Work

A fully implicit log-conformation formulation with an efficient Jacobian strategy for viscoelastic flows

Year: 2026

Type: article

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.

Source: Journal of Non-Newtonian Fluid Mechanics

DOI: 10.1016/j.jnnfm.2026.105687

Authors: Felipe A. González, Ratna Sheal Karunaratne

Institution: RWTH Aachen University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,010

Funder: Deutsche Forschungsgemeinschaft