Higher order lattice boltzmann for thermo-hydrodynamics

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.