A fully implicit log-conformation formulation with an efficient Jacobian strategy for viscoelastic flows
Journal of Non-Newtonian Fluid Mechanics, vol. 351, pp. 105687
Abstract
In this work, we present a fully implicit log-conformation formulation with an efficient Jacobian strategy for incompressible viscoelastic flow simulations. The three-field finite-element formulation is stabilized using the variational multiscale technique. Newton’s method is combined with a hybrid analytical–numerical Jacobian, consisting of an analytical Galerkin Jacobian and a numerical stabilization Jacobian, which is practical to implement and efficient to assemble. First-order eigenvalue perturbation is used during assembly to avoid repeated spectral decompositions and reduce the cost of the numerical Jacobian. The non-linear tensor functions arising from the logarithmic reformulation and their derivatives are evaluated through their spectral representations. This removes the need for dimension-specific derivations and provides a unified implementation for two- and three-dimensional problems. The formulation is validated with the flow past a cylinder and sedimenting sphere benchmarks for the Oldroyd-B and Giesekus models over a wide range of Weissenberg numbers. The numerical results agree well with the literature, even at high Weissenberg numbers, demonstrating the robustness and accuracy of the proposed formulation. It is also found that near-second-order convergence is achieved in both benchmark cases.
Authors 2
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Felipe A. González corresponding Aachen Chair for Computational Analysis of Technical Systems (CATS)
Affiliation as printed
Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, Schinkelstraße 2, Aachen, 52062, Germany
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Affiliation as printed
Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, Schinkelstraße 2, Aachen, 52062, Germany