Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Tuesday, March 8, 2016
10:10 a.m.

PhD Candidate:  Tyler Wilson
Supervisor:  Mary Pugh, Francis Dawson
Thesis title:  Stabilization, Extension and Unification of The Lattice Boltzmann Method Using Information Theory



A novel Lattice Boltzmann method is derived using the Principle of Minimum Discrimination Information (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). Approximations of this method yields the single relaxation time (SRT-LBM), two relaxation time (TRT-LBM), multiple relaxation time (MRT-LBM) Lattice Boltzmann Methods as well as Entropic Lattice Boltzmann Method (ELBM) and Ehrenfest Step LBM (EF-LBM).  Specifi cally it is shown that these methods can be understood as approximations of a method for constrained KLD minimization. By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 2D Poiseulle flow, 1D shock tube and lid-driven cavity flow simulations are carried out and compared to SRT-LBM, TRT-LBM MRT-LBM and EF-LBM.

A copy of the thesis can be found here: twilson-thesis


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