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

Matteo Giacomini, Rubén Sevilla Orcid Logo, Antonio Huerta

Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, Pages: 163 - 201

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1007/978-3-030-37518-8_5

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...

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Published in: Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids
ISBN: 9783030375171 9783030375188
ISSN: 0254-1971 2309-3706
Published: Cham Springer International Publishing 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53621
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.
Start Page: 163
End Page: 201

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