136 research outputs found
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 rigid-body motions. Here we develop a
block-diagonal 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. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method 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 rigid body equations converges in a bounded number of iterations
regardless of the system size. 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 non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
A fluctuating boundary integral method for Brownian suspensions
We present a fluctuating boundary integral method (FBIM) for overdamped
Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid
particles of complex shape immersed in a Stokes fluid. We develop a novel
approach for generating Brownian displacements that arise in response to the
thermal fluctuations in the fluid. Our approach relies on a first-kind boundary
integral formulation of a mobility problem in which a random surface velocity
is prescribed on the particle surface, with zero mean and covariance
proportional to the Green's function for Stokes flow (Stokeslet). This approach
yields an algorithm that scales linearly in the number of particles for both
deterministic and stochastic dynamics, handles particles of complex shape,
achieves high order of accuracy, and can be generalized to three dimensions and
other boundary conditions. We show that Brownian displacements generated by our
method obey the discrete fluctuation-dissipation balance relation (DFDB). Based
on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa
Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017],
near-field contributions to the Brownian displacements are efficiently
approximated by iterative methods in real space, while far-field contributions
are rapidly generated by fast Fourier-space methods based on fluctuating
hydrodynamics. FBIM provides the key ingredient for time integration of the
overdamped Langevin equations for Brownian suspensions of rigid particles. We
demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of
suspensions of starfish-shaped bodies using a random finite difference temporal
integrator.Comment: Submitted to J. Comp. Phy
Recommended from our members
Office of Advanced Scientific Computing Research Applied Mathematics Principal Program Annual PI Meeting Abstracts
Recommended from our members
Schnelle Löser für partielle Differentialgleichungen
[no abstract available
- …