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.
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