Crystallographic lattice boltzmann method

Abstract

In the last two decades, Lattice Boltzmann Method (LBM) has emerged as an e cient alternative for hydrodynamic simulations. In LBM, a ctitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a Cartesian grid for spatial discretization of the kinetic equation. In this thesis, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. This thesis shows that this inversion of the argument of LBM and making of spatial discretization the central point indeed provides lot more freedom and accuracy in the velocity space discretization. We illustrate an order-of-magnitude gain in e ciency for LBM and thus a signi cant progress towards the feasibility of DNS for realistic

ows. This thesis systematically investigates requirements for higher order Lattice Boltzmann Models and shows that it is possible to construct models for compressible ows as well as the description of nite temperature variations on a BCC lattice. For compressible ows, a hybrid methodology to compute discrete equilibrium in an e cient fashion is proposed. vii