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Entropy stable schemes on two-dimensional unstructured grids

by D. Ray and P. Chandrashekar and U. Fjordholm and S. Mishra

(Report number 2014-28)

Abstract
We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. The scheme is constructed using a judicious combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a piecewise linear reconstruction procedure satisfying a suitable sign property. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

Keywords: system of conservation laws; entropy stability; unstructured meshes; Euler equations

@Techreport{RCFM14_578,
  author = {D. Ray and P. Chandrashekar and U. Fjordholm and S. Mishra},
  title = {Entropy stable schemes on two-dimensional unstructured grids},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-28},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-28.pdf },
  year = {2014}
}

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