152 research outputs found
Dynamics of particle sedimentation in viscoelastic fluids: A numerical study on particle chain in two-dimensional narrow channel
In this article we present a numerical method for simulating the
sedimentation of circular particles in two-dimensional channel filled with a
viscoelastic fluid of FENE-CR type, which is generalized from a
domain/distributed Lagrange multiplier method with a factorization approach for
Oldroyd-B fluids developed in [J. Non-Newtonian Fluid Mech. 156 (2009) 95].
Numerical results suggest that the polymer extension limit L for the FENE-CR
fluid has no effect on the final formation of vertical chain for the cases of
two disks and three disks in two-dimensional narrow channel, at least for the
values of L considered in this article; but the intermediate dynamics of
particle interaction before having a vertical chain can be different for the
smaller values of L when increasing the relaxation time. For the cases of six
particles sedimenting in FENE-CR type viscoelastic fluid, the formation of
chain of 4 to 6 disks does depend on the polymer extension limit L. For the
smaller values of L, FENE-CR type viscoelastic fluid can not bring them
together like the case of these particles settling in a vertical chain
formation in Oldroyd-B fluid; but two separated chains of three disks are
formed. Similar results for the case of ten disks are also obtained. The
numerical results of several more particle cases suggest that for smaller
values of L, the length of the vertical chain is shorter and the size of
cluster is smaller.Comment: 20 pages and 13 figures. arXiv admin note: text overlap with
arXiv:1607.0600
Option Pricing Accuracy for Estimated Heston Models
We consider assets for which price and squared volatility are
jointly driven by Heston joint stochastic differential equations (SDEs). When
the parameters of these SDEs are estimated from sub-sampled data , estimation errors do impact the classical option pricing PDEs. We
estimate these option pricing errors by combining numerical evaluation of
estimation errors for Heston SDEs parameters with the computation of option
price partial derivatives with respect to these SDEs parameters. This is
achieved by solving six parabolic PDEs with adequate boundary conditions. To
implement this approach, we also develop an estimator for the
market price of volatility risk, and we study the sensitivity of option pricing
to estimation errors affecting . We illustrate this approach by
fitting Heston SDEs to 252 daily joint observations of the S\&P 500 index and
of its approximate volatility VIX, and by numerical applications to European
options written on the S\&P 500 index
Circular band formation for incompressible viscous fluid--rigid particle mixtures in a rotating cylinder
In this paper we have investigated a circular band formation of fluid-rigid
particle mixtures in a fully filled cylinder horizontally rotating about its
cylinder axis by direct numerical simulation. These phenomena are modeled by
the Navier-Stokes equations coupled to the Euler-Newton equations describing
the rigid solid motion of the non-neutrally particles. The formation of
circular bands studied in this paper is not resulted by mutual interaction
between the particles and the periodic inertial waves in the cylinder axis
direction (as suggested in Phys. Rev. E, 72, 021407 (2005)), but due to the
interaction of particles. When a circular band is forming, the part of the band
formed by the particles moving downward becomes more compact due to the
particle interaction strengthened by the downward acceleration from the
gravity. The part of a band formed by the particles moving upward is always
loosening up due to the slow down of the particle motion by the counter effect
of the gravity. To form a compact circular band (not a loosely one), enough
particles are needed to interact among themselves continuously through the
entire circular band at a rotating rate so that the upward diffusion of
particles can be balanced by the compactness process when these particles
moving downward.Comment: 12 pages; 12 figure
Computational Techniques for Simulating Natural Convection in Three-Dimensional Enclosures with Tetrahedral Finite Elements
This article discusses computational techniques for simulating natural
convection in three-dimensional domains using finite element methods with
tetrahedral elements. These techniques form a new numerical procedure for this
kind of problems. In this procedure, the treatment of advection by a wave
equation approach is extended to three-dimensional unstructured meshes with
tetrahedra.
Numerical results of natural convection of an incompressible Newtonian fluid
in a cubical enclosure at Rayleigh numbers in the range to are
obtained and they are in good agreement with those in literature obtained by
other methods
A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids
We present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD)
method for simulating fluid-particle interaction in Oldroyd-B fluids under
creeping conditions. The results concerning two ball interaction in a three
dimensional (3D) bounded shear flow are obtained for Weissenberg numbers up to
1 . The pass and return trajectories of the two ball mass centers are similar
to those in a Newtonian fluid; but they lose the symmetry due to the effect of
elastic force arising from viscoelastic fluids. A tumbling chain of two balls
(a dipole) may occur, depending on the value of the Weissenberg number and the
initial vertical displacement of the ball mass center to the middle plane
between two walls.Comment: 26 pages and 14 Figure
A New Operator Splitting Method for Euler's Elastica Model
Euler's elastica model has a wide range of applications in Image Processing
and Computer Vision. However, the non-convexity, the non-smoothness and the
nonlinearity of the associated energy functional make its minimization a
challenging task, further complicated by the presence of high order derivatives
in the model. In this article we propose a new operator-splitting algorithm to
minimize the Euler elastica functional. This algorithm is obtained by applying
an operator-splitting based time discretization scheme to an initial value
problem (dynamical flow) associated with the optimality system (a system of
multivalued equations). The sub-problems associated with the three fractional
steps of the splitting scheme have either closed form solutions or can be
handled by fast dedicated solvers. Compared with earlier approaches relying on
ADMM (Alternating Direction Method of Multipliers), the new method has,
essentially, only the time discretization step as free parameter to choose,
resulting in a very robust and stable algorithm. The simplicity of the
sub-problems and its modularity make this algorithm quite efficient.
