## 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 Swift et al. LB model^{1} 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 language | English (US) |
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Pages (from-to) | 1393-1404 |

Number of pages | 12 |

Journal | International Journal of Modern Physics C |

Volume | 9 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1998 |

## Keywords

- 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
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics