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

11/12/2019
by   Matteo Giacomini, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 18

page 20

page 22

page 24

07/02/2019

A mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulation

The Brinkman equations can be regarded as a combination of the Stokes an...
10/28/2019

Higher-order discontinuous Galerkin time discretizations the evolutionary Navier–Stokes equations

Discontinuous Galerkin methods of higher order are applied as temporal d...
05/05/2022

A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry

We introduce a pure–stress formulation of the elasticity eigenvalue prob...
04/22/2020

Approximation of the Axisymmetric Elasticity Equations with Weak Symmetry

In this article we consider the linear elasticity problem in an axisymme...
05/31/2020

Equal higher order analysis of an unfitted discontinuous Galerkin method for Stokes flow systems

In this work, we analyze an unfitted discontinuous Galerkin discretizati...
04/17/2022

Mixed Isogeometric Discretizations for Planar Linear Elasticity

In this article we suggest two discretization methods based on isogeomet...
02/26/2020

An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor

This paper presents an extended Galerkin analysis for various Galerkin m...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.