Lattice Boltzmann Method has been quite successful for incompressible
flows. Its extension for compressible (especially supersonic and hypersonic)
flows has attracted lot of attention in recent time. There have been some
successful attempts but nearly all of them have either resulted in complex
or expensive equilibrium function distributions or in extra energy levels.
Thus, an efficient Lattice Boltzmann Method for compressible fluid flows
is still a research idea worth pursuing for. In this thesis, a new Lattice
Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation
system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a
relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation
of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the
equations of inviscid compressible flows. Since the associated equilibrium
distribution functions of the relaxation system are not based on a low Mach
number expansion, this method is not restricted to the incompressible limit.
Free slip boundary condition is introduced with this new relaxation system
based Lattice Boltzmann method framework. The same scheme is then extended
for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.
| Identifer | oai:union.ndltd.org:IISc/oai:etd.ncsi.iisc.ernet.in:2005/3257 |
| Date | January 2012 |
| Creators | Kotnala, Sourabh |
| Contributors | Raghurama Rao, S V |
| Source Sets | India Institute of Science |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | G26987 |
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