Finite volume method in curvilinear coordinates for hyperbolic conservation laws

Guillard, Hervé; Bonnement, Audrey; Marie, Martin; Fajraoui, T.; Mouton, Alexandre; Nkonga, Boniface; Sangam, Afeintou

doi:10.1051/proc/2011019

Cited by 3 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the sequel, we will designate this method as the projection-discretization method. This approach has one important shortcoming : because the basis vectors are spatially dependent, they do not commute with the differential operators and therefore source terms appear in the equations [1,5]. The expression of these source terms depends on the specific curvilinear system used and their approximation is not obvious if some properties as for instance angular momentum conservation are required.…”

Section: The Discretization-projection Methodsmentioning

confidence: 99%

“…Let us also consider a curvilinear transformation φ : ξ → x, whose determinant of Jacobian is J. It is possible to show [1], that in this coordinate system, the above equation becomes:…”

Section: The Discretization-projection Methodsmentioning

confidence: 99%

“…This auxiliary system is coincident with the curvilinear reference system in center of mass of the cell. The second step is to consider the integral formulation of (1), that is :…”

Section: The Discretization-projection Methodsmentioning

confidence: 99%

See 2 more Smart Citations

A 3D finite volume scheme for the simulation of edge plasma in Tokamaks

Bilanceri¹,

Combe²,

Guillard³

et al. 2013

ESAIM: Proc.

Self Cite

View full text Add to dashboard Cite

Résumé. Une méthode de volumes finis en coordonnées cylindriques pour la simulation de la région du bord dans les tokamaks est proposé. Contrairement aux méthodes classiques, qui sont basés sur la projection deséquations en coordonnées curvilignes, une nouvelle méthode est proposée ici. Cette technique est basée sur la discrétisation de la forme vectorielle deséquations et ensuite sur la projection sur les vecteurs de base du systéme curviligne associéà chaque volume de contrôle. La Méthodologie proposée aété validée sur plusieurs cas-tests simples et appliqué sur une simulation 3D d'un modèle MHD réduit.Abstract. A finite volume method in cylindrical coordinates for the simulation of the edge region in tokamaks is proposed. In contrast to standard methods, which require the projected form of the equations in curvilinear coordinates, a new method is proposed. This technique is based on the discretization on the vector form of the equations and then on the projection on the basis of the curvilinear system associated to each control volume. The proposed methodology has been validated on several simple test cases and applied on a 3D simulation of a reduced MHD model.

show abstract

Section: The Discretization-projection Methodsmentioning

confidence: 99%

Section: The Discretization-projection Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A 3D finite volume scheme for the simulation of edge plasma in Tokamaks

Bilanceri¹,

Combe²,

Guillard³

et al. 2013

ESAIM: Proc.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Put simply in other words, the strong conservative form of equations of the model can be destroyed, introducing artificial source terms if cautions are not considered when manipulating vectorial equations in curvilinear coordinates. The scheme we proposed is based on recent works reported in [9,8] where it is shown that the strong conservative form of the model can be kept whatever the system of curvilinear coordinates used. More precisely, the finite volume scheme designed in this paper is an application of the method described in [9,8] to the two-temperature Euler model in cylindrical coordinates for toroidal problems.…”

Section: Introductionmentioning

confidence: 99%

“…The scheme we proposed is based on recent works reported in [9,8] where it is shown that the strong conservative form of the model can be kept whatever the system of curvilinear coordinates used. More precisely, the finite volume scheme designed in this paper is an application of the method described in [9,8] to the two-temperature Euler model in cylindrical coordinates for toroidal problems. However, such as application is not straightforward due to both the complexity of the two-temperature Euler model and the unstructured tessellation used to adequately mesh the toroidal geometry of the tokamak.…”

Section: Introductionmentioning

confidence: 99%