Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems

Author (s): Giacomini, M., Sevilla, R., and Huerta, A.
Journal: Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids

Volume: 599
Pages: 163 – 201
Date: 2020

Abstract:
A hybridizable discontinuous Galerkin (HDG) formulation of the linearized incompressible Navier-Stokes equations, known as Oseen equations, is presented. The Cauchy stress formulation is considered and the symmetry of the stress tensor and the mixed variable, namely the scaled strain-rate tensor, is enforced pointwise via Voigt notation. Using equal-order polynomial approximations of degree k for all variables, HDG provides a stable discretization. Moreover, owing to Voigt notation, optimal convergence of order k+1 is obtained for velocity, pressure and strain-rate tensor and a local postprocessing strategy is devised to construct an approximation of the velocity superconverging with order k+2, even for low-order polynomial approximations. A tutorial for the numerical solution of incompressible flow problems using HDG is presented, with special emphasis on the technical details required for its implementation.

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Bibtex:

@InCollection{MG-GSH-20,
  author    = {Matteo Giacomini and Ruben Sevilla and Antonio Huerta},
  title     = {Tutorial on {H}ybridizable {D}iscontinuous {G}alerkin ({HDG}) Formulation for 
		Incompressible Flow Problems},
  booktitle = {Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids},
  publisher = {Springer International Publishing},
  year      = {2020},
  editor    = {L. De Lorenzis and A. D\"{u}ster},
  volume    = {599},
  series    = {CISM International Centre for Mechanical Sciences},
  pages     = {163--201},
  doi       = {10.1007/978-3-030-37518-8_5},
}