37 research outputs found
Stochastic fiber dynamics in a spatially semi-discrete setting
We investigate a spatially discrete surrogate model for the dynamics of a
slender, elastic, inextensible fiber in turbulent flows. Deduced from a
continuous space-time beam model for which no solution theory is available, it
consists of a high-dimensional second order stochastic differential equation in
time with a nonlinear algebraic constraint and an associated Lagrange
multiplier term. We establish a suitable framework for the rigorous formulation
and analysis of the semi-discrete model and prove existence and uniqueness of a
global strong solution. The proof is based on an explicit representation of the
Lagrange multiplier and on the observation that the obtained explicit drift
term in the equation satisfies a one-sided linear growth condition on the
constraint manifold. The theoretical analysis is complemented by numerical
studies concerning the time discretization of our model. The performance of
implicit Euler-type methods can be improved when using the explicit
representation of the Lagrange multiplier to compute refined initial estimates
for the Newton method applied in each time step.Comment: 20 pages; typos removed, references adde
Melt-Blowing of Viscoelastic Jets in Turbulent Airflows: Stochastic Modeling and Simulation
In melt-blowing processes mico- and nanofibers are produced by the extrusion
of polymeric jets into a directed, turbulent high-speed airflow. Up to now the
physical mechanism for the drastic jet thinning is not fully understood, since
in the existing literature the numerically computed/predicted fiber thickness
differs several orders of magnitude from those experimentally measured. Recent
works suggest that this discrepancy might arise from the neglect of the
turbulent aerodynamic fluctuations in the simulations. In this paper we confirm
this suggestion numerically. Due to the complexity of the process direct
numerical simulations of the multiscale-multiphase problem are not possible.
Hence, we develop a numerical framework for a growing fiber in turbulent air
that makes the simulation of industrial setups feasible. For this purpose we
employ an asymptotic viscoelastic model for the fiber. The turbulent effects
are taken into account by a stochastic aerodynamic force model where the
underlying velocity fluctuations are reconstructed from a -
turbulence description of the airflow. Our numerical results show the
significance of the turbulence on the jet thinning and give fiber diameters of
realistic order of magnitude
Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets
The spinning of slender viscous jets can be described asymptotically by
one-dimensional models that consist of systems of partial and ordinary
differential equations. Whereas the well-established string models possess only
solutions for certain choices of parameters and set-ups, the more sophisticated
rod model that can be considered as -regularized string is generally
applicable. But containing the slenderness ratio explicitely in the
equations complicates the numerical treatment. In this paper we present the
first instationary simulations of a rod in a rotational spinning process for
arbitrary parameter ranges with free and fixed jet end, for which the hitherto
investigations longed. So we close an existing gap in literature. The numerics
is based on a finite volume approach with mixed central, up- and down-winded
differences, the time integration is performed by stiff accurate Radau methods
Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations
In melt-blowing very thin liquid fiber jets are spun due to high-velocity air
streams. In literature there is a clear, unsolved discrepancy between the
measured and computed jet attenuation. In this paper we will verify numerically
that the turbulent velocity fluctuations causing a random aerodynamic drag on
the fiber jets -- that has been neglected so far -- are the crucial effect to
close this gap. For this purpose, we model the velocity fluctuations as vector
Gaussian random fields on top of a k-epsilon turbulence description and develop
an efficient sampling procedure. Taking advantage of the special covariance
structure the effort of the sampling is linear in the discretization and makes
the realization possible
The WCET Tool Challenge 2011
Following the successful WCET Tool Challenges in 2006 and 2008, the third event in this series was organized in 2011, again with support from the ARTIST DESIGN Network of Excellence. Following the practice established in the previous Challenges, the WCET Tool Challenge 2011 (WCC'11) defined two kinds of problems to be solved by the Challenge participants with their tools, WCET problems, which ask for bounds on the execution time, and flow-analysis problems, which ask for bounds on the number of times certain parts of the code can be executed. The benchmarks to be used in WCC'11 were debie1, PapaBench, and an industrial-strength application from the automotive domain provided by Daimler AG. Two default execution platforms were suggested to the participants, the ARM7 as "simple target'' and the MPC5553/5554 as a "complex target,'' but participants were free to use other platforms as well. Ten tools participated in WCC'11: aiT, Astr\'ee, Bound-T, FORTAS, METAMOC, OTAWA, SWEET, TimeWeaver, TuBound and WCA
A hierarchy of models for multilane vehicular traffic PART I: Modeling
In the present paper multilane models for vehicular traffic are considered. A microscopic multilane model based on reaction thresholds is developed. Based on this model an Enskog like kinetic model is developed. In particular, care is taken to incorporate the correlations between the vehicles. From the kinetic model a fluid dynamic model is derived. The macroscopic coefficients are deduced from the underlying kinetic model. Numerical simulations are presented for all three levels of description in [10]. Moreover, a comparison of the results is given there