666 research outputs found
A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations
A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself
Multiple-Play Bandits in the Position-Based Model
Sequentially learning to place items in multi-position displays or lists is a
task that can be cast into the multiple-play semi-bandit setting. However, a
major concern in this context is when the system cannot decide whether the user
feedback for each item is actually exploitable. Indeed, much of the content may
have been simply ignored by the user. The present work proposes to exploit
available information regarding the display position bias under the so-called
Position-based click model (PBM). We first discuss how this model differs from
the Cascade model and its variants considered in several recent works on
multiple-play bandits. We then provide a novel regret lower bound for this
model as well as computationally efficient algorithms that display good
empirical and theoretical performance
A pressure impulse theory for hemispherical liquid impact problems
Liquid impact problems for hemispherical fluid domain are considered. By
using the concept of pressure impulse we show that the solution of the flow
induced by the impact is reduced to the derivation of Laplace's equation in
spherical coordinates with Dirichlet and Neumann boundary conditions. The
structure of the flow at the impact moment is deduced from the spherical
harmonics representation of the solution. In particular we show that the slip
velocity has a logarithmic singularity at the contact line. The theoretical
predictions are in very good agreement both qualitatively and quantitatively
with the first time step of a numerical simulation with a Navier-Stokes solver
named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of
Mechanics - B/Fluid
Continuum simulation of the discharge of the granular silo: a validation test for the mu(I)-visco-plastic flow law
Using both a continuum Navier-Stokes solver, with the mu(I)-flow-law
implemented to model the viscous behavior, and the discrete Contact Dynamics
algorithm, the discharge of granular silos is simulated in two dimensions from
the early stages of the discharge until complete release of the material. In
both cases, the Beverloo scaling is recovered. We first do not attempt
quantitative comparison, but focus on the qualitative behavior of velocity and
pressure at different locations in the flow. A good agreement is obtained in
the regions of rapid flows, while areas of slow creep are not entirely captured
by the continuum model. The pressure field shows a general good agreement. The
evolution of the free surface implies differences, however, the bulk
deformation is essentially identical in both approaches. The influence of the
parameters of the mu(I)-flow-law is systematically investigated, showing the
importance of the dependence on the inertial number I to achieve quantitative
agreement between continuum and discrete discharge. The general ability of the
continuum model to reproduce qualitatively the granular behavior is found to be
very encouraging.Comment: 12 pages, 15 figure
Comparison of computations of asymptotic flow models in a constricted channel
International audienceWe aim at comparing computations with asymptotic models issued from incom- pressible Navier-Stokes at high Reynolds number: the Reduced Navier-Stokes/Prandtl (RNS/P) equations and the Double Deck (DD) equations. We treat the case of the steady two dimensional flow in a constricted pipe. In particular, finite differences and finite element solvers are compared for the RNS/P equations. It results from this study that the two codes compare well. Numerical examples also illustrate the interest of these asymptotic models as well as the flexibility of the finite element solver
Modelling the human pharyngeal airway: validation of numerical simulations using in vitro experiments
In the presented study, a numerical model which predicts the flow-induced
collapse within the pharyngeal airway is validated using in vitro measurements.
Theoretical simplifications were considered to limit the computation time.
Systematic comparisons between simulations and measurements were performed on
an in vitro replica, which reflects asymmetries of the geometry and of the
tissue properties at the base of the tongue and in pathological conditions
(strong initial obstruction). First, partial obstruction is observed and
predicted. Moreover, the prediction accuracy of the numerical model is of 4.2%
concerning the deformation (mean quadratic error on the constriction area). It
shows the ability of the assumptions and method to predict accurately and
quickly a fluid-structure interaction
The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra
The granular silo is one of the many interesting illustrations of the
thixotropic property of granular matter: a rapid flow develops at the outlet,
propagating upwards through a dense shear flow while material at the bottom
corners of the container remains static. For large enough outlets, the
discharge flow is continuous; however, by contrast with the clepsydra for which
the flow velocity depends on the height of fluid left in the container, the
discharge rate of granular silos is constant. Implementing a plastic rheology
in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constant
friction), we simulate the continuum counterpart of the granular silo. Doing
so, we obtain a constant flow rate during the discharge and recover the
Beverloo scaling independently of the initial filling height of the silo. We
show that lowering the value of the coefficient of friction leads to a
transition toward a different behavior, similar to that of a viscous fluid, and
where the filling height becomes active in the discharge process. The pressure
field shows that large enough values of the coefficient of friction (
0.3) allow for a low-pressure cavity to form above the outlet, and can thus
explain the Beverloo scaling. In conclusion, the difference between the
discharge of a hourglass and a clepsydra seems to reside in the existence or
not of a plastic yield stress.Comment: 6 pages, 6 figure
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