Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics

Ichiki, Kengo; Brady, John F.

doi:10.1063/1.1331320

Cited by 22 publications

(27 citation statements)

References 10 publications

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“…The subject was examined by Ichiki and Brady [26], who showed that the method of reflections is mathematically equivalent to the inversion of a mobility problem performed by the Jacobi method, which is not unconditionally stable. However, the implementation of the method of reflections by these authors, which is based on truncated multipoles, is different from the one presented here and was found to be less stable.…”

Section: Evaluation Of the Hydrodynamic Forcementioning

confidence: 99%

The distribution of stresses in rigid fractal-like aggregates in a uniform flow field

Gastaldi

Vanni

2011

Journal of Colloid and Interface Science

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Section: Evaluation Of the Hydrodynamic Forcementioning

confidence: 99%

The distribution of stresses in rigid fractal-like aggregates in a uniform flow field

Gastaldi

Vanni

2011

Journal of Colloid and Interface Science

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“…For a fixed geometry, as in the lattice calculations described in § 3, the relaxation parameter has no effect. As suggested by Ichiki & Brady (2001), the breakdown of the method of reflections can also be overcome by the use of a conjugate-gradient-type iterative method. The generalized minimum residual method (GMRES) was used here, and it was found that very accurate results can always be obtained with very few iterations.…”

Section: Force Lawsmentioning

confidence: 99%

“…Determining the forces is the resistance formulation of the problem -for a given configuration of particles and particle velocities, the particle forces and force moments are calculated. It has recently been shown (Ichiki & Brady 2001) that the method of reflections (which corresponds to the simplest iterative scheme for the inversion of the mobility matrix) can be divergent when more than two particles are present.…”

Section: Force Lawsmentioning

confidence: 99%

Accelerated Stokesian Dynamics simulations

2001

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A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the many-body longrange interactions, where the Ewald-summed wave-space contribution is calculated as a Fourier transform sum and in the iterative inversion of the now sparse resistance matrix. The new method is applied to problems in the rheology of both structured and random suspensions, and accurate results are obtained with much larger numbers of particles. With access to larger N, the high-frequency dynamic viscosities and short-time self-diffusivities of random suspensions for volume fractions above the freezing point are now studied. The ASD method opens up an entire new class of suspension problems that can be investigated, including particles of non-spherical shape and a distribution of sizes, and the method can readily be extended to other low-Reynolds-number-flow problems. IntroductionNumerical simulations of the behaviour of suspensions of particles provide a valuable tool for understanding many complex rheological phenomena. Through simulations both the macroscopic suspension properties and the suspension microstructure have been studied, and insight into structure-property relationships has been obtained Foss & Brady 2000). Determining the hydrodynamic interactions among particles in Stokes flow (small Reynolds number), however, can be a complicated and computationally expensive task, mainly owing to the long-range nature of the interactions and the presence of strong lubrication effects when particles are in close proximity to each other. The fluid velocity disturbance caused by a particle on which a net external force acts decays as 1/r, where r is the distance from the particle, and therefore the hydrodynamic interactions cannot be truncated and no simple pairwise-additive approximation can be made. In addition, the presence of lubrication effects makes conventional numerical techniques (such as the boundary-integral technique) expensive computationally when two particles approach each other.Durlofsky, Brady & Bossis (1987) developed a method that successfully accounts for both the many-body interactions and the near-field lubrication effects by splitting the hydrodynamic interactions into a far-field mobility calculation and a pairwise additive resistance calculation. The main advantage of the method is that a relatively small number of unknowns per particle is sufficient to solve many dynamic simulation problems adequately. The main disadvantage of the method, however, is that it

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“…I is unit tensor. Ichiki and Brady [16] have shown the equivalence between the method of reflections and inversion of mobility matrix.…”

Section: Accelerated Stokesian Dynamics Without Adjustable Parametermentioning

confidence: 98%

“…This is the essence of reflection method. The method of reflections of the force version can be expressed in a matrix form as follows [16] …”

Section: Accelerated Stokesian Dynamics Without Adjustable Parametermentioning

confidence: 99%

Multi-scale calculation of settling speed of coarse particles by accelerated Stokesian dynamics without adjustable parameter

Wang

Zhou

2009

Acta Mech Sin

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The calculation of settling speed of coarse particles is firstly addressed, with accelerated Stokesian dynamics without adjustable parameters, in which far field force acting on the particle instead of particle velocity is chosen as dependent variables to consider inter-particle hydrodynamic interactions. The sedimentation of a simple cubic array of spherical particles is simulated and compared to the results available to verify and validate the numerical code and computational scheme. The improved method keeps the same computational cost of the order O(N log N ) as usual accelerated Stokesian dynamics does. Then, more realistic random suspension sedimentation is investigated with the help of Mont Carlo method. The computational results agree well with experimental fitting. Finally, the sedimentation of finer cohesive particle, which is often observed in estuary environment, is presented as a further application in coastal engineering.

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Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics

Cited by 22 publications

References 10 publications

The distribution of stresses in rigid fractal-like aggregates in a uniform flow field

The distribution of stresses in rigid fractal-like aggregates in a uniform flow field

Accelerated Stokesian Dynamics simulations

Multi-scale calculation of settling speed of coarse particles by accelerated Stokesian dynamics without adjustable parameter

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