A Hybrid High-Order method for creeping flows of non-Newtonian fluids

Michele Botti (1) , Daniel Castanon Quiroz (2) , Daniele Antonio Di Pietro (2) , André Harnist (2)

1 POLIMI - Politecnico di Milano [Milan]
2 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray-Lions scalar problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau-Yasuda models. Numerical examples complete the exposition.

Mots clés: Hybrid High-Order methods; non-Newtonian fluids; power-law; Carreau-Yasuda law; discrete Korn inequality

Domaines: Analyse numérique [math.NA]

Michele Botti, Daniel Castanon Quiroz, Daniele Antonio Di Pietro, André Harnist. A Hybrid High-Order method for creeping flows of non-Newtonian fluids. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (5), pp.2045-2073. ⟨10.1051/m2an/2021051⟩. ⟨hal-03362663v1⟩