Implicit conservative schemes for the Euler equations.

*(English)*Zbl 0591.76108Summary: A new approach to a characteristic modeling scheme is presented that does not require the governing equations to be written in characteristic variables or the flux terms to be split into positive and negative parts. The method is based on the observation that, for certain finite volume schemes, the upwind influence can be accounted for through the conditions applied at the boundaries of individual cells instead of flux differencing. The method is developed and applied to the one-dimensional nozzle flow equations for subsonic, transonic, and supersonic flows and is then extended to two dimensions using an approximate factorization. For the problem of a shock wave reflecting from a flat plate, the present solution algorithm reduces the computational work per time step by 40% of that required by standard, central difference, implicit, calculations.

##### MSC:

76J20 | Supersonic flows |

76H05 | Transonic flows |

76G25 | General aerodynamics and subsonic flows |

76M99 | Basic methods in fluid mechanics |