An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

D. J. Holdych (), D. Rovas, J. G. Georgiadis and R. O. Buckius
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D. J. Holdych: Department of Mechanical & Industrial Engineering, University of Illinois at Urbana-Champaign, USA
D. Rovas: Department of Mechanical Engineering, National Technical University of Athens, Greece
J. G. Georgiadis: Department of Mechanical & Industrial Engineering, University of Illinois at Urbana-Champaign, USA
R. O. Buckius: Department of Mechanical & Industrial Engineering, University of Illinois at Urbana-Champaign, USA

International Journal of Modern Physics C (IJMPC), 1998, vol. 09, issue 08, 1393-1404

Abstract: 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 Swiftet al. LB model1to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) 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.

Keywords: Lattice-Boltzmann Simulations; Two-Phase Flow; Stress Tensor; Benchmark Flows; Galilean Invariance; Hydrodynamics (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S0129183198001266

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