An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application
✍ Scribed by Luoding Zhu; Guowei He; Shizhao Wang; Laura Miller; Xing Zhang; Qian You; Shiaofen Fang
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 975 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
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.