An improved hydrodynamics formulation for multiphase flow lattice-boltzmann models

D. J. Holdych, D. Rovas, J. G. Georgiadis, R. O. Buckius

Research output: Contribution to journalArticlepeer-review


Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (Mathematica) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier-Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand,allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

Original languageEnglish (US)
Pages (from-to)1393-1404
Number of pages12
JournalInternational Journal of Modern Physics C
Issue number8
StatePublished - Dec 1998
Externally publishedYes


  • Benchmark Flows
  • Galilean Invariance
  • Hydrodynamics
  • Lattice-Boltzmann Simulations
  • Stress Tensor
  • Two-Phase Flow

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mathematical Physics
  • General Physics and Astronomy
  • Statistical and Nonlinear Physics


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