Andreas Meister

NUMERICAL ANALYSIS OF COSSERAT ROD AND STRING MODELS FOR VISCOUS JETS IN ROTATIONAL SPINNING PROCESSES

This work deals with the curling behavior of slender viscous jets in rotational spinning processes. In terms of slender-body theory, an instationary incompressible viscous Cosserat rod model is formulated which differs from the approach of Ribe et al.,18 in the incompressibility approximation and reduces to the string model of Marheineke and Wegener13 for a vanishing slenderness parameter. Focusing exclusively on viscous and rotational effects on the jet in the exit plane near the spinning nozzle, the stationary two-dimensional scenario is described by a two-point boundary value problem of a system of first-order ordinary differential equations for jets center-line, tangent, curvature, velocity, inner shear and traction force and couple. The numerical analysis shows that the rod model covers the string model in an inertia-dominated jet regime. Beyond that it overcomes the limitations of the string model studied by Gotz et al.10 and enables even the handling of the viscous-inertial jet regime. Thus, the rod model shows its applicability for the simulation of industrially relevant parameter ranges and enlarges the domain of validity with respect to the string approach.

Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws

In this paper, we describe a novel formulation of a preconditioned BiCGSTAB algorithm for the solution of ill-conditioned linear systems Ax=b. The developed extension enables the control of the residual rm=b−Axm of the approximate solution xm independent of the specific left, right or two-sided preconditioning technique considered. Thereby, the presented modification does not require any additional computational effort and can be introduced directly into existing computer codes. Furthermore, the proceeding is not restricted to the BiCGSTAB method, hence the strategy can serve as a guideline to extend similar Krylov sub-space methods in the same manner. Based on the presented algorithm, we study the behavior of different preconditioning techniques. We introduce a new physically motivated approach within an implicit finite volume scheme for the system of the Euler equations of gas dynamics which is a typical representative of hyperbolic conservation laws. Thereupon a great variety of realistic flow problems are considered in order to give reliable statements concerning the efficiency and performance of modern preconditioning techniques.

Measurement of phospholipase A2 and 1-alkylglycerophosphocholine acetyltransferase activities in stimulated alveolar macrophages by HPLC analysis of NBD-labeled ether lipids

The importance of phospholipases in cellular signaling and 1-alkylglycerophosphocholine acetyltransferase in the formation of platelet-activating factor (PAF) has stimulated demand for methods to measure these enzyme activities in inflammatory cells. Most of the assays currently used rely on radiolabeled substrates. We have synthesized NBD-labeled ether lipids as substrates for measuring enzyme activities of the PAF cycle and of lysosomal phospholipase A2 (PLA2). The fluorescent lipids were incubated with homogenates of stimulated bovine alveolar macrophages. The generated products were separated from the substrates by HPLC on a normal phase and monitored with a fluorescence detector. NBD-lyso-PAF was well accepted by acetyl- and acyltransferases of the cell-free preparations, which metabolized the substrate into NBD-PAF and NBD-alkyl-acylglycerophosphocholines. Homogenates of stimulated cells showed an enhanced production of NBD-PAF. The increased formation of the biological mediator was dependent on the nature of the stimuli and the time of stimulation. Lysosomal PLA2 was measured with 1-O-(12-NBD-aminododecyl)-2-acyl-sn-glycero-3-phosphocholine as substrate. By varying the pH and the calcium concentration, it was possible to distinguish between the cytosolic PLA2 and the lysosomal PLA2 activity. Optimal conditions for the determination of the lysosomal PLA2 were obtained at pH 4.5 and in the presence of EDTA. Stimulation with particulate agonists induced an enhancement of the lysosomal PLA2 activity in macrophages.

Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets

The spinning of slender viscous jets can be asymptotically described by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas well-established string models only possess solutions for certain choices of parameters and configurations, the more sophisticated rod model is not limited by restrictions. It can be considered as an ?-regularized string model, but containing the slenderness ratio ? in the equations complicates its numerical treatment. We develop numerical schemes for fixed or enlarging (time-dependent) domains, using a finite volume approach in space with mixed central, up- and down-winded differences and stiffly accurate Radau methods for the time integration. For the first time, results of instationary simulations for a fixed or growing jet in a rotational spinning process are presented for arbitrary parameter ranges.

