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

Abstract

The lattice Boltzmann method (LBM) is a numerical solver for the Navier-Stokes equations, based on an underlying molecular dynamic model. Recently, it has been extended towards the simulation of complex fluids. Since the LBM is generally based on a Cartesian grid, it is vulnerable to the loss of node information for moving boundaries. In this study, we use the asymptotic expansion technique to investigate the standard scheme, the initialization problem and possible developments towards moving boundary and fluid-structure interaction (FSI) problems. In particular, we concentrate on the initialization of new fluid nodes created by the variations of the computational fluid domain. An overview of existing possible choices is presented. At the same time, 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 problem, we present three important benchmark problems to validate the developed algorithm. The three benchmark problems chosen are a neutrally buoyant cylinder, a rotating cylinder in a free stream, and a rotating cylinder in a channel. We show that the results of the strain rate model agree with known numerical and experimental solutions. 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. In conclusion, we test the defined code and validate the results of the analysis on two FSI problems.