Abstract
In this paper we discuss several complete flux schemes for advection-diffusion-reaction problems. We consider both scalar equations as well as systems of equations. For the flux approximations in the latter case, we take into account the coupling between the constituent equations. We study conservation laws with discontinuous diffusion matrix/coefficient and show that the (matrix) harmonic average should be employed in the expressions for the numerical fluxes. The vectorial harmonic complete flux schemes are validated for a test problem.
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References
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© 2015 Springer International Publishing Switzerland
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ten Thije Boonkkamp, J.H.M., Liu, L., van Dijk, J., Peerenboom, K.S.C. (2015). Harmonic Complete Flux Schemes for Conservation Laws with Discontinuous Coefficients. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_9
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DOI: https://doi.org/10.1007/978-3-319-10705-9_9
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Online ISBN: 978-3-319-10705-9
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