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

J. ten Thije Boonkkamp; M. Anthonissen; R. Kwant

doi:10.1007/978-3-319-57394-6_46

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

J. ten Thije Boonkkamp, M. Anthonissen, R. Kwant

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

3 Citations (Scopus)

2 Downloads (Pure)

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 language	English
Title of host publication	Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017
Editors	C. Cancès, P. Omnes
Publisher	Springer
Pages	437-445
Number of pages	9
ISBN (Print)	9783319573939
DOIs	https://doi.org/10.1007/978-3-319-57394-6_46
Publication status	Published - 2017
Event	8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017) - Lille, France Duration: 12 Jun 2017 → 16 Jun 2017 Conference number: 8 https://indico.math.cnrs.fr/event/1299/overview https://indico.math.cnrs.fr/event/1299/overview

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Volume	200

Conference

Conference	8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017)
Abbreviated title	FVCA 2017
Country/Territory	France
City	Lille
Period	12/06/17 → 16/06/17
Internet address	https://indico.math.cnrs.fr/event/1299/overview https://indico.math.cnrs.fr/event/1299/overview

Keywords

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

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10.1007/978-3-319-57394-6_46

Cite this

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

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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.",

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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. Springer Proceedings in Mathematics & Statistics, vol. 200, Springer, pp. 437-445, 8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017), Lille, France, 12/06/17. https://doi.org/10.1007/978-3-319-57394-6_46

A two-dimensional complete flux scheme in local flow adapted coordinates. / ten Thije Boonkkamp, J.; Anthonissen, M.; Kwant, R.
Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017. ed. / C. Cancès; P. Omnes. Springer, 2017. p. 437-445 (Springer Proceedings in Mathematics & Statistics; Vol. 200).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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KW - Conservation laws

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

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

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