6,467 research outputs found
An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application
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
A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method
A unified framework to derive discrete time-marching schemes for coupling of
immersed solid and elastic objects to the lattice Boltzmann method is
presented. Based on operator splitting for the discrete Boltzmann equation,
second-order time-accurate schemes for the immersed boundary method, viscous
force coupling and external boundary force are derived. Furthermore, a modified
formulation of the external boundary force is introduced that leads to a more
accurate no-slip boundary condition. The derivation also reveals that the
coupling methods can be cast into a unified form, and that the immersed
boundary method can be interpreted as the limit of force coupling for vanishing
particle mass. In practice, the ratio between fluid and particle mass
determines the strength of the force transfer in the coupling. The integration
schemes formally improve the accuracy of first-order algorithms that are
commonly employed when coupling immersed objects to a lattice Boltzmann fluid.
It is anticipated that they will also lead to superior long-time stability in
simulations of complex fluids with multiple scales
A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
In this work it is shown how the immersed boundary method of (Peskin2002) for
modeling flexible structures immersed in a fluid can be extended to include
thermal fluctuations. A stochastic numerical method is proposed which deals
with stiffness in the system of equations by handling systematically the
statistical contributions of the fastest dynamics of the fluid and immersed
structures over long time steps. An important feature of the numerical method
is that time steps can be taken in which the degrees of freedom of the fluid
are completely underresolved, partially resolved, or fully resolved while
retaining a good level of accuracy. Error estimates in each of these regimes
are given for the method. A number of theoretical and numerical checks are
furthermore performed to assess its physical fidelity. For a conservative
force, the method is found to simulate particles with the correct Boltzmann
equilibrium statistics. It is shown in three dimensions that the diffusion of
immersed particles simulated with the method has the correct scaling in the
physical parameters. The method is also shown to reproduce a well-known
hydrodynamic effect of a Brownian particle in which the velocity
autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times.
A few preliminary results are presented for more complex systems which
demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic
Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-Lattice Boltzmann method
A variant of immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this paper to simulate incompressible viscous flows around moving objects. As compared with the conventional IB-LBM where the force density is computed explicitly by Hook's law or the direct forcing method and the non-slip condition is only approximately satisfied, in the present work, the force density term is considered as the velocity correction which is determined by enforcing the non-slip condition at the boundary. The lift and drag forces on the moving object can be easily calculated via the velocity correction on the boundary points. The capability of the present method for moving objects is well demonstrated through its application to simulate flows around a moving circular cylinder, a rotationally oscillating cylinder, and an elliptic flapping wing. Furthermore, the simulation of flows around a flapping flexible airfoil is carried out to exhibit the ability of the present method for implementing the elastic boundary condition. It was found that under certain conditions, the flapping flexible airfoil can generate larger propulsive force than the flapping rigid airfoil
Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method
The deformation of an initially spherical capsule, freely suspended in simple
shear flow, can be computed analytically in the limit of small deformations [D.
Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule
Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267].
Those analytic approximations are used to study the influence of the mesh
tessellation method, the spatial resolution, and the discrete delta function of
the immersed boundary method on the numerical results obtained by a coupled
immersed boundary lattice Boltzmann finite element method. For the description
of the capsule membrane, a finite element method and the Skalak constitutive
model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes,
Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the
investigation of the presented model for small resolutions to provide a sound
basis for efficient but accurate simulations of multiple deformable particles
immersed in a fluid. We come to the conclusion that details of the membrane
mesh, as tessellation method and resolution, play only a minor role. The
hydrodynamic resolution, i.e., the width of the discrete delta function, can
significantly influence the accuracy of the simulations. The discretization of
the delta function introduces an artificial length scale, which effectively
changes the radius and the deformability of the capsule. We discuss
possibilities of reducing the computing time of simulations of deformable
objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table
Liquid-gas-solid flows with lattice Boltzmann: Simulation of floating bodies
This paper presents a model for the simulation of liquid-gas-solid flows by
means of the lattice Boltzmann method. The approach is built upon previous
works for the simulation of liquid-solid particle suspensions on the one hand,
and on a liquid-gas free surface model on the other. We show how the two
approaches can be unified by a novel set of dynamic cell conversion rules. For
evaluation, we concentrate on the rotational stability of non-spherical rigid
bodies floating on a plane water surface - a classical hydrostatic problem
known from naval architecture. We show the consistency of our method in this
kind of flows and obtain convergence towards the ideal solution for the
measured heeling stability of a floating box.Comment: 22 pages, Preprint submitted to Computers and Mathematics with
Applications Special Issue ICMMES 2011, Proceedings of the Eighth
International Conference for Mesoscopic Methods in Engineering and Scienc
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