Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)

Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Advisor 1

Song-Lin Yang

Committee Member 1

Franz X. Tanner

Committee Member 2

Kazuya Tajiri

Committee Member 3

Youngchul Ra


Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration.