English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the spirit of making high-order discontinuous Galerkin (DG) methods morecompetitive, researchers have developed the hybridized DG methods, a class ofdiscontinuous Galerkin methods that generalizes the Hybridizable DG (HDG), theEmbedded DG (EDG) and the Interior Embedded DG (IEDG) methods. These methodsare amenable to hybridization (static condensation) and thus to morecomputationally efficient implementations. Like other high-order DG methods,however, they may suffer from numerical stability issues in under-resolvedfluid flow simulations. In this spirit, we introduce the hybridized DG methodsfor the compressible Euler and Navier-Stokes equations in entropy variables.Under a suitable choice of the stabilization matrix, the scheme can be shown tobe entropy stable and satisfy the Second Law of Thermodynamics in an integralsense. The performance and robustness of the proposed family of schemes areillustrated through a series of steady and unsteady flow problems in subsonic,transonic, and supersonic regimes. The hybridized DG methods in entropyvariables show the optimal accuracy order given by the polynomial approximationspace, and are significantly superior to their counterparts in conservationvariables in terms of stability and robustness, particularly for under-resolvedand shock flows.

Entropy-stable hybridized discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations