An embedded strategy for the analysis of fluid structure interaction problems

Abstract

A Navier–Stokes solver based on Cartesian structured finite volume discretization with embedded bodies is presented. Fluid structure interaction with solid bodies is performed with an explicit partitioned strategy. The Navier–Stokes equations are solved in the whole domain via a Semi-Implicit Method for Pressure Linked Equations (SIMPLE) using a colocated finite volume scheme, stabilized via the Rhie–Chow discretization. As uniform Cartesian grids are used, the solid interface usually do not coincide with the mesh, and then a second order Immersed Boundary Method is proposed, in order to avoid the loss of precision due to the staircase representation of the surface. This fact also affects the computation of fluid forces on the solid wall and, accordingly, the results in the fluid–structure analysis. In the present work, first and second order approximations for computing the fluid forces at the interface are studied and compared. The solver is specially oriented to General Purpose Graphic Processing Units (GPGPU) hardware and the efficiency is discussed. Moreover, a novel submerged buoy experiment is also reported. The experiment consists of a sphere with positive buoyancy fully submerged in a cubic tank, subject to harmonic displacements imposed by a shake table. The sphere is attached to the bottom of the tank with a string. The position of the buoy is determined from video records with a Motion Capture algorithm. The obtained amplitude and phase curves allow a precise determination of the added mass and drag forces. Due to this aspect the experimental data can be of interest for comparison with other fluid–structure interaction codes. Finally, the numerical results are compared with the experiments, and allow the confirmation of the numerically predicted drag and added mass of the body.