High-Order Isogeometric Methods for Compressible Flows: II: Compressible Euler Equations

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Downloads (Pure)

Abstract

This work extends the high-resolution isogeometric analysis approach established in chapter “High-Order Isogeometric Methods for Compressible Flows. I: Scalar Conservation Laws” (Jaeschke and Möller: High-order isogeometric methods for compressible flows. I. Scalar conservation Laws. In: Proceedings of the 19th International Conference on Finite Elements in Flow Problems (FEF 2017)) to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for the standard Galerkin approximation, which is stabilized by adding artificial viscosities proportional to the spectral radius of the Roe-averaged flux-Jacobian matrix. Excess stabilization is removed in regions with smooth flow profiles with the aid of algebraic flux correction (Kuzmin et al., Flux-corrected transport, chapter Algebraic flux correction II. Compressible Flow Problems. Springer, Berlin, 2012). The underlying principles are reviewed and it is shown that linearized FCT-type flux limiting (Kuzmin, J Comput Phys 228(7):2517–2534, 2009) originally derived for nodal low-order finite elements ensures positivity-preservation for high-order B-Spline discretizations.

Original languageEnglish
Title of host publicationNumerical Methods for Flows - FEF 2017 Selected Contributions
EditorsHarald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza
Place of PublicationCham
PublisherSpringer
Pages31-39
Number of pages9
ISBN (Electronic)978-3-030-30705-9
ISBN (Print)978-3-030-30704-2
DOIs
Publication statusPublished - 2020
Event19th International Conference on Finite Elements in Flow Problems, FEF 2017 - Rome, Italy
Duration: 5 Apr 20177 Apr 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume132
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference19th International Conference on Finite Elements in Flow Problems, FEF 2017
CountryItaly
CityRome
Period5/04/177/04/17

Keywords

  • Compressible flows
  • High-order methods
  • High-resolution methods
  • Isogeometric analysis

Fingerprint Dive into the research topics of 'High-Order Isogeometric Methods for Compressible Flows: II: Compressible Euler Equations'. Together they form a unique fingerprint.

Cite this