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A Lattice-Boltzmann Model for Visco-Elasticity

Author

Listed:
  • Laurent Giraud

    (Laboratoire C.N.R.S.–A.S.C.I., Bât.506, 91405 Orsay Cedex, France;
    Laboratoire de Physique Statistique de l'École Normale Supérieure (Associated to C.N.R.S., Paris VI and Paris VII.) 24, Rue Lhomond, 75321 Paris Cedex 05, France)

  • Dominique d'HumièRes

    (Laboratoire C.N.R.S.–A.S.C.I., Bât.506, 91405 Orsay Cedex, France;
    Laboratoire de Physique Statistique de l'École Normale Supérieure (Associated to C.N.R.S., Paris VI and Paris VII.) 24, Rue Lhomond, 75321 Paris Cedex 05, France)

  • Pierre Lallemand

    (Laboratoire C.N.R.S.–A.S.C.I., Bât.506, 91405 Orsay Cedex, France)

Abstract

The classical lattice-Boltzmann scheme is extended in an attempt to represent visco-elastic fluids in two dimensions. At each lattice site, two new quantities are added. A suitable coupling of these quantities with the viscous stress tensor leads to a nonzero shear modulus and visco-elastic effects. A Chapman–Enskog expansion gives us the equilibrium populations and conditions for isotropy of the model. A finite wave vector analysis is needed to study the relaxation of sound waves and to determine the dependence of the transport coefficients upon the frequency.

Suggested Citation

  • Laurent Giraud & Dominique d'HumièRes & Pierre Lallemand, 1997. "A Lattice-Boltzmann Model for Visco-Elasticity," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 805-815.
    • Handle: RePEc:wsi:ijmpcx:v:08:y:1997:i:04:n:s0129183197000692
    DOI: 10.1142/S0129183197000692
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    Cited by:

    1. Afrouzi, Hamid Hassanzadeh & Ahmadian, Majid & Moshfegh, Abouzar & Toghraie, Davood & Javadzadegan, Ashkan, 2019. "Statistical analysis of pulsating non-Newtonian flow in a corrugated channel using Lattice-Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

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