Asymptotics and numerics for the upper-convected Maxwell model describing transient curved viscoelastic jets

Marheineke N, Liljegren-Sailer B, Lorenz M, Wegener R (2016)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

Publisher: World Scientific Publishing

Book Volume: 26

Pages Range: 569-600

Journal Issue: 3

DOI: 10.1142/S021820251650010X

Abstract

This work deals with the modeling and simulation of non-Newtonian jet dynamics as it occurs in fiber spinning processes. Proceeding from a three-dimensional instationary boundary value problem of upper-convected Maxwell equations, we present a strict systematic derivation of a one-dimensional viscoelastic string model by using asymptotic analysis in the slenderness ratio of the jet. The model allows for the unrestricted motion and shape of the jet's curve, and its deduction extends the hitherto existing uniaxial asymptotic approaches. However, the system of partial differential equations with algebraic constraint has a varying character (hyperbolic, hyperbolic-elliptic, parabolic deficiency). Its applicability range turns out to be limited depending on the physical parameters and the boundary conditions (i.e. singular perturbation). Numerical results are discussed for the hyperbolic regime of gravitational inflow-outflow set-ups which become relevant in drawing and extrusion processes. The simulations are performed with a normal form total upwind scheme in space and an implicit time-integration ensuring convergence of first order.

Authors with CRIS profile

Nicole Marheineke Professur für Wissenschaftliches Rechnen Björn Liljegren-Sailer Professur für Wissenschaftliches Rechnen

Involved external institutions

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) / Fraunhofer Institute for Industrial Mathematics DE Germany (DE)

How to cite

APA:

Marheineke, N., Liljegren-Sailer, B., Lorenz, M., & Wegener, R. (2016). Asymptotics and numerics for the upper-convected Maxwell model describing transient curved viscoelastic jets. Mathematical Models & Methods in Applied Sciences, 26(3), 569-600. https://doi.org/10.1142/S021820251650010X

MLA:

Marheineke, Nicole, et al. "Asymptotics and numerics for the upper-convected Maxwell model describing transient curved viscoelastic jets." Mathematical Models & Methods in Applied Sciences 26.3 (2016): 569-600.

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