AERC logo 10th Annual European Rheology Conference
Golden Jubilee Meeting of Groupe Français de Rhéologie
April 14-17, 2015 - Nantes, France
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Simulations and computational rheology

A new log-conformation formulation

15 April 2015 (Wednesday) 12:00

Track 4 / Room KL

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  1. Knechtges, Philipp (RWTH Aachen, Chair for Computational Analysis of Technical Systems)
  2. Behr, Marek (RWTH Aachen, Chair for Computational Analysis of Technical Systems)
  3. Elgeti, Stefanie (RWTH Aachen, Chair for Computational Analysis of Technical Systems)

(in printed abstract book)
Philipp Knechtges, Marek Behr, and Stefanie Elgeti
Chair for Computational Analysis of Technical Systems, RWTH Aachen, Aachen 52056, Germany

Knechtges, Philipp

The robust and stable simulation of viscoelastic flows has been and still is a struggle of computational rheology. Since its discovery in 2004, the log-conformation formulation by Kupferman and Fattal has been employed numerous times in numerical codes. One of the reasons that make the formulation so successful and popular is that it preserves by design the positive-definiteness of the conformation tensor, which has been proven to be an important ingredient for the numerical stability of viscoelastic simulations. However, it carries the small intricacy that the formulation of the constitutive equation requires an algebraic decomposition of the velocity gradient field. In addition to hindering the closed formulation of the full system of partial differential equations in combination with the Navier–Stokes equations, this also complicates the application of further analytical tools. One of these tools with particular importance for numerical simulations is the Newton–Raphson algorithm, which promises quadratic convergence for the solution of the whole system.

In this talk we will present our recent development of a fully-implicit log-conformation formulation [1]. The key concept is the same as in the original log-conformation formulation: We substitute the polymeric stress or the conformation tensor as our primal variables by the logarithm of the conformation tensor. As such we also inherit the property that the conformation tensor is positive-definite by design. The substantial difference to the original method is that we can formulate a constitutive equation in the new variable that completely avoids the algebraic decomposition of the velocity gradient and thus paves the way for the Newton–Raphson algorithm. Following the theoretical description of the method, the talk will subsequently cover results of an implementation in our in-house flow solver, ranging from benchmark problems to die swell simulations.

[1] P. Knechtges, M. Behr, and S. Elgeti. JNNFM, Vol. 214, 78–87, 2014. arXiv:1406.6988