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Communication Dans Un Congrès Année : 2005

Fictitious domain methods to solve convection-diffusion problems with general boundary conditions

Résumé

Since a few years, fictitious domain methods have been arising for Computational Fluid Dynamics. The main idea of these methods consists in immersing the original physical domain in a geometrically bigger and simply-shaped other one called fictitious domain. As the spatial discretization is then performed in the fictitious domain, simple structured meshes can be used. The aim of this paper is to solve convection-diffusion problems with fictitious domain methods which can easily simulate free-boundary with possibly deformations of the boundary without increasing the computational cost. Two fictitious domain approaches performing either a spread interface or a thin interface are introduced. These two approaches require neither the modification of the numerical scheme near the immersed interface nor the use of Lagrange multipliers. Several ways to impose general embedded boundary conditions (Dirichlet, Robin or Neumann) are presented. The spread interface approach is computed using a finite element method as a finite volume method is used for the thin interface approach. The numerical schemes conserve the first- order accuracy with respect to the discretization step as observed in the numerical results reported here. The spread interface approach is then combined with a local adaptive mesh refinement algorithm in order to increase the precision in the vicinity of the immersed boundary. The results obtained are full of promise, more especially as convection-diffusion equations are the core of the resolution of Navier-Stokes equations.
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Dates et versions

hal-00274448 , version 1 (18-04-2008)

Identifiants

  • HAL Id : hal-00274448 , version 1

Citer

Isabelle Ramière, Philippe Angot, Michel Belliard. Fictitious domain methods to solve convection-diffusion problems with general boundary conditions. Proc. in the 17th Computational Fluid Dynamics Conference AIAA, Jun 2005, Toronto, Canada. Session : "Numerical methods and code optimization I". ⟨hal-00274448⟩
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