|An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application|
|Zhu LD; He GW(何国威); Wang SZ(王士召); Miller L; Zhang X(张星); You Q; Fang SF; Zhu, LD (reprint author), Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA
|Source Publication||Computers & Mathematics With Applications
|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. (C) 2010 Elsevier Ltd. All rights reserved.|
|Keyword||Immersed Boundary Method
Lattice Boltzmann Method
Computational Fluid Dynamics
Incompressible Viscous Flow
|Subject Area||Computer Science
|WOS Keyword||FLUID-STRUCTURE INTERACTIONS
; INCOMPRESSIBLE VISCOUS-FLOW
; LEVEL-SET METHOD
; ELASTIC BOUNDARIES
; SIMULATING FLUID
; INTERFACE METHOD
; NONIDEAL GASES
; FLEXIBLE FIBER
|WOS Research Area||Mathematics
|WOS Subject||Mathematics, Applied
|Corresponding Author||Zhu, LD (reprint author), Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA|
Zhu LD,He GW,Wang SZ,et al. An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application[J]. Computers & Mathematics With Applications,2011,61(12):3506-3518.
Zhu LD.,何国威.,王士召.,Miller L.,张星.,...&Zhu, LD .(2011).An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application.Computers & Mathematics With Applications,61(12),3506-3518.
Zhu LD,et al."An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application".Computers & Mathematics With Applications 61.12(2011):3506-3518.