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Article Dans Une Revue International Journal for Numerical Methods in Fluids Année : 2014

A fictitious domain approach for the Stokes problem based on the extended finite element method

Sébastien Court
  • Fonction : Auteur

Résumé

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by extended finite element method and studied for the Poisson problem in a paper of Renard and Haslinger of 2009. The method allows computations in domains whose boundaries do not match. A mixed FEM is used for the fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for the velocity and the Lagrange multiplier. Convergence analysis is given, and several numerical tests are performed to illustrate the capabilities of the method. Copyright
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Dates et versions

hal-01978110 , version 1 (28-01-2019)

Identifiants

  • HAL Id : hal-01978110 , version 1

Citer

Sébastien Court, Michel Fournié, Alexei Lozinski. A fictitious domain approach for the Stokes problem based on the extended finite element method. International Journal for Numerical Methods in Fluids, 2014, 74, pp.73 - 99. ⟨hal-01978110⟩
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