Extension of the Complete Flux Scheme to Systems of Conservation Laws

Authors:
J. H. Thije Boonkkamp;J. Dijk;L. Liu;K. S. Peerenboom
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands and FOM Institute for Plasma Physics Rijnhuizen, Nieuwegein, The Netherlands
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

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.