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Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
,
Antonio Huerta
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: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa53621 |
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| 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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| Start Page: |
163 |
| End Page: |
201 |