Commun. Comput. Phys., 7 (2010), pp. 423-444.


Improved Lattice Boltzmann Without Parasitic Currents for Rayleigh-Taylor Instability

Daniele Chiappini 1*, Gino Bella 1, Sauro Succi 2, Federico Toschi 3, Stefano Ubertini 4

1 University of Rome Tor Vergata, Via del Politecnico 1, I-00133, Rome, Italy.
2 IAC-CNR, Viale del Policlinico 137, I-00161, Rome, Italy.
3 IAC-CNR, Viale del Policlinico 137, I-00161, Rome, Italy; and Department of Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
4 University of Naples Parthenope, Isola C4 - Centro Direzionale, I-80143, Naples, Italy.

Received 13 January 2009; Accepted (in revised version) 3 June 2009
Available online 1 September 2009
doi:10.4208/cicp.2009.09.018

Abstract

Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest as a numerical solver for multiphase flows. However most of the LB variants proposed to date are still faced with discreteness artifacts in the form of spurious currents around fluid-fluid interfaces. In the recent past, Lee et al. have proposed a new LB scheme, based on a higher order differencing of the non-ideal forces, which appears to virtually free of spurious currents for a number of representative situations. In this paper, we analyze the Lee method and show that, although strictly speaking, it lacks exact mass conservation, in actual simulations, the mass-breaking terms exhibit a self-stabilizing dynamics which leads to their disappearance in the long-term evolution. This property is specifically demonstrated for the case of a moving droplet at low-Weber number, and contrasted with the behaviour of the Shan-Chen model. Furthermore, the Lee scheme is for the first time applied to the problem of gravity-driven Rayleigh-Taylor instability. Direct comparison with literature data for different values of the Reynolds number, shows again satisfactory agreement. A grid-sensitivity study shows that, while large grids are required to converge the fine-scale details, the large-scale features of the flow settle-down at relatively low resolution. We conclude that the Lee method provides a viable technique for the simulation of Rayleigh-Taylor instabilities on a significant parameter range of Reynolds and Weber numbers.

AMS subject classifications: 76T02, 68U02

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Key words: Lattice-Boltzmann, multiphase, parasitic currents, Rayleigh-Taylor Instability.

*Corresponding author.
Email: chiappini@ing.uniroma2.it (D. Chiappini), bella@uniroma2.it (G. Bella), succi@iac.cnr.it (S. Succi), toschi@iac.cnr.it (F. Toschi), stefano.ubertini@uniparthenope.it (S. Ubertini)
 

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