An Implicit Finite Volume Approach of the k - ε Turbulence Model on Unstructured Grids

This paper is devoted to the development of a finite volume method for the computation of turbulent flow fields on unstructured grids. The discretization of the inviscid fluxes is accomplished by means of the modern upwind scheme AUSMDV [35], whereby linear ansatz functions are considered on each control volume to achieve high resolution properties. Furthermore, a central scheme is used for the approximation of the viscous fluxes. The involved operator splitting technique leads to low memory requirement, yields high flexibility concerning the use of particular turbulence models, and preserves a possibly included second order time discretization. The time discretization is performed is an implicit manner, which enables large time steps in comparison with an explicit formulation. The linearization of the numerical flux functions as well as the turbulent and axisymmetric source terms leads to a linear system of equations including a large, sparse, and nonsymmetric matrix. Recently, a systematic investigation and comparison of different preconditioned Krylov subspace methods in the context of real engineering applications was presented [18]. Based on these results, the BiCGSTAB algorithm [31] preconditioned by an incomplete LU factorization is used to solve the linear system of equations. The scheme is finally validated on specific test cases, whereby the results are compared with experimental data, analytical solutions, and numerical simulations of other authors. Die Arbeit beschreibt die Entwicklung einer Finite-Volumen-Methode zur Berechnung turbulenter Stromungsfelder auf unstrukturierten Gittern. Die Diskretisierung der konvektiven Flusse wird mit Hilfe des modernen Upwind-Verfahrens AUSMDV [35] durchgefuhrt, wobei zur Erzielung einer hoheren Auflosung lineare Ansatzfunktionen auf jedem Kontrollvolumen betrachtet werden. Zudem wird ein zentrales Verfahren zur Approximation der viskosen Flusse verwendet. Die genutzte Operator-Splitting-Technik fuhrt zu geringem Speicherplatzbedarf, liefert eine hohe Flexibilitat bezuglich der Nutzung unterschiedlicher Turbulenzmodelle und erhalt die Zeitdiskretisierung zweiter Ordnung. Zur Zeitdiskretisierung wird ein implizites Verfahren genutzt, das im Vergleich zu einer expliziten Formulierung grose Zeitschritte erlaubt. Die Linearisierung der numerischen Flusfunktionen wie auch der turbulenten und axialsymmetrischen Quellterme fuhrt auf ein lineares Gleichungssystem mit einer grosen, schwachbesetzten und unsymmetrischen Matrix. Kurzlich wurde eine systematische Untersuchung und ein Vergleich verschiedener prakonditionierter Krylov-Unterraum-Methoden im Kontext praktischer Ingenieuranwendungen vorgestellt [18]. Basierend auf diesen Resultaten wird der mittels einer unvollstandigen LU-Zerlegung vorkonditionierte BiCGSTAB Algorithmus [31] zur Losung des linearen Gleichungssystems verwendet. Das Verfahren wird abschliesend an verschiedenen Testfallen validiert, wobei die Resultate mit experimentellen Ergebnissen, analytischen Losungen und numerischen Simulationen anderer Autoren verglichen werden.

The Thermoregulation of Infants: Modeling and Numerical Simulation

A mathematical model is developed and used for a computer simulation of the thermoregulation of premature infants. We propose a finite volume technique for the solution of the associated partial differential equation on an unstructured grid. Emphasis is laid on the model and the validation of the numerical scheme. Beside various test runs using real life data, we present a discrete maximum principle for the steady state solution with respect to the non-convex computational domain.

Numerical Treatment of Non-stationary Viscous Cosserat Rod in a Two-Dimensional Eulerian Framework

This work deals with the modeling and simulation of the dynamics of a slender viscous jet as it arises in spinning processes. There exist two classes of asymptotic one-dimensional models for such a jet, string and more complex rod models, that are given by systems of partial and ordinary differential equations. In this paper, we present non-stationary simulations of a rod in an Eulerian framework for arbitrary parameter ranges of 2d spinning where the string models failed so far. The numerical treatment is based on a finite volume approach with mixed central, up- and downwinded differences, the time integration is performed by a Radau method.

A Numerical Method for Compressible and Low Mach Number Fluid Flow

The development of stable and highly accurate numerical methods which can be employed to simulate incompressible as well as compressible flow fields represents an exciting and important task of the future in computational fluid dynamics. The paper is devoted to the investigation and extension of a compressible finite volume method to the low Mach number regime. The scheme represents a box-type method on unstructured grids and the numerical flux function is given by a special combination of the AUSMDV and the Lax-Friedrichs scheme. Nevertheless, the proceeding can be straightforwardly employed within different existing high resolution schemes.

Preconditioned krylov subspace methods for Hyperbolic conservation laws

Implicit finite volume discretizations for hyperbolic conservation laws lead to the problem of solving ill-conditioned linear systems Ax = b. Krylov subspace methods represent an efficient way of solving these systems if they are combined with an appropriate preconditioning strategy. Here, we describe a preconditioned BiCGSTAB algorithm which enables the control of the residual of the approximate solution xm independent of the specific left, right or two-sided preconditioning technique considered. Our presentation allows a systematic comparison of preconditioning techniques which we exploit to demonstrate the efficiency of a physically motivated approach to preconditioning. Our ‘characteristic preconditioner’ takes account of the hyperbolicity of the governing equations and turns out to be competitive with approved strategies like the incomplete LU-factorization. Furthermore, we demonstrate by experiments the superiority of right to left preconditioning.