Abstract
Stationary solutions are a prominent subset of solutions to hyperbolic systems of PDEs. Failure of numerical methods to maintain stationarity is easily visible which makes these solutions an important class. Consider finite volume schemes solving multi-d linearized Euler equations on equidistant Cartesian grids. We formulate conditions for a scheme to have stationary states that are discretizations of all analytic stationary states. Such schemes are termed stationarity preserving. Stationarity preservation for the linearized Euler equations is shown to be equivalent to vorticity preservation.
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Note that in this paper indices never denote derivatives.
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All such statements are understood “up to machine error”.
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Barsukow, W. (2017). Stationarity and Vorticity Preservation for the Linearized Euler Equations in Multiple Spatial Dimensions. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_38
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DOI: https://doi.org/10.1007/978-3-319-57397-7_38
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