A preconditioner for linearized Navier-Stokes problem in exterior domains

Jennequin, Delphine

Document type :

Rapport de recherche: Autre communication scientifique (congrès sans actes - poster - séminaire...)

Title :

A preconditioner for linearized Navier-Stokes problem in exterior domains

Author(s) :

Jennequin, Delphine [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Institution :

INRIA

Publication date :

2006

English keyword(s) :

EXTERIOR DOMAINS
EXPONENTIAL MESH
SADDLE-POINT PROBLEMS
PRECONDITIONING
NAVIER-STOKES EQUATIONS

HAL domain(s) :

Informatique [cs]/Autre [cs.OH]

English abstract : [en]

We aim to approach the solution of the stationary incompressible Navier-Stokes equations in a three-dimensional exterior domain. Therefore, we cut the exterior domain by a sphere of radius $R$ and we impose some suitable ...
Show more >We aim to approach the solution of the stationary incompressible Navier-Stokes equations in a three-dimensional exterior domain. Therefore, we cut the exterior domain by a sphere of radius $R$ and we impose some suitable approximate boundary conditions (ABC) to the truncation boundary of the computational domain: the minimal requirement of these conditions is to ensure the solvability of the truncated system and the decay of the truncation error if $R$ grows. We associate to the truncated problem a mesh made of homothetic layers, called exponential mesh, such that the number of degrees of freedom only grows logarithmically with $R$ and such that the optimal error estimate holds. In order to reduce the storage, we are interested in discretizations by equal-order velocity-pressure finite elements with additional stabilization terms. Therefore, the linearisation inside a quasi-Newton or fixed-point method leads to a generalized saddle-npoint problem, that may be solved by a Krylov method applied on the preconditioned complete system matrix. We introduce a bloc-triangular preconditioner such that the decay rate of the Krylov method is independent of the mesh size $h$ and we give an estimate for this rate in function of the truncation radius and of the Reynolds number. Some three-dimensional numerical results well confirm the theory and show the robustness of our method.Show less >

Language :

Anglais

Comment :

Projet SIMPAF

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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