Doctor of Philosophy (PhD)
Civil and Environmental Engineering
The aim of this dissertation is to extend the lattice Boltzmann method (LBM) to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media, as well as investigating the stability and accuracy. Although the LBM is a well known and effective numerical method to solve fluid flows, LBM has not been extensively applied to mass transport equations in porous medium flow yet, and only a few works can be found on improving LBM to cope with mass transport equations other than the diffusion and advection-diffusion equations. One of the reasons why LBM has not been extensively used is because it is not clearly understood how LBM solve mass transport equations. We first focus on investigating what type of partial differential equation (PDE) the LBM recovers. The recovery procedure is carried out in detail up to third order accuracy and including the effect of forcing terms. Once the recovered PDE is known, LBM can be tailored to solve targeted mass transport equations. In order to improve the accuracy of LBM, the analysis is based on the lattice Boltzmann equation with a two-relaxation-time collision operator. Regarding the stability of LBM, the von Neumann stability analysis is used and linear stability boundaries are found under different scenarios. By an appropriate selection of the equilibrium distribution functions (EDF) and forcing terms, LBM is able to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media. The relaxation times offer some degrees of freedom that allows LBM to improve the accuracy without decreasing computational efficiency. For validation purposes LBM has been implemented to simulate saltwater intrusion in the Henry problem and modified versions, and the results are in good agreement with available analytical solutions and numerical solutions obtained by other methods.
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Servan Camas, Borja, "Lattice Boltzmann modeling for mass transport equations in porous media" (2008). LSU Doctoral Dissertations. 1953.
Tsai, Frank Tsung-Chen