### Abstract

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Riemann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.

Original language | English |
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Pages (from-to) | 611-626 |

Number of pages | 16 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 12 |

Issue number | 8 |

DOIs | |

Publication status | Published - 5 May 1991 |

### Keywords

- equations of state
- mathematical techniques
- numerical methods
- Euler equations
- upwind methods
- real gases
- gas dynamics

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## Cite this

Drikakis, D., & Tsangaris, S. (1991). Implicit characteristic-flux-averaging method for the Euler equations for real gases.

*International Journal for Numerical Methods in Fluids*,*12*(8), 611-626. https://doi.org/10.1002/fld.165012080