Smoothed profile method for particulate flows: Error analysis and simulations

Luo, Xian; Maxey, Martin; Karniadakis, George Em

doi:10.1016/j.jcp.2008.11.006

Cited by 85 publications

(106 citation statements)

References 46 publications

(85 reference statements)

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“…By varying s in a certain range, for example, 0 ≤ s ≤ ∆x, one can smoothly increase the support of the kernel and thus increase the hydrodynamic radius of the blob by as much as a factor of two. While in principle one can increase the width of the kernels arbitrarily, if the support of the kernel grows beyond 5-6 cells it better to abandon the minimally-resolved blob approach and employ a more resolved representation of the particle [14,39]. We do not use split kernels in this work but have found them to work as well as the unshifted kernels, while allowing increased flexibility in varying the grid spacing relative to the hydrodynamic radius of the particles.…”

Section: Discrete Interpolation and Spreading Operatorsmentioning

confidence: 99%

“…requires converting the particle boundary conditions into body forces or some interaction equations [11,13,14]. The present work focuses on this second group, sometimes called mixed EulerianLagrangian methods.…”

mentioning

confidence: 99%

“…High spatial resolution requires substantial computational effort; the largest simulations so far reached O(10 3 ) particles [35,40,41]. The smoothed particle method (SPM) [13,14] works with a mixed (particle-fluid) velocity field constructed with a smooth characteristic function which discriminates particle and fluid cells. This permits an intermediate resolution with a typical particle radius R 5h (here h is the mesh size) requiring O(10 3 ) fluid cells per particle.…”

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confidence: 99%

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Inertial coupling method for particles in an incompressible fluctuating fluid

Usabiaga

Delgado‐Buscalioni

Griffith

et al. 2014

Computer Methods in Applied Mechanics and Engineering

155

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We develop an inertial coupling method for modeling the dynamics of point-like "blob" The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatiotemporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels allow the blob to provide an effective model of a particle; specifically, the volume, mass, and hydrodynamic properties of the blob are remarkably grid-independent. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems. In the deterministic setting, we find the blob to be a remarkably robust approximation to a rigid sphere, at both low and high Reynolds numbers. In the stochastic setting, we study in detail the short and long-time behavior of the velocity autocorrelation function and observe agreement with all of the known behavior for rigid sphere immersed in a fluctuating fluid. The proposed inertial coupling method provides a low-cost coarse-grained (minimal resolution) model of particulate flows over a wide range of time-scales ranging from 2 Brownian to convection-driven motion.

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Section: Discrete Interpolation and Spreading Operatorsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Inertial coupling method for particles in an incompressible fluctuating fluid

Usabiaga

Delgado‐Buscalioni

Griffith

et al. 2014

Computer Methods in Applied Mechanics and Engineering

155

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“…Several analytical forms of the smoothed pro le for the spherical particles can be found in the literature [9,17]. The most widely used one is:…”

Section: Fluid-solid Interaction Simulation Using Smoothed Pro Le Metmentioning

confidence: 99%

Particle flow simulation in a channel with symmetric protuberances using combination of lattice Boltzmann and smoothed profile methods

et al. 2017

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Abstract. In the present study, a combination of Lattice Boltzmann Method (LBM) and Smoothed Pro le Method (SPM) is used to simulate one, two, and many particles motion in a planar channel with two symmetric protuberances. LBM is applied as the uid ow solver and SPM is used to satisfy the no-slip boundary condition at particles surfaces. Bounceback boundary conditions are used for lower and upper walls while pressure boundary conditions are applied for the uid inlet and outlet boundaries. Horizontal, vertical, and angular velocities of particles are recorded during the simulation. It is concluded that the combined LBM-SPM can be considered as a good candidate for simulation of particle motion in a channel with stenotic geometry.

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“…We use the smoothed profile method (SPM) 11,12 , which is applicable to a compressible fluid 13,14 . In SPM, rigid fixed wall boundaries can be imposed similar to the representation of rigid particles 15 . The accuracy of SPM for the present system is confirmed by calculating the steady-state mobility of the particle, which is compared with the approximate analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Velocity relaxation of a particle in a confined compressible fluid

Tatsumi

Yamamoto

2013

The Journal of Chemical Physics

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The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is transmitted in the ambient fluid by viscous diffusion and sound wave propagation, and the fluid flow accompanied by each mechanism has a different character and affects the particle motion differently. Because of the bounding walls, viscous diffusion is hampered, and the accompanying shear flow is gradually diminished. However, the sound wave is repeatedly reflected and spreads diffusely. As a result, the particle motion is governed by the sound wave and backtracks differently in a bulk fluid. The time when the backtracking of the particle occurs changes non-monotonically with respect to the compressibility factor ε = ν/ac and is minimized at the characteristic compressibility factor. This factor depends on the wall spacing, and the dependence is different at small and large wall spacing regions based on the different mechanisms causing the backtracking.

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Smoothed profile method for particulate flows: Error analysis and simulations

Cited by 85 publications

References 46 publications

Inertial coupling method for particles in an incompressible fluctuating fluid

Inertial coupling method for particles in an incompressible fluctuating fluid

Particle flow simulation in a channel with symmetric protuberances using combination of lattice Boltzmann and smoothed profile methods

Velocity relaxation of a particle in a confined compressible fluid

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