Applications to the numerical solution of smoothing test problems demonstrate
the efficiency and robustness of the proposed methodology
The dynamics of inextensible capsules in shear flow under the effect of the nature state
The effect of the nature state on the motion of an inextensible capsule in
simple shear flow has been studied in this paper. Besides the viscosity ratio
of the internal fluid and external fluid of the capsule, the nature state
effect also plays a role for having the transition between two well known
motions, tumbling and tank-treading (TT) with the long axis oscillating about a
fixed inclination angle (a swinging mode), when varying the shear rate. The
intermittent region between tumbling and TT with a swinging mode of the capsule
with a biconcave rest shape has been obtained in a narrow range of the
capillary number. In such region, the dynamics of the capsule is a mixture of
tumbling and TT with a swinging mode; when having the tumbling motion, the
membrane tank-tread backward and forward within a small range. As the capillary
number is very close to and below the threshold for the pure TT with a swinging
mode, the capsule tumbles once after several TT periods in each cycle. The
number of TT periods in one cycle decreases with respect to the decreasing of
the capillary number, until the capsule has one tumble and one TT period
alternatively and such alternating motion exists over a range of the capillary
number; and then the capsule performs more tumbling between two consecutive TT
periods when reducing the capillary number further, and finally shows pure
tumbling. The critical value of the swelling ratio for having the intermittent
region has been estimated
An oscillating motion of a red blood cell and a neutrally buoyant particle in Poiseuille flow in a narrow channel
Two motions of oscillation and vacillating breathing (swing) of a red blood
cell have been observed in bounded Poiseuille flows (Phys. Rev. E 85, 16307
(2012)). To understand such motions, we have studied the oscillating motion of
a neutrally buoyant rigid particle of the same shape in Poiseuille flow in a
narrow channel and obtained that the crucial point is to have the particle
interacting with Poiseuille flow with its mass center moving up and down in the
channel central region. Since the mass center of the cell migrates toward the
channel central region, its oscillating motion of the inclination angle is
similar to the aforementioned motion as long as the cell keeps the shape of
long body. But as the up-and-down oscillation of the cell mass center damps
out, the oscillating motion of the inclination angle also damps out and the
cell inclination angle approaches to a fixed angle.Comment: 15 pages, 17 figure
A Modular, Operator Splitting Scheme for Fluid-Structure Interaction Problems with Thick Structures
We present an operator-splitting scheme for fluid-structure interaction (FSI)
problems in hemodynamics, where the thickness of the structural wall is
comparable to the radius of the cylindrical fluid domain. The equations of
linear elasticity are used to model the structure, while the Navier-Stokes
equations for an incompressible viscous fluid are used to model the fluid. The
operator splitting scheme, based on Lie splitting, separates the elastodynamics
structure problem, from a fluid problem in which structure inertia is included
to achieve unconditional stability. We prove energy estimates associated with
unconditional stability of this modular scheme for the full nonlinear FSI
problem defined on a moving domain, without requiring any sub-iterations within
time steps. Two numerical examples are presented, showing excellent agreement
with the results of monolithic schemes. First-order convergence in time is
shown numerically. Modularity, unconditional stability without temporal
sub-iterations, and simple implementation are the features that make this
operator-splitting scheme particularly appealing for multi-physics problems
involving fluid-structure interaction.Comment: International Journal for Numerical Methods in Fluid
Discrete Dynamical System Approaches For Boolean Polynomial Optimization
In this article, we discuss the numerical solution of Boolean polynomial
programs by algorithms borrowing from numerical methods for differential
equations, namely the Houbolt and Lie schemes, and a Runge-Kutta scheme. We
first introduce a quartic penalty functional (of Ginzburg-Landau type) to
approximate the Boolean program by a continuous one and prove some convergence
results as the penalty parameter converges to . We prove also
that, under reasonable assumptions, the distance between local minimizers of
the penalized problem and the (finite) set of solutions of the Boolean program
is of order . Next, we introduce algorithms for the numerical
solution of the penalized problem, these algorithms relying on the Houbolt, Lie
and Runge-Kutta schemes, classical methods for the numerical solution of
ordinary or partial differential equations. We performed numerical experiments
to investigate the impact of various parameters on the convergence of the
algorithms. Numerical tests on random generated problems show good performances
for our approaches. Indeed, our algorithms converge to local minimizers often
close to global minimizers of the Boolean program, and the relative
approximation error being of order .Comment: 29 pages, 30 figure
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