DEVELOPPEMENT DE METHODES DE VOLUMES FINIS POUR LA MECANIQUE DES FLUIDES

Sarah Delcourte 1
1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tesselations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriored. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle--point problem at each iteration. We give a particular interest to this linear problem by testing some preconditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes.
Document type :
Theses
Complete list of metadatas

Cited literature [103 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00200833
Contributor : Sarah Delcourte <>
Submitted on : Friday, December 21, 2007 - 3:34:57 PM
Last modification on : Thursday, May 3, 2018 - 1:32:55 PM
Long-term archiving on : Thursday, September 27, 2012 - 1:20:10 PM

Identifiers

  • HAL Id : tel-00200833, version 1

Collections

Citation

Sarah Delcourte. DEVELOPPEMENT DE METHODES DE VOLUMES FINIS POUR LA MECANIQUE DES FLUIDES. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2007. Français. ⟨tel-00200833⟩

Share

Metrics

Record views

1081

Files downloads

4952