Ghost Fluid Lattice Boltzmann Methods for Complex Geometries

Abstract

Lattice Boltzmann method (LBM) is a widely recognized alternate numerical approach to simulate flow dynamics. In the conventional approach, the Navier–Stokes equations (conservation of mass, momentum and energy) are solved to obtain velocity, pressure and temperature fields. In LBM, on the other hand, the reduced version of the microscopic Boltzmann kinetic equations is solved numerically to determine particle distribution functions, which are then averaged to obtain macroscopic variables. Accurate enforcement of non-conforming and/or moving boundary conditions has been a challenge for LBM because the primary solution variables (particle distribution functions) are not the macroscopic variables on which boundary conditions are typically imposed. While macroscopic variables can be obtained from the particle distribution functions by weighted averaging, the reverse process is not as straightforward. Several researchers have developed strategies to accurately enforce boundary conditions. In this chapter, we first present an overview of the boundary issues in LBM and various approaches that have been developed to resolve them. We then discuss the implementation of immersed boundary method (IBM) on LBM, with particular emphasis on the ghost fluid approach. This technique based on ghost cells was first introduced to LBM by Tiwari and Vanka (Int J Numer Methods Fluids 69(2):481–498, 2012), who developed the so-called ghost fluid immersed boundary lattice Boltzmann method (GF-IB-LBM) based on extrapolation of particle distribution functions. The method is simple and efficient and is applicable to general boundary conditions. Another key advantage is the strict imposition of hydrodynamic conditions at the boundaries. Additionally, the method is local, thus maintains high parallelism of LBM. The application of this approach on several problems is discussed here, including its parallelization using graphical processing units (GPUs), and its coupling with molecular dynamics (MD) simulations. The chapter ends with a brief discussion on recent advances in this approach.