A modified Lagrange-Galerkin method for a fluid-rigid system with discontinuous density

Jorge San Martin (1) , Jean-François Scheid (2, 3) , Loredana Smaranda (1, 4)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications
4 DIM - Departamento de Ingeniería Matemática [Santiago]

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 different. 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 $t_{k+1}$ into the approximate rigid body at time $t_k$. Convergence results are proved for both semi-discrete and fully-discrete schemes.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Jorge San Martin, Jean-François Scheid, Loredana Smaranda. A modified Lagrange-Galerkin method for a fluid-rigid system with discontinuous density. Numerische Mathematik, 2012, 122 (2), pp.341-382. ⟨10.1007/s00211-012-0460-1⟩. ⟨hal-00531433⟩