A lattice BGK model for advection and anisotropic dispersion equation

This paper presents a lattice Boltzmann model (LBM) for 2-D advection and anisotropic dispersion equation (AADE) based on the Bhatnagar, Gross and Krook (BGK) model. In the proposed model, the particle speed space is discretized using a rectangular lattice that has four speeds in nine directions, and the single relaxation time is assumed to be directionally dependent. To ensure that the collision is mass-invariant when the relaxation time is directionally dependent, the concentration is calculated from a weighted summation of the particle distribution functions. The proposed model was verified against benchmark problems and the finite difference solution of solute transport with spatially variable dispersion coefficients and non-uniform velocity field. The significant results are that it conserves mass perfectly and offers accurate and efficient solutions for both dispersion-dominated and advection-dominated problems.

[1]  L. Luo,et al.  A priori derivation of the lattice Boltzmann equation , 1997 .

[2]  S. Chen,et al.  Lattice methods and their applications to reacting systems , 1993, comp-gas/9312001.

[3]  Shiyi Chen,et al.  Stability Analysis of Lattice Boltzmann Methods , 1993, comp-gas/9306001.

[4]  Feder,et al.  Hydrodynamic dispersion at stagnation points: Simulations and experiments. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Shi Jin,et al.  Physical symmetry and lattice symmetry in the lattice Boltzmann method , 1997 .

[6]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[7]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[8]  J. Bear.  Hydraulics of Groundwater , 1979 .

[9]  Taehun Lee,et al.  A characteristic Galerkin method for discrete Boltzmann equation , 2001 .

[10]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[11]  Peter M. A. Sloot,et al.  Lattice dependence of reaction-diffusion in lattice Boltzmann modeling , 2000 .

[12]  R. Sman,et al.  Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices , 2000 .

[13]  SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS , 2000 .

[14]  Zhao,et al.  Lattice boltzmann method for compressible flows with high mach numbers , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  S. Chou,et al.  Finite-volume lattice Boltzmann method. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[17]  B. R. Sehgal,et al.  Evaluation of the Darcy's law performance for two-fluid flow hydrodynamics in a particle debris bed using a lattice-Boltzmann model , 2000 .

[18]  Chen,et al.  Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Peng Lin,et al.  Lattice Boltzmann Models for Anisotropic Diffusion of Images , 2004, Journal of Mathematical Imaging and Vision.

[20]  Steven A. Orszag,et al.  Scalings in diffusion-driven reactionA+B→C: Numerical simulations by lattice BGK models , 1995 .

[21]  Yang Guangwu.  A Lattice Boltzmann Equation for Waves , 2000 .

[22]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[23]  Wei Shyy,et al.  On the Finite Difference-Based Lattice Boltzmann Method in Curvilinear Coordinates , 1998 .

[24]  Byron Goldstein,et al.  Lattice Boltzmann Simulation of Diffusion-Convection Systems with Surface Chemical Reaction , 2000 .

[25]  Lin,et al.  Lattice boltzmann method on composite grids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[27]  T. Abe.  Derivation of the Lattice Boltzmann Method by Means of the Discrete Ordinate Method for the Boltzmann Equation , 1997 .

[28]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .