Complete flux scheme for conservation laws containing a linear source

J.H.M. ten Thije Boonkkamp, B.V. Rathish Kumar, S. Kumar, M. Pargaei

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Abstract

We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, the remaining nonlinear part is included in the inhomogeneous flux. This approach gives rise to modified homogeneous and inhomogeneous fluxes, which reduce to the classical fluxes for vanishing linear source. On the other hand, if the linear source is large, the solution of the underlying boundary value problem is oscillatory, resulting in completely different numerical fluxes. We demonstrate the performance of the homogeneous flux approximation.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications - ENUMATH 2015
EditorsB. Karasozen, M. Manguoglu, M. Tezer-Sezgin, S. Goktepe, O. Ugur
PublisherSpringer
Pages23-31
Number of pages8
ISBN (Electronic)978-3-319-39929-4
ISBN (Print)978-3-319-39927-0
DOIs
Publication statusPublished - 2016
Event2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015) - Middle East Technical University, Ankara, Turkey
Duration: 14 Sep 201518 Sep 2015

Publication series

NameLecture Notes in Computational Science and Engineering (LNCSE)
PublisherSpringer
Volume112

Conference

Conference2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015)
Abbreviated titleENUMATH 2015
CountryTurkey
CityAnkara
Period14/09/1518/09/15

Cite this

ten Thije Boonkkamp, J. H. M., Rathish Kumar, B. V., Kumar, S., & Pargaei, M. (2016). Complete flux scheme for conservation laws containing a linear source. In B. Karasozen, M. Manguoglu, M. Tezer-Sezgin, S. Goktepe, & O. Ugur (Eds.), Numerical Mathematics and Advanced Applications - ENUMATH 2015 (pp. 23-31). (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 112). Springer. https://doi.org/10.1007/978-3-319-39929-4_3