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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:294

Article

Arne, Walter¹  Marheineke, Nicole²  Meister, Andreas³  Schiessl, Stefan²  Wegener, Raimund¹ 

[1] Fraunhofer ITWM, D-67663 Kaiserslautern, Germany

[2] FAU Erlangen Nurnberg, Lehrstuhl Angew Math 1, D-91058 Erlangen, Germany

[3] Univ Kassel, FB Math & Nat Wissensch, D-34132 Kassel, Germany

关键词: Rotational spinning process;    Viscous fiber;    Special Cosserat theory;    Partial differential algebraic equations;    Quaternions;    Finite volume scheme;   

DOI  :  10.1016/j.jcp.2015.03.042

来源: Elsevier

【 摘 要 】

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 epsilon-regularized string model, but containing the slenderness ratio epsilon 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free