A nonlinear flux approximation scheme for the viscous burgers equation

N. Kumar; J.H.M. ten Thije Boonkkamp; B. Koren; A. Linke

doi:10.1007/978-3-319-57394-6_48

A nonlinear flux approximation scheme for the viscous burgers equation

N. Kumar, J.H.M. ten Thije Boonkkamp, B. Koren, A. Linke

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

3 Citations (Scopus)

1 Downloads (Pure)

Abstract

We present a nonlinear flux approximation scheme for the spatial discretization of the viscous Burgers equation. We derive the numerical flux function from a local two-point boundary value problem (BVP), which results in a nonlinear equation that depends on the local boundary values and the diffusion constant. The flux scheme is consistent and stable (does not introduce any spurious oscillations), as demonstrated by the numerical results.

Original language	English
Title of host publication	Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems
Subtitle of host publication	FVCA 8, Lille, France, June 2017
Editors	C. Cancès , P. Omnes
Place of Publication	Dordrecht
Publisher	Springer
Pages	457-465
Number of pages	9
ISBN (Electronic)	978-3-319-57394-6
ISBN (Print)	978-3-319-57393-9
DOIs	https://doi.org/10.1007/978-3-319-57394-6_48
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

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

Nonlinear local BVP
Numerical flux
Viscous burgers equation

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10.1007/978-3-319-57394-6_48

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Kumar, N., ten Thije Boonkkamp, J. H. M., Koren, B., & Linke, A. (2017). A nonlinear flux approximation scheme for the viscous burgers equation. In C. Cancès , & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017 (pp. 457-465). Springer. https://doi.org/10.1007/978-3-319-57394-6_48

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title = "A nonlinear flux approximation scheme for the viscous burgers equation",

abstract = "We present a nonlinear flux approximation scheme for the spatial discretization of the viscous Burgers equation. We derive the numerical flux function from a local two-point boundary value problem (BVP), which results in a nonlinear equation that depends on the local boundary values and the diffusion constant. The flux scheme is consistent and stable (does not introduce any spurious oscillations), as demonstrated by the numerical results.",

keywords = "Nonlinear local BVP, Numerical flux, Viscous burgers equation",

author = "N. Kumar and {ten Thije Boonkkamp}, J.H.M. and B. Koren and A. Linke",

year = "2017",

doi = "10.1007/978-3-319-57394-6_48",

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booktitle = "Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems",

publisher = "Springer",

address = "Germany",

note = "8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017), FVCA 2017 ; Conference date: 12-06-2017 Through 16-06-2017",

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Kumar, N, ten Thije Boonkkamp, JHM , Koren, B & Linke, A 2017, A nonlinear flux approximation scheme for the viscous burgers equation. in C Cancès & P Omnes (eds), Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017. Springer, Dordrecht, pp. 457-465, 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_48

A nonlinear flux approximation scheme for the viscous burgers equation. / Kumar, N.; ten Thije Boonkkamp, J.H.M.; Koren, B. et al.
Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017. ed. / C. Cancès ; P. Omnes. Dordrecht: Springer, 2017. p. 457-465.

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

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T1 - A nonlinear flux approximation scheme for the viscous burgers equation

AU - Kumar, N.

AU - ten Thije Boonkkamp, J.H.M.

AU - Koren, B.

AU - Linke, A.

N1 - Conference code: 8

PY - 2017

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N2 - We present a nonlinear flux approximation scheme for the spatial discretization of the viscous Burgers equation. We derive the numerical flux function from a local two-point boundary value problem (BVP), which results in a nonlinear equation that depends on the local boundary values and the diffusion constant. The flux scheme is consistent and stable (does not introduce any spurious oscillations), as demonstrated by the numerical results.

AB - We present a nonlinear flux approximation scheme for the spatial discretization of the viscous Burgers equation. We derive the numerical flux function from a local two-point boundary value problem (BVP), which results in a nonlinear equation that depends on the local boundary values and the diffusion constant. The flux scheme is consistent and stable (does not introduce any spurious oscillations), as demonstrated by the numerical results.

KW - Nonlinear local BVP

KW - Numerical flux

KW - Viscous burgers equation

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DO - 10.1007/978-3-319-57394-6_48

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SN - 978-3-319-57393-9

SP - 457

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BT - Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems

A2 - Cancès , C.

A2 - Omnes, P.

PB - Springer

CY - Dordrecht

T2 - 8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017)

Y2 - 12 June 2017 through 16 June 2017

ER -

A nonlinear flux approximation scheme for the viscous burgers equation

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