5,726 research outputs found
Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method
A meshfree Lagrangian method for the fluctuating hydrodynamic equations
(FHEs) with fluid-structure interactions is presented. Brownian motion of the
particle is investigated by direct numerical simulation of the fluctuating
hydrodynamic equations. In this framework a bidirectional coupling has been
introduced between the fluctuating fluid and the solid object. The force
governing the motion of the solid object is solely due to the surrounding fluid
particles. Since a meshfree formulation is used, the method can be extended to
many real applications involving complex fluid flows. A three-dimensional
implementation is presented. In particular, we observe the short and long-time
behaviour of the velocity autocorrelation function (VACF) of Brownian particles
and compare it with the analytical expression. Moreover, the Stokes-Einstein
relation is reproduced to ensure the correct long-time behaviour of Brownian
dynamics.Comment: 24 pages, 2 figure
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
Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations
We present analysis for the reduction of an inertial description of
fluid-structure interactions subject to thermal fluctuations. We show how the
viscous coupling between the immersed structures and the fluid can be
simplified in the regime where this coupling becomes increasingly strong. Many
descriptions in fluid mechanics and in the formulation of computational methods
account for fluid-structure interactions through viscous drag terms to transfer
momentum from the fluid to immersed structures. In the inertial regime, this
coupling often introduces a prohibitively small time-scale into the temporal
dynamics of the fluid-structure system. This is further exacerbated in the
presence of thermal fluctuations. We discuss here a systematic reduction
technique for the full inertial equations to obtain a simplified description
where this coupling term is eliminated. This approach also accounts for the
effective stochastic equations for the fluid-structure dynamics. The analysis
is based on use of the Infinitesmal Generator of the SPDEs and a singular
perturbation analysis of the Backward Kolomogorov PDEs. We also discuss the
physical motivations and interpretation of the obtained reduced description of
the fluid-structure system. Working paper currently under revision. Please
report any comments or issues to [email protected]: 19 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1009.564
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. 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 spatio-temporal
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
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. 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...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
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