HR: 17:15h
AN: H34A-06    [Abstracts]
TI: Development Of A Least-Squares Finite-Element Based Lattice Boltzmann Method For Modeling Fluid Flow In Porous Media
AU: * Li, Y
EM: yusong.li@vanderbilt.edu
AF: Vanderbilt University, Department of Civil & Environmental Engineering, Nashville, TN 37235 United States
AU: LeBoeuf, E J
EM: eugene.j.leboeuf@vanderbilt.edu
AF: Vanderbilt University, Department of Civil & Environmental Engineering, Nashville, TN 37235 United States
AU: Basu, P K
EM: prodyot.k.basu@vanderbilt.edu
AF: Vanderbilt University, Department of Civil & Environmental Engineering, Nashville, TN 37235 United States
AB: In the last few decades, lattice Boltzmann method (LBM) has been developed as a promising method for simulating fluid flow in natural porous media. Traditional LBM, however, is restricted to a uniform grid. This limitation seriously affects further applications of LBM, where representations of complex pore geometry requires a very fine uniform lattice, thus necessitating additional computing resources. In this study, a new numerical model of LBM utilizing least-squares finite element in space and Crank-Nicolson method in time is developed. The new method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using finite-element method's flexibility and numerical stability, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived from the method for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and much less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.
DE: 5112 Microstructure
DE: 5114 Permeability and porosity
DE: 5139 Transport properties
DE: 3210 Modeling
DE: 1829 Groundwater hydrology
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting