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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Recently, it was discovered that the entropy-conserving/dissipativehigh-order split-form discontinuous Galerkin discretizations have robustnessissues when trying to solve the simple density wave propagation example for thecompressible Euler equations. The issue is related to missing local linearstability, i.e. the stability of the discretization towards perturbations addedto a stable base flow. This is strongly related to an anti-diffusion mechanism,that is inherent in entropy-conserving two-point fluxes, which are a keyingredient for the high-order discontinuous Galerkin extension. In this paper,we investigate if pressure equilibrium preservation is a remedy to theserecently found local linear stability issues ofentropy-conservative/dissipative high-order split-form discontinuous Galerkinmethods for the compressible Euler equations. Pressure equilibrium preservationdescribes the property of a discretization to keep pressure and velocityconstant for pure density wave propagation. We present the full theoreticalderivation, analysis, and show corresponding numerical results to underline ourfindings. In addition, we characterize numerical fluxes for the Euler equationsthat are entropy-conservative, kinetic-energy-preserving,pressure-equilibrium-preserving, and have a density flux that does not dependon the pressure. The source code to reproduce all numerical experimentspresented in this article is available online (DOI: 10.5281/zenodo.4054366).

Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes