A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Reis, T.; Dellar, P.J.

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Type

Article

Authors

Reis, T.
Dellar, P.J.

KAUST Grant Number

KUK-C1-013-04

Date

2011-07

Abstract

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the widths of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee (1990) [3] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin (2000) [1] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving, gives correct average propagation speeds over many timesteps, and is shown to significantly delay the onset of pinning as the interface width is reduced. © 2010 Elsevier Ltd.

Citation

Reis T, Dellar PJ (2011) A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations. Computers & Fluids 46: 417–421. Available: http://dx.doi.org/10.1016/j.compfluid.2010.12.005.

Acknowledgements

The authors’ research is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST); and by an Advanced Research Fellowship, Grant number EP/E054625/1, from the UK’s Engineering and Physical Sciences Research Council (EPSRC).