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Entropy stable ENO scheme

by U. S. Fjordholm and S. Mishra and E. Tadmor

(Report number 2011-05)

Abstract
We prove the first stability estimates for the ENO reconstruction procedure. They take the form of a sign property: we show that the jump in the reconstructed pointvalues at each cell interface has the same sign as the jump in underlying cell averages (cell centered values) across the interface. Moreover their ratio is upper bounded. These estimates hold for arbitrary orders of accuracy of the reconstruction as well as for non-uniform meshes. We then combine the ENO reconstruction together with entropy conservative fluxes to construct new entropy stable ENO schemes of arbitrary order.

Keywords:

@Techreport{FMT11_103,
  author = {U. S. Fjordholm and S. Mishra and E. Tadmor},
  title = {Entropy stable ENO scheme},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-05.pdf },
  year = {2011}
}

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