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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa53621
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last_indexed 2020-09-17T03:16:58Z
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spelling 2020-02-24T09:58:34.8301014 v2 53621 2020-02-24 Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2020-02-24 CIVL 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. Book chapter Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids 163 201 Springer International Publishing Cham 9783030375171 9783030375188 0254-1971 2309-3706 1 1 2020 2020-01-01 10.1007/978-3-030-37518-8_5 http://dx.doi.org/10.1007/978-3-030-37518-8_5 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-02-24T09:58:34.8301014 2020-02-24T09:58:34.8301014 Matteo Giacomini 1 Rubén Sevilla 0000-0002-0061-6214 2 Antonio Huerta 3
title Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
spellingShingle Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
Rubén Sevilla
title_short Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
title_full Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
title_fullStr Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
title_full_unstemmed Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
title_sort Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Matteo Giacomini
Rubén Sevilla
Antonio Huerta
format Book chapter
container_title Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids
container_start_page 163
publishDate 2020
institution Swansea University
isbn 9783030375171
9783030375188
issn 0254-1971
2309-3706
doi_str_mv 10.1007/978-3-030-37518-8_5
publisher Springer International Publishing
url http://dx.doi.org/10.1007/978-3-030-37518-8_5
document_store_str 0
active_str 0
description 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.
published_date 2020-01-01T04:06:40Z
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score 11.016235

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