Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

Paillère, H.; Quéré, Patrick Le; Weisman, Catherine; Vierendeels, Jan; Dick, Erik; Braack, Malte; Dabbene, F.; Beccantini, A.; Studer, Etienne; Kloczko, Thibaud; Corre, Christophe Eric; Heuveline, Vincent; Darbandi, Masoud; Hosseinizadeh, S.F.

doi:10.1051/m2an:2005025

Cited by 48 publications

(46 citation statements)

References 5 publications

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“…As shown in Table 2, our results are in excellent agreement with benchmark solutions [19]. Relative differences less than 0.005% are anew exhibited in bold.…”

Section: Rayleigh Number Ra = 10supporting

confidence: 79%

“…In Table 1 are indicated the relative errors, with respect to solutions obtained with our scheme with a 304 × 304 rectangular grid, for the results computed on Delaunay triangles and drawn from [19]. Relative differences of benchmark solutions being smaller than 1%, our reference result is in good agreement with the literature.…”

Section: Rayleigh Number 10supporting

confidence: 75%

“…We consider the problem handled in the benchmark [19], stated in the above dimensionless form, which concerns the natural convection flow in a differentially heated square cavity. The vertical walls are isothermal at the uniform temperatures T (0, y) = T h = 1/2 and T (1, y) = T c = −1/2 with 0 ≤ y ≤ 1, and the bottom and top boundaries are adiabatic.…”

Section: Benchmark Comparisonsmentioning

confidence: 99%

“…As in [19], we use the Sutherland law (Eq. 20) for the viscosity and assume µ(T )/k(T ) constant, which leads to a similar law for the thermal conductivity.…”

Section: Benchmark Comparisonsmentioning

confidence: 99%

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Simulation of natural convection with the collocated clustered finite volume scheme

Touazi¹,

Chénier²,

Eymard³

2008

Computers & Fluids

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To cite this version:O. Touazi, Eric Chénier, Robert Eymard. Simulation of natural convection with the Collocated Clustered Finite Volume scheme. Computers and Fluids, Elsevier, 2008, 37 (9) Then we present the finite volume scheme with the principles and the spatial discretization used. Analytical tests illustrate the numerical behavior of this scheme according to the type of grid, of the pressure stabilization method and check the robustness of this scheme. Next, the results obtained on the square thermally driven cavity under large temperature differences show that the CCFV scheme accurately fits the reference results.

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“…As shown in Table 2, our results are in excellent agreement with benchmark solutions [19]. Relative differences less than 0.005% are anew exhibited in bold.…”

Section: Rayleigh Number Ra = 10supporting

confidence: 79%

Section: Rayleigh Number 10supporting

confidence: 75%

Section: Benchmark Comparisonsmentioning

confidence: 99%

“…As in [19], we use the Sutherland law (Eq. 20) for the viscosity and assume µ(T )/k(T ) constant, which leads to a similar law for the thermal conductivity.…”

Section: Benchmark Comparisonsmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of natural convection with the collocated clustered finite volume scheme

Touazi¹,

Chénier²,

Eymard³

2008

Computers & Fluids

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“…A test case was designed, extending the well-known de Vahl Davis benchmark problem [5] to cases with large temperature differences. In January 2000, CEA and LIMSI organized a first international benchmark [11] dealing with this test case, with the objective of establishing reference (i.e. grid and model independent) solutions from a code-to-code comparison of various flow models and solvers.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

et al. 2005

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Abstract. There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 10 6 (constant property and variable property cases) and Ra = 10 7 (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established.Mathematics Subject Classification. 65M50, 76M10, 76M12, 76M20, 76M22, 76R10.

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Low‐cost implicit schemes for all‐speed flows on unstructured meshes

Kloczko

Corre

Beccantini

2008

Numerical Methods in Fluids

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SUMMARYMatrix-free implicit treatments are now commonly used for computing compressible flow problems: a reduced cost per iteration and low-memory requirements are their most attractive features. This paper explains how it is possible to preserve these features for all-speed flows, in spite of the use of a lowMach preconditioning matrix. The proposed approach exploits a particular property of a widely used low-Mach preconditioner proposed by Turkel. Its efficiency is demonstrated on some steady and unsteady applications.

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Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

Cited by 48 publications

References 5 publications

Simulation of natural convection with the collocated clustered finite volume scheme

Simulation of natural convection with the collocated clustered finite volume scheme

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

Low‐cost implicit schemes for all‐speed flows on unstructured meshes

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