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An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application

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Title: An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application
Authors: Zhu, Luoding1 lzhu@math.iupui.edu, He, Guowei2, Wang, Shizhao2, Miller, Laura3, Zhang, Xing2, You, Qian4, Fang, Shiaofen4
Source: Computers & Mathematics with Applications. Jun2011, Vol. 61 Issue 12, p3506-3518. 13p.
Subjects: Lattice Boltzmann methods, Viscous flow, Fluid dynamics, Numerical analysis, Navier-Stokes equations, Simulation methods & models, Fourier transforms
Abstract: Abstract: The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier–Stokes (N–S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N–S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N–S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) within the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are: (1) the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; (2) the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow. [Copyright &y& Elsevier]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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: An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application
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  Data: <searchLink fieldCode="AR" term="%22Zhu%2C+Luoding%22">Zhu, Luoding</searchLink><relatesTo>1</relatesTo><i> lzhu@math.iupui.edu</i><br /><searchLink fieldCode="AR" term="%22He%2C+Guowei%22">He, Guowei</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Wang%2C+Shizhao%22">Wang, Shizhao</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Miller%2C+Laura%22">Miller, Laura</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Xing%22">Zhang, Xing</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22You%2C+Qian%22">You, Qian</searchLink><relatesTo>4</relatesTo><br /><searchLink fieldCode="AR" term="%22Fang%2C+Shiaofen%22">Fang, Shiaofen</searchLink><relatesTo>4</relatesTo>
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  Data: <searchLink fieldCode="DE" term="%22Lattice+Boltzmann+methods%22">Lattice Boltzmann methods</searchLink><br /><searchLink fieldCode="DE" term="%22Viscous+flow%22">Viscous flow</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+dynamics%22">Fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink>
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  Data: Abstract: The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier–Stokes (N–S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N–S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N–S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) within the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are: (1) the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; (2) the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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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      – SubjectFull: Viscous flow
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      – SubjectFull: Fluid dynamics
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              Text: Jun2011
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