A two-dimensional complete flux scheme in local flow adapted coordinates

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Abstract

We present a formulation of the two-dimensional complete flux (CF) scheme in terms of local orthogonal coordinates adapted to the flow, i.e., one coordinate axis is aligned with the local velocity field and the other one is perpendicular to it. This approach gives rise to an advection-diffusion-reaction boundary value problem (BVP) for the flux component in the local flow direction. For the other (diffusive) flux component we use central differences. We will demonstrate the performance of the scheme for several examples.

Original languageEnglish
Title of host publicationFinite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017
EditorsC. Cancès, P. Omnes
PublisherSpringer
Pages437-445
Number of pages9
ISBN (Print)9783319573939
DOIs
Publication statusPublished - 2017
Event8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017) - Lille, France
Duration: 12 Jun 201716 Jun 2017
Conference number: 8
https://indico.math.cnrs.fr/event/1299/overview
https://indico.math.cnrs.fr/event/1299/overview

Publication series

NameSpringer Proceedings in Mathematics & Statistics
Volume200

Conference

Conference8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017)
Abbreviated titleFVCA 2017
CountryFrance
CityLille
Period12/06/1716/06/17
Internet address

Keywords

  • Complete flux scheme
  • Conservation laws
  • Finite volume method
  • Local orthogonal coordinates
  • Numerical flux

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    ten Thije Boonkkamp, J., Anthonissen, M., & Kwant, R. (2017). A two-dimensional complete flux scheme in local flow adapted coordinates. In C. Cancès, & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017 (pp. 437-445). (Springer Proceedings in Mathematics & Statistics; Vol. 200). Springer. https://doi.org/10.1007/978-3-319-57394-6_46