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Title: A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.
Authors:
 [1] ;  [1] ;  [1] ;  [2] ; ;  [3] ;  [4]
  1. Institut Jean Le Rond d'Alembert, UMR 7190, UPMC Univ. Paris 06 and CNRS, F-75005 Paris (France)
  2. (France)
  3. Computer Science, Columbia University, New York, NY (United States)
  4. Institute for Numerical and Applied Mathematics, University of Göttingen, 37083 Göttingen (Germany)
Publication Date:
OSTI Identifier:
22230819
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 253; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 42 ENGINEERING; BENDING; COORDINATES; DEGREES OF FREEDOM; DIFFERENTIAL GEOMETRY; EQUATIONS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; ORIENTATION; ROTATION; STRESSES; SURFACE TENSION; VARIATIONAL METHODS