Numerical Defects of the HLL Scheme and Dissipation Matrices for the Euler Equations

@article{Wang2014NumericalDO,
  title={Numerical Defects of the HLL Scheme and Dissipation Matrices for the Euler Equations},
  author={Yue Wang and Jiequan Li},
  journal={SIAM J. Numer. Anal.},
  year={2014},
  volume={52},
  pages={207-219}
}
The Harten--Lax--van Leer scheme is popularly used in the CFD community. However, oscillations are observed from shock tube problems for stiffened gases when the adiabatic index is greater than 3. To understand this phenomenon, the dissipation effect of the scheme is evaluated quantitatively in terms of dissipation matrices. We have proven and numerically demonstrated that lack of positive definiteness is the root of numerical defects. 
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