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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Samenvatting

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.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's19
StatusGepubliceerd - 2012

Publicatie series

NaamCASA-report
Volume1205
ISSN van geprinte versie0926-4507

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Citeer dit

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). Eindhoven: Technische Universiteit Eindhoven.