A modified Lagrange Galerkin method for a fluid rigid system

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A modified Lagrange-Galerkin method for a fluid-rigid system with discontinuous density Jorge San Martín ? , Jean-François Scheid † , Loredana Smaranda ‡ Abstract In this paper, we propose a new characteristics method for the discretization of the two dimensional fluid-rigid body problem in the case where the densities of the fluid and the solid are di?erent. The method is based on a global weak formulation involving only terms defined on the whole fluid-rigid domain. To take into account the material derivative, we construct a special characteristic function which maps the approximate rigid body at the discrete time level tk+1 into the approximate rigid body at time tk. Convergence results are proved for both semi-discrete and fully-discrete schemes. 1 Introduction The aim of this paper is to present a modified characteristics method for the discretization of the equations modelling the motion of a rigid solid immersed into a viscous incompressible fluid. Our method is a generalisation of the numerical scheme presented in San Martín, Scheid, Takahashi and Tucsnak [18] for the case where the fluid and the solid have di?erent densities. The fluid-rigid system occupies a bounded and regular domain O ? R2. The solid is assumed to be a ball of radius 1 whose center, at time t, is denoted by ?(t).

  • rigid body

  • discrete formulation

  • has given

  • stokes equations

  • lagrange-galerkin method

  • semi-discretization scheme

  • characteristic function

  • domain has

  • ?0 ?


Publié le : mardi 19 juin 2012
Lecture(s) : 33
Source : iecn.u-nancy.fr
Nombre de pages : 24
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