New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models

Young Ju Lee, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

We propose a class of new discretization schemes for solving the rate-type non-Newtonian constitutive equations. The so-called conformation tensor has been known to be symmetric and positive definite in a large class of constitutive equations. Preserving such a positivity property on the discrete level is believed to be crucially important but difficult. High Weissenberg number problems on numerical instabilities have been often associated with this issue. In this paper, we present various discretization schemes that preserve the positive-definiteness of the conformation tensor regardless of the time and spatial resolutions. Moreover, the robustness of the algorithm has been also demonstrated by the stability analysis using the discrete analogue of energy estimates. New schemes presented in this paper are constructed based upon the newly discovered relationship between the rate-type constitutive equations and the symmetric matrix Riccati differential equations.

Original languageEnglish (US)
Pages (from-to)1180-1206
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number9-12
DOIs
StatePublished - Feb 1 2006

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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