SECOND-ORDER PURE LAGRANGE-GALERKIN METHODS FOR FLUID-STRUCTURE INTERACTION PROBLEMS

In this paper, we propose a second-order (both in time and in space) pure LagrangeGalerkin method for the numerical solution of fluid-structure interaction problems. The proposed scheme is written in material coordinates and in terms of displacements in the structure and of displacements and pressures in the fluid. Pure-Lagrangian displacement methods are useful for solving free surface problems and fluid-structure interaction problems because the computational domain is independent of time, and fluid-structure coupling at the interphase is straightforward. Unfortunately, for moderate-to high-Reynolds number flows, pure-Lagrangian methods can lead to high distortion of the mesh elements, and as a consequence inaccurate approximations can be obtained. Before this happens, it is necessary to remesh and reinitialize the motion. In the present paper, we also deal with this problem by proposing a method to be combined with the pure LagrangeGalerkin method we introduce that preserves the order. In order to assess the performance of the overall numerical method, we solve different problems in two space dimensions. In particular, numerical results for the two-dimensional motion of an elastic circular cylinder in a fluid and a sloshing problem with an elastic submerged cylinder in a rectangular tank are presented.