arXiv subjects

Raimund Wegener

Publications and source records attributed to Raimund Wegener.

15 recordsLinked to original sources

arXiv2026

Data-driven subsampling rates for diffusion parameter estimation of SDEs

We study the problem of diffusion parameter estimation for stochastic differential equation (SDE) models in scenarios where data and model are compatible only on specific scales that have yet to be determined. We introduce a simple and efficient method for selecting suitable rates at which given time series data should be subsampled in order to ensure that the statistical structure of the subsampled data is consistent with the behavior of the SDE model on an infinitesimal scale. Our approach is based on analyzing the statistics of the lengths of monotonically increasing or decreasing segments in the subsampled data sequence, which we refer to as monotone runs. As an analytical foundation, we prove for a large class of SDEs with additive noise that the lengths of monotone runs at an infinitesimal scale are approximately geometrically distributed with success probability $1/2$. This universal characterization is employed to derive an automated method for selecting appropriate subsampling rates for given time series data that is directly applicable in real-world scenarios and does not rely on an asymptotic framework of multiscale diffusions. The approach is demonstrated using an application from industrial mathematics concerning surrogate models for fiber lay-down curves in production processes of nonwoven textiles.

math.PR↗

arXiv2025

Random field reconstruction of inhomogeneous turbulence. Part II: Numerical approximation and simulation

A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors. This article concerns the numerical discretization and implementation of the model and discusses its key features by means of numerical simulations. We present a suitable discretization scheme that combines a randomized quadrature method for stochastic integrals with a local linearization of the non-uniform advection of the turbulent structures by the mean flow. The convergence of the scheme towards the continuous model is verified analytically. Moreover, we describe an efficient algorithmic implementation that allows for flexible local evaluations of the simulated turbulence field. The main features of the model are illustrated by a variety of simulation results, each highlighting specific aspects such as the influence of the inhomogeneous model parameters on the generated fluctuations, spatio-temporal ergodicity properties under inhomogeneous flow conditions, and the validity of Kolmogorov's two-thirds law in dependence on the local turbulence Reynolds number.

physics.flu-dyn↗

arXiv2024

Viscoelastic model hierarchy for fiber melt spinning of semi-crystalline polymers

In the fiber melt spinning of semi-crystalline polymers, the degree of crystallization can be non-homogeneous over the cross-section of the fiber, affecting the properties of the end product. For simulation-based process design, the question arises as to which fiber quantities and hence model equations must be resolved in radial direction to capture all practically relevant effects and at the same time imply a model that can be computed with reasonable effort. In this paper, we present a hierarchy of viscoelastic two-phase fiber models ranging from a complex, fully resolved and highly expensive three-dimensional description to a cross-sectionally averaged, cheap-to-evaluate one-dimensional model. In particular, we propose a novel stress-averaged one-two-dimensional fiber model, which circumvents additional assumptions on the inlet profiles needed in the established stress-resolved fiber model by Doufas et al.\ (2001). Simulation results demonstrate the performance and application regime of the dimensionally reduced models. The novel stress-averaged variant provides fast and reliable results, especially in the regime of low flow-enhanced crystallization.

physics.flu-dyn↗

arXiv2024

Simulation-based High-Speed Elongational Rheometer for Carreau-type Materials

For the simulation-based design of fiber melt spinning processes, the accurate modeling of the processed polymer with regard to its material behavior is crucial. In this work, we develop a high-speed elongational rheometer for Carreau-type materials, making use of process simulations and fiber diameter measurements. The procedure is based on a unified formulation of the fiber spinning model for all material types (Newtonian and non-Newtonian), whose material laws are strictly monotone in the strain rate. The parametrically described material law for the elongational viscosity implies a nonlinear optimization problem for the parameter identification, for which we propose an efficient, robust gradient-based method. The work can be understood as a proof of concept, a generalization to other, more complex materials is possible.

math.NA↗

arXiv2023

Random field reconstruction of inhomogeneous turbulence. Part I: Modeling and analysis

We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation of the model properties and efficient numerical simulation. The model is fully continuous and based on an explicit representation formula in terms of stochastic integrals combining moving average and Fourier-type representations in time and space, respectively. The structure of the model is systematically derived from spectral representations of homogeneous fields by means of suitable stochastic integral transformations that ensure the preservation of consistency properties when progressing to the case of inhomogeneous flow characteristics. Moreover, we employ a two-scale approach that separates a macro scale related to the variations of the characteristic flow quantities from a representative turbulence scale on which the fluctuations are modeled, allowing to assess the model properties by asymptotic analysis w.r.t. the scale ratio. In particular, a novel inhomogeneous ergodicity result establishes the recovery of the inhomogeneous characteristic flow quantities by means of local averages of a single sample path in time and space.

math.PR↗

arXiv2021

On flow-enhanced crystallization in fiber spinning: Asymptotically justified boundary conditions for numerics of a stiff viscoelastic two-phase model

For flow-enhanced crystallization in fiber spinning, the viscoelastic two-phase fiber models by Doufas et al. (J. Non-Newton. Fluid Mech., 2000) and Shrikhande et al. (J. Appl. Polym. Sci., 2006) are state of the art. However, the boundary conditions associated to the onset of crystallization are still under discussion, as their choice might cause artificial boundary layers and numerical difficulties. In this paper we show that the model class of ordinary differential equations is singularly perturbed in a small parameter belonging to the semi-crystalline relaxation time and derive asymptotically justified boundary conditions. Their effect on the overall solution behavior is restricted to a small region near the onset of crystallization. But their impact on the performance of the numerical solvers is huge, since artificial layering, ambiguities and parameter tunings are avoided. The numerics becomes fast and robust and opens the field for simulation-based process design and material optimization.

