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Numerical Mathematics and Advanced Applications - ENUMATH 2013 pp 95–103Cite as

Harmonic Complete Flux Schemes for Conservation Laws with Discontinuous Coefficients

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

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

  1. N.J. Higham, Functions of Matrices, Theory and Computation (SIAM, Philadelphia, 2008)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    J. H. M. ten Thije Boonkkamp

  2. Department of Applied Physics, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    L. Liu, J. van Dijk & K. S. C. Peerenboom

Authors
  1. J. H. M. ten Thije Boonkkamp
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  2. L. Liu
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  3. J. van Dijk
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  4. K. S. C. Peerenboom
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Corresponding author

Correspondence to J. H. M. ten Thije Boonkkamp .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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© 2015 Springer International Publishing Switzerland

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Cite this paper

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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