A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour

@article{Pietro2021AHH,
  title={A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour},
  author={Daniele A. Di Pietro and Daniel Castanon Quiroz and Andr'e Harnist},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.14950}
}
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection laws, that are associated with possibly different Sobolev exponents r ∈ (1,∞) and s ∈ (1,∞). After providing a novel weak formulation of the continuous problem, we study its well-posedness highlighting how a subtle interplay between the exponents r and s… 
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A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes
TLDR
A novel divergence-preserving velocity reconstruction is introduced that hinges on the solution inside each element of a mixed problem on a subtriangulation, then is used to design discretizations of the body force and convective terms that lead to pressure robustness.

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