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Derivation of the Lattice Boltzmann Method by Means of the Discrete Ordinate Method for the Boltzmann Equation

1997; Elsevier BV; Volume: 131; Issue: 1 Linguagem: Inglês

10.1006/jcph.1996.5595

1090-2716

Takashi Abe,

Fluid Dynamics and Heat Transfer

A mass-conserving finite element lattice Boltzmann equation (FE-LBE) method for the simulation of a bubble rising in viscous fluid at high Reynolds number with large material property contrast is presented in this work. The presented model consists of the conservative phase-field equation for interface capturing and the pressure-velocity formulation of lattice Boltzmann equation (LBE) for recovering the hydrodynamic properties. In this computational framework, LBE is regarded as a special space time discretization of the discrete Boltzmann equation in the characteristic direction and the streaming step is carried out by solving a linear advection equation in an Eulerian framework. We conduct extensive investigations for numerical accuracy and stability through performing multiple benchmark simulations for single bubble rising in a viscous fluid in different flow regimes. The complex dynamics of a high Reynolds number bubble rising with path and shape oscillations are studied and compared to available experimental results. The simulated evolution of the bubble mean shape with Archimedes number, path and shape oscillations in different oscillation regimes, and wake dynamics of the bubble show a good agreement with available experimental data. The current model offers a remarkable improvement in mass conservation compared to the Cahn-Hilliard based FE-LBE model.