Coupling Algorithms for Fluid Structure Interaction at Low Density Ratios

M. Ottosson. Master thesis, Chalmers University of Technology, 12 June 2018. Supervisor Andreas Mark and Christoffer Cromvik.


In recent years the interest of numerical predictions of fluid-structure interaction has grown in industrial applications as well as in the research of the phenomenon due to the increase in computational power. Numerical predictions of fluid-structure interaction typically suffers from instabilities when the density ratio of solid to fluid becomes small. The instability issues are most severe when weak coupling, without sub-iterations within each time step, procedures are used. Further, the weak coupling introduces the so-called artificial added mass effect, that introduces an error in the coupling.

At FCC a state-of-the-art multiphase solver, IBOFlow, and a structural solver, LaStFEM, are developed. IBOFlow handles moving boundaries using the hybrid immersed boundary method with adaptive grid refinements and the incompressible Navier-Stokes equations together with the boundary conditions at the structural interface are solved on a Eulerian grid using the finite volume method. LaStFEM solves the structural equations together with the forces acting on the structural interface on a Lagrangian grid using the finite element method. In previous work, a strong coupling, with sub-iterations within each time step,  and a simple weak coupling procedure has been implemented.

In this thesis different weak coupling procedures are implemented, compared and analyzed in the existing frame work. The accuracy and stability of the weak coupling algorithms are investigated and compared to the existing strong coupling procedure. The investigation is done by the usage of three benchmarking cases: A rigid sphere attached to a undamped spring in stokes flow, a rigid cylinder attached to a damped spring in a laminar flow and a elastic beam attached to a rigid cylinder in a laminar flow. The temporal accuracy and spatial accuracy are both found to be second-order. The lowest density ratio of solid to fluid where a stable solution were achived using a weak coupling algorithm is well below one and much smaller than what has been found in the literature.

Photo credits: Nic McPhee