Research Article

A lattice Boltzmann-BGK algorithm for a diffusion equation with Robin boundary condition—application to NMR relaxation

  1. A. Hiorth1,*,
  2. U. H. a Lad2,
  3. S. Evje1,
  4. S. M. Skjæveland2

Article first published online: 28 APR 2008

DOI: 10.1002/fld.1822

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Volume 59, Issue 4, pages 405–421, 10 February 2009

Additional Information

How to Cite

Hiorth, A., a Lad, U. H., Evje, S. and Skjæveland, S. M. (2009), A lattice Boltzmann-BGK algorithm for a diffusion equation with Robin boundary condition—application to NMR relaxation. International Journal for Numerical Methods in Fluids, 59: 405–421. doi: 10.1002/fld.1822

Author Information

  1. 1

    IRIS-International Research Institute of Stavanger, P.O. Box 8046, N-4068 Stavanger, Norway

  2. 2

    Petroleum Department, University of Stavanger, N-4036 Stavanger, Norway

*IRIS-International Research Institute of Stavanger, P.O. Box 8046, N-4068 Stavanger, Norway

Publication History

  1. Issue published online: 22 DEC 2008
  2. Article first published online: 28 APR 2008
  3. Manuscript Accepted: 8 MAR 2008
  4. Manuscript Revised: 20 DEC 2007
  5. Manuscript Received: 16 APR 2007

Funded by

  • ConocoPhillips and the Ekofisk Coventurers
  • TOTAL
  • ENI
  • Hydro
  • Statoil
  • Petoro

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Keywords:

  • lattice Boltzmann;
  • LBGK;
  • NMR;
  • Robin boundary condition;
  • diffusion;
  • relaxation

Abstract

We present a lattice Boltzmann-BGK (LBGK) algorithm for a diffusion equation together with a Robin boundary condition, which we apply in the case of nuclear magnetic resonance relaxation. The boundary condition we employ is independent of the direction of the wall. This makes the algorithm very suitable for complicated geometries, such as porous media. We discuss the effect of lattice topology by using, respectively, an eight-speed and a four-speed lattice. The numerical algorithm is compared with analytical results for a square and an equilateral triangle. The eight-speed lattice performs well in both cases. The four-speed lattice performs well for the square, but fails in the case of an equilateral triangle. Comparison with a random walk algorithm is also included. The LBGK algorithm presented here can also be used for a convective diffusion problem if the speed of the fluid can be neglected close to the boundary. Copyright © 2008 John Wiley & Sons, Ltd.

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