Lattice Boltzmann method for non-Newtonian (power-law) fluids

Susana Gabbanelli, German Drazer, Joel Koplik

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186 Scopus citations

Abstract

We study an ad hoc extension of the lattice Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution.

Original languageEnglish (US)
Article number046312
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number4
DOIs
StatePublished - Oct 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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