A Hybridizable Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations

By Jaime Peraire, Ngoc Cuong Nguyen, Bernardo Cockburn. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010

153 citations recorded by the source corpus.

In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the solution of the compressible Euler and Navier-Stokes equations. The method is devised by using the discontinuous Galerkin approximation with a special choice of the numerical fluxes and weakly imposing the continuity of the normal component of the numerical fluxes across the element interfaces. This allows the approximate conserved variables defining the discontinuous Galerkin solution to be locally condensed, thereby resulting in a reduced system which involves only the degrees of freedom of the approximate traces of the solution. The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties. In particular, we show that HDG produces optimal converges rates for both the conserved quantities as well as the viscous stresses and the heat fluxes. We present some numerical results to demonstrate the accuracy and convergence properties of the method.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/5dcc6bffc2df1cb338861b1135ce954b7c211d0f

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In Computational Mechanics

Citations in the corpus

An Embedded Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations (2011, unknown): “As before, we take the interior numerical ﬂuxes of form where the stabilization matrix S can be selected by extending the form for the Euler equations as The deﬁnition of the boundary numerical ﬂux (cid:98) B h depends on the types of boundary conditions and can be found in [21].”
Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems (2016, methodology): “Since its introduction, the HDG has been objective of intensive research and has been applied to a large number of problems in different areas, including fluid mechanics (Nguyen et al., 2010, 2011a; Peraire et al., 2010), wave propagation (Nguyen et al.”
Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩ (2014, unknown): “As in [46], the mesh is reﬁned around the airfoil to capture the boundary layer, and further reﬁned at the leading and trailing edges.”
A moving discontinuous Galerkin finite element method for flows with interfaces (2018, background): “(28) The proposed formulation is also related to the hybridized DG formulation [55, 56], which introduces an interface variable ŷ 2 W to obtain a weak formulation: find (y, ŷ) 2 Y ⇥W , Â k2T (— ·F (y) ,v)”