| In the numerical calculation of flows for viscoelastic liquids by finite difference and finite element techniques, the convergence of the results obtained on increasingly refined meshes seems to be a generally accepted postulate both for the physical soundness of a constitutive equation and for the mathematical soundness of a numerical method. In this letter, we argue that the existence of a meaningful limit for vanishing mesh size cannot generally be established by physical arguments, and we show how to estimate the lower limit of physically acceptable mesh sizes in numerical simulations of real flow experiments when using certain constitutive equations based on molecular models of dilute polymer solutions (Oldroyd B, FENE). We discuss the breakdown of continuum mechanics, not as an esoteric philosophical problem, but as a serious obstacle in simulating and understanding flow experiments.
for LaTeX users @article{HC\"Ottinger1995-39,
author = {H. C. \"Ottinger},
title = {Mesh refinement limits in viscoelastic flow calculations?},
journal = {J. Rheol.},
volume = {39},
pages = {987-992},
year = {1995}
}
\bibitem{HC\"Ottinger1995-39} H.C. \"Ottinger,
Mesh refinement limits in viscoelastic flow calculations?,
J. Rheol. {\bf 39} (1995) 987-992.HC\"Ottinger1995-39
H.C. \"Ottinger
Mesh refinement limits in viscoelastic flow calculations?
J. Rheol.,39,1995,987-992 |
mk@mat.ethz.ch
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