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High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure

  • A. BaezaEmail author
  • P. Mulet
  • D. Zorío
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

This paper deals with the scheme proposed by the authors in Zorío, Baeza and Mulet (J Sci Comput 71(1):246–273, 2017). This scheme is an alternative to the techniques proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185–2198, 2003) to obtain high-order accurate schemes using Weighted Essentially Non Oscillatory finite differences and approximating the flux derivatives required by the Cauchy-Kovalevskaya procedure by simple centered finite differences. We analyse how errors in first-order terms near discontinuities propagate through both versions of the Cauchy-Kovalevskaya procedure. We propose a fluctuation control, for which the approximation of the first-order derivative to be used in the Cauchy-Kovalevskaya procedure is obtained from a Weighted Essentially Non Oscillatory (WENO) interpolation of flux derivatives, instead of the usual finite difference of WENO flux reconstructions. The numerical results that we obtain confirm the benefits of this fluctuation control.

Notes

Acknowledgements

This research was partially supported by Spanish MINECO project MTM2014-54388.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat de ValènciaValènciaSpain

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