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

Markus Hütter (Corresponding author), Hans Christian Öttinger

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Uittreksel

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.
TaalEngels
Artikelnummer104145
Aantal pagina's11
TijdschriftJournal of Non-Newtonian Fluid Mechanics
Volume271
DOI's
StatusGepubliceerd - 5 aug 2019

Vingerafdruk

Conformation
Square root
Gages
Tensors
Conformations
Gauge
Tensor
tensors
Decomposition
decomposition
Cholesky Decomposition
Decompose
Numerical Accuracy
Viscoelasticity
Nonuniqueness
viscoelasticity
Stationarity
Positive definite
Multiplicative
Model

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    Citeer dit

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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.",
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    Gauge conditions on the "square root" of the conformation tensor in rheological models. / Hütter, Markus (Corresponding author); Öttinger, Hans Christian.

    In: Journal of Non-Newtonian Fluid Mechanics, Vol. 271, 104145, 05.08.2019.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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    AU - Öttinger,Hans Christian

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    N2 - 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.

    AB - 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.

    KW - Gauge conditions

    KW - Symmetric square root

    KW - Cholesky decomposition

    KW - Conformation tensor

    KW - Viscoelasticity

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    DO - 10.1016/j.jnnfm.2019.104145

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    T2 - Journal of Non-Newtonian Fluid Mechanics

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