A new finite volume discretization scheme to solve 3D incompressible thermal flows on unstructured meshes

Perron, Sébastien; Boivin, Sylvain; Hérard, Jean-Marc

doi:10.1016/j.ijthermalsci.2003.12.002

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…Various FV discretisation techniques have been developed for unstructured meshes including, edge-based schemes that employ dual control volumes and edge-based data structures, [2,[21][22][23] as well as others [24][25][26] who use cell-based gradient reconstruction, Jameson et al [27] who used cell vertex techniques, Chakrabartty [28] who employed a vertex-centred scheme for flow past complex geometries and Boivin et al [29,30] who stored solved variables at the cell-circumcenters to enable solutions on unstructured meshes. Any discretisation technique that employs the standard linear central differencing scheme can encounter difficulties when approximating the control volume face derivative on a non-orthogonal grid.…”

Section: Introductionmentioning

confidence: 99%

A coupled finite volume method for the computational modelling of mould filling in very complex geometries

McBride¹,

Croft²,

Cross³

2008

Computers & Fluids

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Section: Introductionmentioning

confidence: 99%

A coupled finite volume method for the computational modelling of mould filling in very complex geometries

McBride¹,

Croft²,

Cross³

2008

Computers & Fluids

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“…However, the method is not robust on an unstructured non-orthogonal mesh and computation of the fluxes is problematic on a non-orthogonal grid. Various discretisation techniques have been developed for unstructured meshes including, edge-based schemes that employ dual control volumes and edge-based data structures (Barth, 1992;Lyra et al, 1994;Crumpton and Giles, 1995;Sorensen et al, 1999) as well as others (Coirier, 1994;Mavriplis, 1995;Haselbacher and Blasek, 2000) who use cell based gradient reconstruction (Jameson et al, 1986) who used cell vertex techniques (Chakrabartty, 1990) who employed a vertex-centred scheme for flow past complex geometries (Boivin et al, 2000;Perron et al, 2004) and who stored solved variables at the cell-circumcenters to enable solutions on unstructured meshes.…”

Section: Introductionmentioning

confidence: 99%

Finite volume method for the solution of flow on distorted meshes

McBride

Croft

Cross

2007

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -To improve flow solutions on meshes with cells/elements which are distorted/ non-orthogonal. Design/methodology/approach -The cell-centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non-orthogonal shapes, as can occur when modelling very complex geometries. A co-located vertex-based (VB) discretisation and partially staggered, VB/cell-centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes. Findings -The co-located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co-located VB simulation results always converge whilst its accuracy appears to grace-fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co-located vertex based method and are as expensive computationally; thus, offering no obvious advantage. Research limitations/implications -Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail Originality/value -This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non-orthogonal cells/elements.

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A coupled finite volume method for the solution of flow processes on complex geometries

McBride

Croft

Cross

2006

Numerical Methods in Fluids

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SUMMARYCFD modelling of 'real-life' thermo-fluid processes often requires solutions in complex three-dimensional geometries, which can result in meshes containing aspects that are badly distorted. Cell-centred finite volume methods (CC-FV), typical of most commercial CFD tools, are computationally efficient, but can lead to convergence problems on meshes that feature cells with highly non-orthogonal shapes. The control volume-finite element method (CVFE) uses a vertex-based approach and handles distorted meshes with relative ease, but is computationally expensive. A combined vertex-based-cell-centre technique (CFVM), detailed in this paper, allows solutions on distorted meshes where purely cell-centred solutions procedures fail. The method utilizes the ability of the vertex-based approach to resolve the flow field on a distorted mesh, enabling well established cell-centred physical models to be employed in the solution of other transported quantities. The vertex-based flow code is verified against a manufactured 3D solution and error norms are compared on meshes with various degrees of distortion. The CFVM method is validated with benchmark solutions for thermally driven flow and turbulent flow. Finally, the method is illustrated on three-dimensional turbulent flow over an aircraft wing on a distorted mesh where purely cell-centred techniques fail. The CFVM is relatively straightforward to embed within generic CC based CFD tools allowing it to be employed in a wide variety of processing applications.

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A new finite volume discretization scheme to solve 3D incompressible thermal flows on unstructured meshes

Cited by 6 publications

References 18 publications

A coupled finite volume method for the computational modelling of mould filling in very complex geometries

A coupled finite volume method for the computational modelling of mould filling in very complex geometries

Finite volume method for the solution of flow on distorted meshes

A coupled finite volume method for the solution of flow processes on complex geometries

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