Extension of the complete flux scheme to systems of conservation laws

J.H.M. Thije Boonkkamp, ten, J. Dijk, van, L. Liu, K.S.C. Peerenboom

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88 Downloads (Pure)

Abstract

We present the extension of the complete ¿ux scheme to advection-diffusion-reaction systems. For stationary problems, the ¿ux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical ¿ux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical ¿ux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete ¿ux scheme results in an implicit semidiscretisation. The complete ¿ux scheme is validated for several test problems. Keywords: Advection-diffusion-reaction systems, ¿ux (vector), ¿nite volume method, integral representation of the ¿ux, Green’s matrix, numerical ¿ux, matrix functions, Péclet matrix.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages19
Publication statusPublished - 2012

Publication series

NameCASA-report
Volume1205
ISSN (Print)0926-4507

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  • Cite this

    Thije Boonkkamp, ten, J. H. M., Dijk, van, J., Liu, L., & Peerenboom, K. S. C. (2012). Extension of the complete flux scheme to systems of conservation laws. (CASA-report; Vol. 1205). Technische Universiteit Eindhoven.