Master of Science (MS)


Physics and Astronomy

Document Type



In this work, results from a 2-D Lattice Boltzmann (LB) solver are presented simulating flow past rectangular square cylinders at low Reynolds numbers (< 250). The LBGK equation is a hyperbolic equation that approximates the Navier Stokes equations in the nearly incompressible limit. It is a system of 9 one dimensional partial differential Hamiltonian-Jacobian equations, consisting of an advection and diffusive portion. The LB method is an alternative computational fluid dynamics (CFD) method used to numerically predict incompressible viscous flow. The current LB method uses a statistical mechanics formulation to solve the Boltzmann equation. The LB model captures the nonlinear Navier Stokes advection terms using linear streaming operators. In this thesis, the LB model is classified as an explicit, Lagrangian, finite-hyperbolicity and weakly compressible approximation of the Navier Stokes equations. The momentum flux tensor is captured locally as opposed to a pressure field eliminating the need to solve the Poisson equation. This allows the fluid structure interactions (FSI) behavior to be calculated elegantly at the interface through the mesoscopic momentum transfer between the fluid and structure. At this level, the forces are simultaneously calculated. The LB equations are discretized both in time and phase space using a standard D2Q9 lattice model. Validation tests for flow around single square cylinders at different aspect ratio at low Reynolds numbers are presented. Good agreement with other investigators is achieved. Flow past multiple bluff bodies (representing building in a city) is also presented. The vortex shedding simulations presented provide preliminary indications in terms of St that the LB method can be used to simulate high Re flow.



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Committee Chair

Jannette Frandsen