High-Order Isogeometric Methods for Compressible Flows: I: Scalar Conservation Laws

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Abstract

Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compressible flow problems that require the accurate resolution of boundary layers. The convection-diffusion solver presented in this chapter, is an indispensable step on the way to developing a compressible solver for complex viscous industrial flows. It is well known that the standard Galerkin finite element method and its isogeometric counterpart suffer from spurious oscillatory behaviour in the presence of shocks and steep solution gradients. As a remedy, the algebraic flux correction paradigm is generalized to B-Spline basis functions to suppress the creation of oscillations and occurrence of non-physical values in the solution. This work provides early results for scalar conservation laws and lays the foundation for extending this approach to the compressible Euler equations in the next chapter.

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
Pages21-29
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

  • Algebraic flux correction
  • Compressible flows
  • Isogeometric analysis

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