Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state
<|reference_start|>Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state: This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation by parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state.<|reference_end|>
@article{aiello2024entropy,
    title={Entropy conservative discretization of compressible Euler equations with
  an arbitrary equation of state},
    author={Alessandro Aiello and Carlo De Michele and Gennaro Coppola},
    journal={arXiv preprint arXiv:2408.01235},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.01235},
    primaryClass={physics.flu-dyn cs.NA math.NA}
}