A cell-centred pressure-correction scheme for the compressible Euler equations

@article{Herbin2019ACP,
  title={A cell-centred pressure-correction scheme for the compressible Euler equations},
  author={Rapha{\`e}le Herbin and Jean-Claude Latch{\'e} and Chady Zaza},
  journal={IMA Journal of Numerical Analysis},
  year={2019}
}
We propose a robust pressure-correction scheme for the numerical solution of the compressible Euler equations discretized by a collocated finite volume method. The scheme is based on an internal energy formulation, which ensures that the internal energy is positive. More generally, the scheme enjoys fundamental stability properties: without restriction on the time step, both the density and the internal energy are positive, the integral of the total energy over the computational domain is… 

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