An immersed boundary formulation for lattice Boltzmann simulations of low-Reynolds fluid–structure interaction problems

Fluid–solid interaction problems are encountered in various natural phenomena and engineering applications. Specifically, when the fluid passes through a solid body, the resultant oscillatory forces may induce the structure to vibrate. In this work, the immersed boundary formulation has been implemented in the lattice Boltzmann approach to study complex fluid–structure interaction problems in a two-dimensional domain. The immersed boundary method has been used for its capability to describe complex geometries on a separate grid with respect to the one used to solve the fluid motion: a Eulerian one, fixed in the space, for the fluid domain, and a Lagrangian one, which can move freely to describe the body motion. The main advantage of using immersed boundary is the possibility to simulate the presence of a body through forces applied to the fluid domain, defining a discrete delta function necessary to distribute such forces. The presented approach has been applied to different Reynolds number flow conditions ranging from 20 up to 200 and different geometries starting from a plain cylinder. The validation results from the cylinder test case demonstrated excellent agreement with the literature, particularly in terms of drag and lift coefficients and the Strouhal number. The proposed algorithm captures significant high-frequency contributions arising from the interaction between vortices in the wake. Applications to both the cylinder-plate configuration and vibrating cylinder cases confirmed that this approach based on the weak fluid–structure interaction coupling can be effectively applied to a wide range of low Reynolds number scenarios.