physics.flu-dyn↗

arXiv2020

Efficient Graph-based Tensile Strength Simulations of Random Fiber Structures

In this paper, we propose a model-simulation framework for virtual tensile strength tests of random fiber structures, as they appear in nonwoven materials. The focus is on the efficient handling with respect to the problem-inherent multi-scales and randomness. In particular, the interplay of the random microstructure and deterministic structural production-related features on the macro-scale makes classical homogenization-based approaches computationally complex and costly. In our approach we model the fiber structure to be graph-based and of truss-type, equipped with a nonlinear elastic material law. Describing the tensile strength test by a sequence of force equilibria with respect to varied boundary conditions, its embedding into a singularly perturbed dynamical system is advantageous with regard to statements about solution theory and convergence of numerical methods. A problem-tailored data reduction provides additional speed-up, Monte-Carlo simulations account for the randomness. This work serves as a proof of concept and opens the field to optimization.

math.NA↗

arXiv2019

Modeling and Simulation of Curved Fibers in Dry Spinning Scenarios

Dry spinning is characterized by the simultaneous production of multiple thin polymeric fibers in airflows and the evaporation of the solvent contained in these fibers. This involves fiber-air interactions as well as radial diffusion effects over the fiber cross-sections. Recent models for fibers in such production processes assume the fiber curves to be strictly uni-axial. But there are industrial setups showing airflow induced lateral movements of the fibers which creates the need for curved fiber models. In this paper we present a special Cosserat rod model that describes curved fibers in such dry spinning processes. Adapting the efficient simulation framework from the uni-axial fiber setting makes the simulation of industrial setups for multiple curved fibers with two-way coupled airflows possible, for which we present results for the first time in literature.

physics.app-ph↗

arXiv2019

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 $k$-$\epsilon$ 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.

physics.flu-dyn↗

arXiv2018

An Efficient Numerical Framework for Fiber Spinning Scenarios with Evaporation Effects in Airflows

In many spinning processes, as for example in dry spinning, solvent evaporates out of the spun jets and leads to thinning and solidification of the produced fibers. Such production processes are significantly driven by the interaction of the fibers with the surrounding airflow. Faced with industrial applications producing up to several hundred fibers simultaneously, the direct numerical simulation of the three-dimensional multiphase, multiscale problem is computationally extremely demanding and thus in general not possible. In this paper, we hence propose a dimensionally reduced, efficiently evaluable fiber model that enables the realization of fiber-air interactions in a two-way coupling with airflow computations. For viscous dry spinning of an uni-axial two-phase flow, we deduce one-dimensional equations for fiber velocity and stress from cross-sectional averaging and combine them with two-dimensional advection-diffusion equations for polymer mass fraction and temperature revealing the radial effects that are observably present in experiments. For the numerical treatment of the resulting parametric boundary value problem composed of one-dimensional ordinary differential equations and two-dimensional partial differential equations we develop an iterative coupling algorithm. Thereby, the solution of the advection-diffusion equations is implicitly given in terms of Green's functions and leads for the surface values to Volterra integral equations of second kind with singular kernel, which we can solve very efficiently by the product integration method. For the ordinary differential equations a suitable collocation-continuation procedure is presented. Compared with the referential solution of a three-dimensional setting, the numerical results are very convincing. They provide a good approximation while drastically reducing the computational time.

physics.flu-dyn↗

arXiv2017

Whipping of electrified visco-capillary jets in airflows

An electrified visco-capillary jet shows different dynamic behavior, such as cone forming, breakage into droplets, whipping and coiling, depending on the considered parameter regime. The whipping instability that is of fundamental importance for electrospinning has been approached by means of stability analysis in previous papers. In this work we alternatively propose a model framework in which the instability can be computed straightforwardly as the stable stationary solution of an asymptotic Cosserat rod description. For this purpose, we adopt a procedure by Ribe (Proc. Roy. Soc. Lond. A, 2004) describing the jet dynamics with respect to a frame rotating with the a priori unknown whipping frequency that itself becomes part of the solution. The rod model allows for stretching, bending and torsion, taking into account inertia, viscosity, surface tension, electric field and air drag. For the resulting parametric boundary value problem of ordinary differential equations we present a continuation-collocation method. On top of an implicit Runge-Kutta scheme of fifth order, our developed continuation procedure makes the efficient and robust simulation and navigation through a high-dimensional parameter space possible. Despite the simplicity of the employed electric force model the numerical results are convincing, the whipping effect is qualitatively well characterized.

physics.flu-dyn↗

arXiv2016

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.

math.PR↗

arXiv2015

Low-Mach-number--slenderness limit for elastic Cosserat rods

This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e. low-Mach-number--slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a spatial Gauss-Legendre collocation and an $\alpha$-method in time.

math.AP↗

arXiv2012

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.

math-ph↗

arXiv2012

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 $\epsilon$-regularized string is generally applicable. But containing the slenderness ratio $\epsilon$ 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.

math-ph↗