On Preserving Spherical Symmetry on a Spherical Grid in the Cartesian Coordinate System When Calculating Gas-Dynamic Currents by Euler Finite-Volume Schemes

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Abstract

The sufficient conditions for finite-volume Euler schemes for calculating gas-dynamic currents in the Cartesian coordinate system using the Gaussian method for the divergence and gradient operators and the midpoint method for approximating integrals over cell faces to preserve spherical symmetry on a spherical grid are determined. Two approaches to ensuring the geometric condition on the ratio of the areas of the corner faces to the volume of the cell are proposed, viz. correction of areas and special selection of partitioning with respect to the polar angle. As an example of preserving the symmetry when the sufficient conditions are met, the calculation of the spherical problem of discontinuity breakdown by the Euler scheme of the Godunov type is considered.

About the authors

I. V Glazyrin

FSUE RFNC-VNIITF named after Acad. E.I. Zababakhin

Email: i.v.glazyrin@vniitf.ru
Snezhinsk, Chelyabinsk region, Russia

N. A Mikhaylov

FSUE RFNC-VNIITF named after Acad. E.I. Zababakhin

Email: n.a.mikhaylov@vniitf.ru
Snezhinsk, Chelyabinsk region, Russia

N. L Frolova

FSUE RFNC-VNIITF named after Acad. E.I. Zababakhin

Email: natalya.l.frolova@mail.ru
Snezhinsk, Chelyabinsk region, Russia

M. N Chizhkov

FSUE RFNC-VNIITF named after Acad. E.I. Zababakhin

Email: m.n.chizhkov@vniitf.ru
Snezhinsk, Chelyabinsk region, Russia

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