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Numerical study of a sphere descending along an inclined slope in a liquid
The descending process of a sphere rolling and/or sliding along an inclined
slope in a liquid involves interactions between the hydrodynamic forces on the sphere
and the contact forces between the sphere and the plane. In this study, the descending
process of sphere in a liquid was examined using coupled LBM-DEM technique. The
effects of slope angle, viscosity and friction coefficient on the movement of a sphere
were investigated. Two distinct descending patterns were observed: (a) a stable
rolling/sliding movement along the slope, and (b) a fluctuating pattern along the slope.
Five dimensionless coefficients (Reynolds number (Re), drag coefficient, lift
coefficient, moment coefficient and rolling coefficient) were used to analyze the
observed processes. The vortex structure in the wake of the sphere gives a lift force to
the sphere, which in turn controls the different descending patterns. It is found that the
generation of a vortex is not only governed by Re, but also by particle rotation.
Relationships between the forces/moments and the dimensionless coefficients are
established
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
Truncation errors of the D3Q19 lattice model for the lattice Boltzmann method
We comment on the truncation error analysis and numerical artifacts of the D3Q19 lattice Boltzmann model reported in Silva et al. [3]. We present corrections for specific spatial truncation error terms in the momentum conservation equations. By introducing an improved discrete equilibrium for the D3Q19 stencil, we show that the reported spurious currents in a square channel duct flow are caused by the form of the discrete equilibrium and are not due to the structure and isotropy properties of the D3Q19 velocity set itself. Numerical experiments on a square channel and a more complex nozzle geometry confirm these results
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