Geodesic
Application of geodesic grids for modeling the hydrodynamic processes in spherical objects
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 77-87

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We propose a new numerical method that bases on the mathematical apparatus of geodesic grids. This approach allows us to simulate spherical objects without any singularities that occur in using the spherical or cylindrical coordinates. Solution of the hyperbolic equations is described in detail. The method is expanded to solve the equations of hydrodynamics and tested on the Sedov point explosion problem. The numerical method and the approach to grid construction make it possible to compute a rotation invariant solution in Cartesian coordinates. This in turn allows us to use this approach effectively for simulating various spherical astrophysical objects.
Keywords: numerical simulation, computational astrophysics, geodesic grid. . 
@article{SJIM_2020_23_4_a5,
     author = {I. M. Kulikov and E. I. Vorobyov and I. G. Chernykh and V. G. Elbakyan},
     title = {Application of geodesic grids for modeling the hydrodynamic processes in spherical objects},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {77--87},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a5/}
}
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I. M. Kulikov; E. I. Vorobyov; I. G. Chernykh; V. G. Elbakyan. Application of geodesic grids for modeling the hydrodynamic processes in spherical objects. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 77-87. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a5/