Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach
We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigidbody motions. Here we develop a blockdiagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blobblob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the RotnePragerYamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single noslip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodicmore »
 Authors:

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 New York Univ., New York, NY (United States)
 New York Univ., New York, NY (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of North Carolina, Chapel Hill, NC (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Communications in Applied Mathematics and Computational Science
 Additional Journal Information:
 Journal Volume: 11; Journal Issue: 2; Journal ID: ISSN 15593940
 Publisher:
 Mathematical Sciences Publishers
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 National Science Foundation (NSF); USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Stokes flow; colloidal suspensions; Stokesian dynamics; immersed boundary method
 OSTI Identifier:
 1393005
Usabiaga, Florencio Balboa, Kallemov, Bakytzhan, Delmotte, Blaise, Bhalla, Amneet Pal Singh, Griffith, Boyce E., and Donev, Aleksandar. Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach. United States: N. p.,
Web. doi:10.2140/camcos.2016.11.217.
Usabiaga, Florencio Balboa, Kallemov, Bakytzhan, Delmotte, Blaise, Bhalla, Amneet Pal Singh, Griffith, Boyce E., & Donev, Aleksandar. Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach. United States. doi:10.2140/camcos.2016.11.217.
Usabiaga, Florencio Balboa, Kallemov, Bakytzhan, Delmotte, Blaise, Bhalla, Amneet Pal Singh, Griffith, Boyce E., and Donev, Aleksandar. 2016.
"Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach". United States.
doi:10.2140/camcos.2016.11.217. https://www.osti.gov/servlets/purl/1393005.
@article{osti_1393005,
title = {Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach},
author = {Usabiaga, Florencio Balboa and Kallemov, Bakytzhan and Delmotte, Blaise and Bhalla, Amneet Pal Singh and Griffith, Boyce E. and Donev, Aleksandar},
abstractNote = {We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigidbody motions. Here we develop a blockdiagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blobblob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the RotnePragerYamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single noslip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigidbody immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigidbody equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the blockdiagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of nonBrownian active nanorods sedimented against a wall.},
doi = {10.2140/camcos.2016.11.217},
journal = {Communications in Applied Mathematics and Computational Science},
number = 2,
volume = 11,
place = {United States},
year = {2016},
month = {1}
}