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Extension of the complete flux scheme to systems of conservation laws

By JHM Jan ten Thije Boonkkamp, J Jan van Dijk, L Lei Liu and KSC Kim Peerenboom

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

Publisher: Technische Universiteit Eindhoven
Year: 2012
OAI identifier: oai:library.tue.nl:732121
Provided by: Repository TU/e
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