Abstract:
In the last two decades, lattice Boltzmann method has emerged as one of the alternatives to do
complex isothermal and incompressible CFD simulations. It is based on kinetic theory which is
a molecular description of the transport phenomenon in liquids and gases. In lattice Boltzmann
method, similar to discrete velocity methods, one solves simplified Boltzmann equation over a
grid/lattice. Thus, lattice Boltzmann method involves discrete velocity space and time. The
present thesis is an attempt to examine such a discrete description from theoretical and computational
point of view for its utility in modelling Navier-Stokes-Fourier thermo-hydrodynamics.
The present thesis deals with the construction and implementation of an “higher order lattice
Boltzmann model” for thermal flows. The objective here is that the model so constructed should
not only be accurate but also be computationally efficient to simulate Navier-Stokes-Fourier
thermo-hydrodynamics. In this thesis, it is shown that this can be done by adding just 6
more velocities to the discrete velocity set of D3Q27 model. A “multi-speed on lattice thermal
lattice Boltzmann model” with 33 velocities in 3D with a consistent H-theorem is obtained. The
numerical studies have been performed for a variety of isothermal and thermal flows like unidirectional
flows, lid driven cavity set up, Rayleigh-B´enard instability, velocity and temperature
slip in micro flows. It is shown that the procedure outlined in this thesis for higher order model
construction can then be utilized to construct more better and accurate models.
