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2020 | OriginalPaper | Buchkapitel

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

verfasst von : Matteo Giacomini, Ruben Sevilla, Antonio Huerta

Erschienen in: Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Practical Computational Fluid Dynamics with the Finite Volume Method

Nächstes Kapitel Non Intrusive Global/Local Coupling Techniques in Solid Mechanics: An Introduction to Different Coupling Strategies and Acceleration Techniques

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Titel: Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems
verfasst von: Matteo Giacomini
Ruben Sevilla
Antonio Huerta
Verlag: Springer International Publishing
Buch: Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids
Print ISBN: 978-3-030-37517-1

Electronic ISBN: 978-3-030-37518-8

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-37518-8_5

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