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

Abstract

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 scalar Leray-Lions 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.

28 pages, 4 figures

References in corpus (1)

• Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems

Cited by in corpus (4)

• A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour
• Non-isothermal non-Newtonian fluids: the stationary case
• A class of space-time discretizations for the stochastic $p$-Stokes system
• A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes