Abstract
We present a well-balanced finite volume solver for the compressible Euler equations with gravity. The Riemann solver used in the finite volume method is approximated by a so-called relaxation Riemann solution. Besides the well-balanced property, the scheme is also positivity preserving regarding the density and internal energy. The scheme is able to capture not only isothermal and polytropic stationary solutions of the hydrostatic equilibrium but also to preserve more general steady states up to machine precision. The scheme is tested on numerical examples including the preservation of arbitrary steady states and the evolution of small perturbations of stationary solutions to demonstrate the properties of the designed scheme.
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Acknowledgements
The authors want to thank Praveen Chandrashekar for pointing out to us the potential usefulness of reference [5].
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Klingenberg, C., Thomann, A. (2018). On Computing Compressible Euler Equations with Gravity. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_12
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DOI: https://doi.org/10.1007/978-3-319-91548-7_12
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