Date of Award

Winter 2015

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Li-Shi Luo

Committee Member

Richard Noren

Committee Member

Fang Q. Hu

Committee Member

Yan Peng

Committee Member

Taehun Lee


In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed and I obtain better precision. Second, to model the velocity profile, the analysis of Couette flows with pure diffusive boundary condition is given. My results show that the velocity profile is most appropriately approximated by a cubic polynomial. Meanwhile, the analysis also discloses the Knudsen number dependences of microscopic and macroscopic slip velocities and of the half channel mass flow rate. Finally, the modeling and simulation of molecular Couette flow in Navier-Stokes framework is carried out. To obtain density and velocity profiles including the Van der Waals effects near walls, high Knudsen number gaseous Couette flows are simulated by using molecular dynamics simulation (MD). Based on high precision solutions of the integral equations and MD results of velocity and density, macroscopic moments of molecular Couette flows are modeled by using effective radial distribution functions. Then, with these modeled velocity and density profiles, the effective viscosity in the stress tensor of Navier-Stokes equation is constructed. The velocity and density profiles are reproduced by two-relaxation time lattice Boltzmann method in Navier-Stokes framework by the effective viscosity model.