Analysis of the immersed boundary method for turbulent fluid-structure interaction with Lattice Boltzmann method

Abstract

An efficient and new methodology to deal with fluid structure interaction at high Reynolds number flows is presented in this article. It relies on the coupling of the lattice Boltzmann method and the immersed boundary method with a second order predictor corrector model for the structure. The effect of the lagrangian weight of the immersed boundary method is also analyzed in the context of fluid structure interaction. Both curved and moving boundaries are considered, and several methods to calculate the lagrangian weight are compared on relevant test-cases: the laminar flow around a cylinder at Reynolds number Re=100, the Poiseuille flow in a 2D channel and a 3D fluid-structure interaction test case: a deformable flapping flag immersed in a laminar flow. A convergence study in space and time is performed and the three following parameters are investigated: the number of lagrangian markers along the boundary, the value of the lagrangian weight and the shape of the discrete delta function used in the immersed boundary. Finally, the novelty of the paper is two-fold: a new expression of the lagrangian weight which is found to reduce the error by 20% in the case of fluid-structure interaction, and the coupling of a turbulence model with a second order predictor corrector model for improved stability and accuracy. This numerical methodology is found here to be accurate for challenging cases with high added mass effect and high Reynolds number flows.