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Acta Mechanica

, Volume 230, Issue 3, pp 729–747 | Cite as

Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor

  • Adam Janečka
  • Josef Málek
  • Vít PrůšaEmail author
  • Giordano Tierra
Original Paper

Abstract

We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure–velocity–apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has—on the discrete level—a solution, and using the proposed scheme, we numerically solve several flow problems.

Mathematics Subject Classification

76D99 74A20 65M60 

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Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles University, PraguePraha 8Czech Republic
  2. 2.Department of MathematicsTemple UniversityPhiladelphiaUSA

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