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Comptes Rendus de l Académie des Sciences - Series I - Mathematics 348, 11-12 (2010) 697-702

A fictitious domain model for the Stokes/Brinkman problem with jump embedded boundary conditions

Philippe Angot 1

(09/06/2010)

We present and analyse a new fictitious domain model for the Brinkman or Stokes/Brinkman problems in order to handle general jump embedded boundary conditions (J.E.B.C.) on an immersed interface. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\S$ separating two subdomains: they are well chosen to get the coercivity of the operator. It is issued from a generalization to vector elliptic problems of a previous model stated for scalar problems with jump boundary conditions (Angot (2003, 2005) \cite{Ang03,Ang05}). The proposed model is first proved to be well-posed in the whole fictitious domain and some sub-models are identified. A family of fictitious domain methods can be then derived within the same unified formulation which provides various interface or boundary conditions, e.g. a given stress of Neumann or Fourier type or a velocity Dirichlet condition. In particular, we prove the consistency of the given-traction E.B.C. method including the so-called {\em do nothing} outflow boundary condition.

1 :	Laboratoire d'Analyse, Topologie, Probabilités (LATP)
	CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III

Domaine

:

Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse numérique Sciences de l'ingénieur/Mécanique

Mots Clés : Fictitious domain model – Immersed interface conditions – Immersed boundary conditions – Jump embedded boundary conditions – Stokes/Brinkman problem – Transmission problem – Well-posedness – PDE's

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Contributeur : Philippe Angot <>

Soumis le : Lundi 26 Avril 2010, 19:06:55

Dernière modification le : Jeudi 17 Juin 2010, 18:06:12