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Two‐relaxation‐time lattice Boltzmann method for the anisotropic dispersive Henry problem
Author(s) -
ServanCamas Borja,
Tsai Frank T.C.
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr007837
Subject(s) - lattice boltzmann methods , anisotropy , mechanics , statistical physics , physics , mathematical analysis , mathematics , quantum mechanics
This study develops a lattice Boltzmann method (LBM) with a two‐relaxation‐time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity‐dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional‐speed‐of‐sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo‐EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection‐dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).