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Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, Pages: 163 - 201
Swansea University Author:
Rubén Sevilla
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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...
Published in: | Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids |
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ISBN: | 9783030375171 9783030375188 |
ISSN: | 0254-1971 2309-3706 |
Published: |
Cham
Springer International Publishing
2020
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Online Access: |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa53621 |
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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 ACEM 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 Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM 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 |
2020-01-01T14:49:57Z |
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1823319940092919808 |
score |
11.049404 |