Convergence of a Lagrange--Galerkin method for a fluid-rigid body system in ALE formulation

Guillaume Legendre (1) , Takéo Takahashi (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CORIDA - Robust control of infinite dimensional systems and applications

In this paper, we propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid, modeled by the Navier-Stokes equations. Our method combines a finite element approximations and the use of the method of characteristics to solve an Arbitrary Lagrangian Eulerian formulation of the problem. We derive error estimates for this scheme which imply its convergence.

Mots clés: Fluid-structure interaction; Incompressible Navier–Stokes equations; Arbitrary Lagrangian Eulerian; Lagrange–Galerkin method

Domaines: Equations aux dérivées partielles [math.AP]

Guillaume Legendre, Takéo Takahashi. Convergence of a Lagrange--Galerkin method for a fluid-rigid body system in ALE formulation. ESAIM: Mathematical Modelling and Numerical Analysis, 2008, 42 (4), pp.609-644. ⟨10.1051/m2an:2008020⟩. ⟨hal-00142870v2⟩