Virtual Element methods for non-Newtonian shear-thickening fluid flow problems

Keywords

Advanced Numerical Methods for Scientific Computing
SC4I/Digitization, Innovation, and Competitiveness of the Production System
Code:
02/2026
Title:
Virtual Element methods for non-Newtonian shear-thickening fluid flow problems
Date:
Thursday 8th January 2026
Author(s):
Antonietti, P.F.; Beirao da Veiga, L.; Botti, M.; Harnist, A.; Vacca, G.; Verani, M.
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Abstract:
In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r >2) including both degenerate (\delta= 0) and non-degenerate (\delta > 0) cases. The proposed Virtual Element method features two distinguishing advantages: the construction of an exactly divergence-free discrete velocity field and compatibility with general polygonal meshes. The analysis presented in this work extends the results of [55], where only shear-thinning behavior (1 < r < 2) was considered. Indeed, the theoretical analysis of the shear-thickening setting requires several novel analytical tools, including: an infsup stability analysis of the discrete velocity-pressure coupling in non-Hilbertian norms, a stabilization term specifically designed to address the nonlinear structure as the exponent r >2; and the introduction of a suitable discrete norm tailored to the underlying nonlinear constitutive relation. Numerical results demonstrate the practical performance of the proposed formulation.