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Semi‐Lagrangian discretization of the upper‐convective derivative in Non‐Newtonian fluid flow
Author(s) -
Wensch Jörg,
Naumann Andreas
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210371
Subject(s) - discretization , material derivative , newtonian fluid , non newtonian fluid , lagrangian , mechanics , time derivative , flow (mathematics) , derivative (finance) , convection , generalized newtonian fluid , physics , contraction (grammar) , classical mechanics , mathematics , mathematical analysis , viscosity , thermodynamics , shear rate , medicine , financial economics , economics
Non‐Newtonian fluid flow is governed by the Navier‐Stokes equations with an additional source term resulting from Non‐Newtonian stresses. The Non‐Newtonian stresses evolve along particle paths according to an evolution equation. The temporal derivative in this case is the upper convected derivative. We describe a semi‐Lagrangian discretization of the upper convected derivative. Numerical results for the flow over a contraction are given. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)