …”

Section: Multi-layered Shallow Water Equationsmentioning

confidence: 99%

Section: −Humentioning

confidence: 99%

Section: Wind-driven Circulation Flowmentioning

confidence: 99%

See 2 more Smart Citations

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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“…1 and that of the bottom by z=-h(x, y). The values of z, U, V and W are to be obtained from a hydrodynamic model such as that of Shankar et al (1996) [7] . ¦ Ζ…”

Section: Governing Equationsmentioning

confidence: 99%

A Higher Order Upwind Scheme for Three-Dimensional Finite Difference Model of Conservative Pollutants Transport

Liu

Gao

2010

2010 Asia-Pacific Power and Energy Engineering Conference

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Abstract-A three-dimensional finite difference transport model appropriate for the coastal environment is developed for the solution of the three-dimensional convection-diffusion equation. A higher order upwind scheme is used for the convective terms of the convection-diffusion equation, to minimize the numerical diffusion. The validity of the numerical model is verified through a test problem, whose exact solutions are known.Keywords-convection-diffusion equation; a higher order upwind scheme; finite difference method I. INTRODUCTION Mathematical modeling of the transport of salinity, pollutants and suspended matter in shallow waters involves the numerical solution of convection-diffusion equation. Numerical studies show that the use of central differencing for the convective terms of the convection-diffusion equation results in negative species concentration. Lam (1975) [1] points out that the central difference approximation will overestimate the advective flux so much that it often causes a negative concentration to appear in the neighbouring cell. To circumvent such a shortcoming of central differencing, the upwind or donor cell method introduced by Gentry et al. (1966) [2] is generally used. To overcome the shortcomings of numerical dispersion, Leonard (1979) [3] introduced an upstream interpolation method, namely QUICK (Quadratic Upstream Interpolation Convective Kinematics) for one-dimensional unsteady flow. Later, Leonard (1988) [4] gave an improved version of the QUICK scheme, eliminating the wiggles completely by introducing exponential integration into regions with sharp fronts. Chen and Falconer (1994) [5] showed that the QUICK scheme is only second-order accurate in space and presented different forms of the third-order convection, second-order diffusion for the solution of the convection-diffusion equation. In the present study, super-upwinding difference scheme as given in Barrett, K., S(1982) [6] has been used for the convection terms of the convection-diffusion equation.

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Development of a cascaded lattice Boltzmann model for two‐layer shallow water flows

Di Francesco,

Venturi,

Padrone

et al. 2024

Numerical Methods in Fluids

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SummaryMany environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multi‐layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi‐layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi‐layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two‐layered liquid Lattice‐Boltzmann model (CaLB‐2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.

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Multilevel finite-difference model for three-dimensional hydrodynamic circulation

Cited by 28 publications

References 6 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

A Higher Order Upwind Scheme for Three-Dimensional Finite Difference Model of Conservative Pollutants Transport

Development of a cascaded lattice Boltzmann model for two‐layer shallow water flows

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