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

Research output: Contribution to journalArticleAcademicpeer-review

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We present the extension of the complete flux scheme to advection-diffusion-reaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux 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 flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems. Keywords: Advection-diffusion-reaction systems · Flux (vector) · Finite volume method · Integral representation of the flux · Green’s matrix · Numerical flux · Matrix functions · Peclet matrix
Original languageEnglish
Pages (from-to)552-568
Number of pages17
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 2012


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