Gauge conditions on the "square root" of the conformation tensor in rheological models

Markus Hütter (Corresponding author), Hans Christian Öttinger

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
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Abstract

Symmetric positive-definite conformation-tensors are ubiquitous in models of viscoelasticity. In this paper, the multiplicative decomposition of the conformation tensor is revisited. The nonuniqueness in this decomposition is exploited (i) to ensure stationarity of the decomposed dynamics whenever the conformation tensor is stationary, and (ii) to impose gauge conditions (cf. symmetric square root, or Cholesky decomposition) in the dynamics, for both deterministic and stochastic settings. The general procedure developed in this paper is exemplified on the upper-convected Maxwell model, and a (typically) increased numerical accuracy of the modified dynamics is found.
Original languageEnglish
Article number104145
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Volume271
DOIs
Publication statusPublished - Sep 2019

Keywords

  • Gauge conditions
  • Symmetric square root
  • Cholesky decomposition
  • Conformation tensor
  • Viscoelasticity

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