TY - JOUR
T1 - A scalable computational platform for particulate Stokes suspensions
AU - Yan, Wen
AU - Corona, Eduardo
AU - Malhotra, Dhairya
AU - Veerapaneni, Shravan
AU - Shelley, Michael
N1 - Funding Information:
We thank E. Lushi for useful conversations. EC and SV acknowledge support from NSF under grants DMS-1454010 and DMS-1719834 . The work of SV was also supported by the Flatiron Institute. DM acknowledges support from Office of Naval Research under award number N00014-17-1-2451 and Simons Foundation/SFARI ( 560651 , AB). MJS acknowledges the support of NSF Grants DMR-1420073 (NYU MRSEC), DMS-1463962 , and DMS-1620331 .
Funding Information:
We thank E. Lushi for useful conversations. EC and SV acknowledge support from NSF under grants DMS-1454010 and DMS-1719834. The work of SV was also supported by the Flatiron Institute. DM acknowledges support from Office of Naval Research under award number N00014-17-1-2451 and Simons Foundation/SFARI (560651, AB). MJS acknowledges the support of NSF Grants DMR-1420073 (NYU MRSEC), DMS-1463962, and DMS-1620331. Our implementation of this framework will be released on GitHub (https://github.com/wenyan4work/SphereSimulator) as an open-source software following the publication of this article.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric ‘non-overlapping’ constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8×104 particles with approximately 4×107 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.
AB - We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric ‘non-overlapping’ constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8×104 particles with approximately 4×107 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.
KW - Boundary integral methods
KW - Collision resolution
KW - Constrained optimization
KW - Fluid dynamics
KW - Suspensions
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U2 - 10.1016/j.jcp.2020.109524
DO - 10.1016/j.jcp.2020.109524
M3 - Article
AN - SCOPUS:85085201377
VL - 416
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 109524
ER -