Steady Fluid-Structure Interaction Using Fictitious Domain

Abstract

International audienceWe present a formulation for a steady fluid-structure interaction problem using fictitious domain technique with penalization. Numerical results are presented

Numerical Simulation of Dynamic Fluid-Structure Interaction with Elastic Structure–Rigid Obstacle Contact

“…The problem has a unique solution, see [19,20] for example in the steady case. As a consequence of the penalization term in (30), we get the weak equality of fluid velocity and structure velocity over the whole structure domain Ω S n+1 and it implies the condition (10) on the fluid-structure interface.…”

“…However, when the structure touches the rigid obstacle, the fluid domain is not necessary a Lipschitz domain. Existing results for fluid-structure interactions are presented in [19,20,22,23] and the references are given there. In [19,20,22], the fictitious domain method was used and this technique could be more appropriate to handle the structure-obstacle contact in the fluid-structure interaction framework.…”

“…Then, the surface forces from the fluid acting on the structure are computed by using the right-hand side of (35). As in [19,20], by using the change of variable formula, we get…”

“…In [18], the fictitious domain method with penalization presented in [19,20] was used in order to handle the contact between a linear elastic structure and a rigid obstacle in a fluid-structure interaction problem. The surface forces at the fluid-structure interface were computed using the fluid solution in the structure domain.…”