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Title:  Development Of A New FiniteVolume Lattice Boltzmann Formulation And Studies On Benchmark Flows 
Authors:  Vilasrao, Patil Dhiraj 
Advisors:  Lakshmisha, K N 
Keywords:  Flow Visualization Boltzmann Equation Lattice Boltzmann Formulation ChapmanEnskog Analysis Benchmark Flows 
Submitted Date:  Jul2010 
Series/Report no.:  G23819 
Abstract:  This thesis is concerned with the new formulation of a finitevolume lattice Boltzmann equation method and its implementation on unstructured meshes. The finitevolume discretization with a cellcentered tessellation is employed. The new formulation effectively adopts a total variation diminishing concept. The formulation is analyzed for the modified partial differential equation and the apparent viscosity of the model. Further, the highorder extension of the present formulation is laid out. Parallel simulations of a variety of twodimensional benchmark flows are carried out to validate the formulation.
In Chapter 1, the important notions of the kinetic theory and the most celebrated equation in the kinetic theory, ‘the Boltzmann equation’ are given. The historical developments and the theory of a discrete form of Boltzmann equation are briefly discussed. Various offlattice schemes are introduced. Various methodologies adopted in the past for the solution of the lattice Boltzmann equation on finitevolume discretization are reviewed. The basic objectives of this thesis are stated.
In Chapter2,the basic formulations of lattice Boltzmann equation method with a rational behind different boundary condition implementations are discussed. The benchmark flows are studied for various flow phenomenon with the parallel code developed inhouse. In particular, the new benchmark solution is given for the flow induced inside a rectangular, deep cavity.
In Chapter 3, the need for offlattice schemes and a general introduction to the finitevolume approach and unstructured mesh technology are given. A new mathematical formulation of the offlattice finitevolume lattice Boltzmann equation procedure on a cellcentered, arbitrary triangular tessellation is laid out. This formulation employs the total variation diminishing procedure to treat the advection terms. The implementation of the boundary condition is given with an outline of the numerical implementation. The ChapmanEnskog (CE) expansion is performed to derive the conservation equations and an expression for the apparent viscosity from the finitevolume lattice Boltzmann equation formulation in Chapter 4. Further, the numerical investigations are performed to analyze the apparent viscosity variation with respect to the grid resolution.
In Chapter 5, an extensive validation of the newly formulated finitevolume scheme is presented. The benchmark flows considered are of increasing complexity and are namely
(1) Posieuille flow, (2) unsteady Couette flow, (3) liddriven cavity flow, (4) flow past a backward step and (5) steady flow past a circular cylinder. Further, a sensitivity study to the various limiter functions has also been carried out.
The main objective of Chapter6is to enhance the order of accuracy of spatiotemporal calculations in the newly presented finitevolume lattice Boltzmann equation formulation. Further, efficient implementation of the formulation for parallel processing is carried out. An appropriate decomposition of the computational domain is performed using a graph partitioning tool. The orderofaccuracy has been verified by simulating a flow past a curved surface. The extended formulation is employed to study more complex unsteady flows past circular cylinders.
In Chapter 7, the main conclusions of this thesis are summarized. Possible issues to be examined for further improvements in the formulation are identified. Further, the potential applications of the present formulation are discussed. 
Abstract file URL:  http://etd.ncsi.iisc.ernet.in/abstracts/1629/G23819Abs.pdf 
URI:  http://hdl.handle.net/2005/1250 
Appears in Collections:  Aerospace Engineering (aero)

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