Title page for ETD etd-04212010-111944

Type of Document Dissertation
Author Tubbs, Kevin
Author's Email Address ktubbs2@lsu.edu
URN etd-04212010-111944
Title Lattice Boltzmann Modeling for Shallow Water Equations Using High Performance Computing
Degree Doctor of Philosophy (Ph.D.)
Department Engineering Science (Interdepartmental Program)
Advisory Committee
Advisor Name Title
Tsai, Frank T.-C. Committee Chair
Allen, Gabrielle Committee Member
Chen, Qin J Committee Member
White, Christopher D Committee Member
Larock, Paul A Dean's Representative
  • Lattice Boltzmann
  • Shallow Water Equations
  • High Performance Computing
  • GPU Computing
  • OpenMP
Date of Defense 2010-04-13
Availability unrestricted
The aim of this dissertation project is to extend the standard Lattice Boltzmann method (LBM) for shallow water flows in order to deal with three dimensional flow fields.

The shallow water and mass transport equations have wide applications in ocean, coastal, and hydraulic engineering, which can benefit from the advantages of the LBM. The LBM has recently become an attractive numerical method to solve various fluid dynamics phenomena; however, it has not been extensively applied to modeling shallow water flow and mass transport. Only a few works can be found on improving the LBM for mass transport in shallow water flows and even fewer on extending it to model three dimensional shallow water flow fields. The application of the LBM to modeling the shallow water and mass transport equations has been limited because it is not clearly understood how the LBM solves the shallow water and mass transport equations.

The project first focuses on studying the importance of choosing enhanced collision operators such as the multiple-relaxation-time (MRT) and two-relaxation-time (TRT) over the standard single-relaxation-time (SRT) in LBM. A (MRT) collision operator is chosen for the shallow water equations, while a (TRT) method is used for the advection-dispersion equation. Furthermore, two speed-of-sound techniques are introduced to account for heterogeneous and anisotropic dispersion coefficients.

By selecting appropriate equilibrium distribution functions, the standard LBM is extended to solve three-dimensional wind-driven and density-driven circulation by introducing a multi-layer LB model. A MRT-LBM model is used to solve for each layer coupled by the vertical viscosity forcing term. To increase solution stability, an implicit step is suggested to obtain stratified flow velocities. Numerical examples are presented to verify the multi-layer LB model against analytical solutions. The modelís capability of calculating lateral and vertical distributions of the horizontal velocities is demonstrated for wind- and density- driven circulation over non-uniform bathymetry.

The parallel performance of the LBM on central processing unit (CPU) based and graphics processing unit (GPU) based high performance computing (HPC) architectures is investigated showing attractive performance in relation to speedup and scalability.

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