Asymptotics and numerics for the upper-convected Maxwell model describing transient curved viscoelastic jets
| Autor: | Nicole Marheineke, Björn Liljegren-Sailer, Raimund Wegener, Maike Lorenz |
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| Přispěvatelé: | Publica |
| Rok vydání: | 2016 |
| Předmět: |
Singular perturbation
Asymptotic analysis Jet (fluid) Partial differential equation Applied Mathematics Mathematical analysis Upwind scheme 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics symbols.namesake Maxwell's equations Modeling and Simulation Upper-convected Maxwell model 0103 physical sciences symbols Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Mathematical Models and Methods in Applied Sciences. 26:569-600 |
| ISSN: | 1793-6314 0218-2025 |
| DOI: | 10.1142/s021820251650010x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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