A strain-rate model for a lattice Boltzmann BGK model in fluid-structure interactions

Since the traditional lattice Boltzmann method (LBM) is generally based on a Cartesian grid, it is vulnerable to the loss of node information for moving boundaries. In this study, we propose a simple, accurate, and stable scheme that can refill the lost fluid node information in a Cartesian grid system using a strain rate model. To evaluate whether the suggested method is suitable for moving boundaries, and especially for addressing the fluid-structure interaction (FSI) problem, we present four important benchmark problems to validate the developed algorithm and show that the results of the strain rate model agree with known numerical and experimental solutions. The four benchmark problems chosen are a neutrally buoyant cylinder, a rotating cylinder in a free stream, a flexible plate oscillating in a cavity, and a rotating cylinder in a channel. We also use a convergence test to demonstrate improved stability over previous methods. The results agree with known numerical and experimental solutions. Numerical results using the proposed strain rate model show almost second-order accuracy for two-dimensional problems.