Constitutive laws for the matrix-logarithm of the conformation tensor

By Raanan Fattal, Raz Kupferman. 2004

581 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/f54510e44ebc61b8035917c9d90d410c113f1185

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

Citations in the corpus

Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation (2005, methodology): “The work [7] was supplemented with preliminary numerical results exhibiting stability at parameter regimes far beyond the breakdown threshold reported in the literature.”
Perspectives on viscoelastic flow instabilities and elastic turbulence (2021, methodology): “Consequently, numerical schemes have been devised so that they guarantee that c always remains positive definite, such as the log-conformation tensor methodology proposed by Fattal and Kupperman [125, 126] or the matrix decomposition proposed by Vaithianathan and Collins [127].”
Flow of viscoelastic fluids past a cylinder at high Weissenberg number : stabilized simulations using matrix logarithms (2005, methodology): “In [1] this evolution quation has been derived by a decomposition of the vel radient.”
Multiphysics modelling of manufacturing processes: A review (2018, methodology): “The simulations crash when the conformation tensor c= tp G + I ð12Þ a non-dimensional internal variable representing the strain of the polymer chains, which should be symmetric positive definite by definition,105 looses its positive definiteness.105–107 Moreover, the loss of positive definiteness ha”
Numerical Methods for Viscoelastic Fluid Flows (2021, methodology): “For the conformation tensor formulation, the choice is typically between some of the above techniques to solve for A in addition to the log-conformation (Fattal & Kupferman 2004), the square-root-conformation (Balci et al. 2011), or the kernel-conformation methods (Afonso et al. 2012c).”
An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows (2007, background): “One way around this, proposed recently [13,14], is to simulate what amounts to the logarithm of the polymer stress tensor, whose growth is only linear in time in these regions.”
Decoupled second-order transient schemes for the flow of viscoelastic fluids without a viscous solvent contribution (2010, methodology): “As a final remark, we note that in order to keep the equations simple, the log-conformation transformation [7, 29] has not been applied.”