Abstract
The aim of this work is to derive a well-balanced numerical scheme to approximate the solutions of the Euler equations with a gravitational potential. This system admits an infinity of steady state solutions which are not all known in an explicit way. Among all these solutions, the hydrostatic atmosphere has a special physical interest. We develop an approximate Riemann solver using the formalism of Harten, Lax and van Leer, which takes into account the source term. The resulting numerical scheme is proven to be robust, to preserve exactly the hydrostatic atmosphere and to preserve an approximation of all the other steady state solutions.
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Acknowledgments
This work was partially supported by ANR-12-IS01-0004-01 GEONUM
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Desveaux, V., Zenk, M., Berthon, C., Klingenberg, C. (2014). A Well-Balanced Scheme for the Euler Equation with a Gravitational Potential. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_20
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DOI: https://doi.org/10.1007/978-3-319-05684-5_20
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