This article is cited in 3 papers

Application of geodesic grids for modeling the hydrodynamic processes in spherical objects

I. M. Kulikov^a, E. I. Vorobyov^b, I. G. Chernykh^a, V. G. Elbakyan<sup>c

a</sup> Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentyeva 6, Novosibirsk 630090, Russia
^b Department of Astrophysics, University of Vienna, Tuerkenschanzstrasse 17, Vienna 1180, Austria
^c Research Institute of Physics, Southern Federal Univeristy, pr. Stachki 194, Rostov-on-Don 344090, Russia

Abstract: 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. .

UDC: 519.4

Received: 14.02.2020
Revised: 28.04.2020
Accepted: 10.09.2020

DOI: 10.33048/SIBJIM.2020.23.406

 English version: Journal of Applied and Industrial Mathematics, 2020, 14:4, 672–680

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