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A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio

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Title: A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
Authors: Lee, Taehun1, Lin, Ching-Long ching-long-lin@uiowa.edu
Source: Journal of Computational Physics. Jun2005, Vol. 206 Issue 1, p16-47. 32p.
Subjects: Multiphase flow, Fluid dynamics, Surface tension, Thick films
Abstract: Abstract: A stable discretization of the lattice Boltzmann equation (LBE) for non-ideal gases is presented for simulation of incompressible two-phase flows having high density and viscosity ratios. The stiffness of the discretized forcing terms in LBE for non-ideal gases is known to trigger severe numerical instability and restrict practical application of the LBE method. Use of a proper pressure updating scheme is also crucial to the stability of the LBE method because of non-negligible pressure variation across the phase interface. To deal with these issues, we propose a stable discretization scheme, which assumes the low Mach number approximation, and utilizes the stress and potential forms of the surface tension force, the incompressible transformation, and the consistent discretization of the intermolecular forcing terms. The proposed stable discretization scheme is applied to simulate 1-D advection equation with a source term, a stationary droplet, droplet oscillation and droplet splashing and deposition on a thin film at a density ratio of 1000 with varying Reynolds numbers. The numerical solutions of stationary and oscillatory droplets agree well with analytic solutions including the Laplace’s law. The time history of the spread factor of the liquid sheet emitted after the droplet impact also follows the known spreading power law. [Copyright &y& Elsevier]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
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  Data: <searchLink fieldCode="AR" term="%22Lee%2C+Taehun%22">Lee, Taehun</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Lin%2C+Ching-Long%22">Lin, Ching-Long</searchLink><i> ching-long-lin@uiowa.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Jun2005, Vol. 206 Issue 1, p16-47. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Multiphase+flow%22">Multiphase flow</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+dynamics%22">Fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+tension%22">Surface tension</searchLink><br /><searchLink fieldCode="DE" term="%22Thick+films%22">Thick films</searchLink>
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  Data: Abstract: A stable discretization of the lattice Boltzmann equation (LBE) for non-ideal gases is presented for simulation of incompressible two-phase flows having high density and viscosity ratios. The stiffness of the discretized forcing terms in LBE for non-ideal gases is known to trigger severe numerical instability and restrict practical application of the LBE method. Use of a proper pressure updating scheme is also crucial to the stability of the LBE method because of non-negligible pressure variation across the phase interface. To deal with these issues, we propose a stable discretization scheme, which assumes the low Mach number approximation, and utilizes the stress and potential forms of the surface tension force, the incompressible transformation, and the consistent discretization of the intermolecular forcing terms. The proposed stable discretization scheme is applied to simulate 1-D advection equation with a source term, a stationary droplet, droplet oscillation and droplet splashing and deposition on a thin film at a density ratio of 1000 with varying Reynolds numbers. The numerical solutions of stationary and oscillatory droplets agree well with analytic solutions including the Laplace’s law. The time history of the spread factor of the liquid sheet emitted after the droplet impact also follows the known spreading power law. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jcp.2004.12.001
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      – Code: eng
        Text: English
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        PageCount: 32
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      – SubjectFull: Multiphase flow
        Type: general
      – SubjectFull: Fluid dynamics
        Type: general
      – SubjectFull: Surface tension
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      – SubjectFull: Thick films
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      – TitleFull: A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
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              Text: Jun2005
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