Nonlinear flux approximation scheme for Burgers equation derived from a local BVP

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.
LanguageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
EditorsF.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. Pop
Place of PublicationCham
PublisherSpringer
Pages1015-1023
Number of pages9
ISBN (Electronic)978-3-319-96415-7
ISBN (Print)978-3-319-96414-0
DOIs
StatePublished - 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway
Duration: 25 Sep 201729 Sep 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume126

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
CountryNorway
CityVoss
Period25/09/1729/09/17

Fingerprint

Approximation Scheme
Burgers Equation
Inviscid Limit
Iterative Solution
Two-point Boundary Value Problem
Boundary Value
Viscosity
Nonlinear Equations

Cite this

ten Thije Boonkkamp, J. H. M., Kumar, N., Koren, B., van der Woude, D. A. M., & Linke, A. (2019). Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (pp. 1015-1023). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. DOI: 10.1007/978-3-319-96415-7_96
ten Thije Boonkkamp, J.H.M. ; Kumar, N. ; Koren, B. ; van der Woude, D.A.M. ; Linke, A./ Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. Numerical Mathematics and Advanced Applications ENUMATH 2017. editor / F.A. Radu ; K. Kumar ; I. Berre ; J.M. Nordbotten ; I.S. Pop. Cham : Springer, 2019. pp. 1015-1023 (Lecture Notes in Computational Science and Engineering).
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abstract = "We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.",
author = "{ten Thije Boonkkamp}, J.H.M. and N. Kumar and B. Koren and {van der Woude}, D.A.M. and A. Linke",
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ten Thije Boonkkamp, JHM, Kumar, N, Koren, B, van der Woude, DAM & Linke, A 2019, Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. in FA Radu, K Kumar, I Berre, JM Nordbotten & IS Pop (eds), Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, pp. 1015-1023, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25/09/17. DOI: 10.1007/978-3-319-96415-7_96

Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. / ten Thije Boonkkamp, J.H.M.; Kumar, N.; Koren, B.; van der Woude, D.A.M.; Linke, A.

Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / F.A. Radu; K. Kumar; I. Berre; J.M. Nordbotten; I.S. Pop. Cham : Springer, 2019. p. 1015-1023 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.

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ten Thije Boonkkamp JHM, Kumar N, Koren B, van der Woude DAM, Linke A. Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. In Radu FA, Kumar K, Berre I, Nordbotten JM, Pop IS, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. p. 1015-1023. (Lecture Notes in Computational Science and Engineering). Available from, DOI: 10.1007/978-3-319-96415-7_96