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

  • Authors:

  • Luoding Zhu;Guowei He;Shizhao Wang;Laura Miller;Xing Zhang;Qian You;Shiaofen Fang

  • Affiliations:

  • Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, United States;State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 10088, PR China;State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 10088, PR China;Department of Mathematics, University of North Carolina Chapel Hill, Chapel Hill, NC 27599, United States;State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 10088, PR China;Department of Computer Science, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, United States;Department of Computer Science, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, United States

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2011

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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.