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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 4, Pages 77–87
DOI: https://doi.org/10.33048/SIBJIM.2020.23.406 (Mi sjim1110) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

I. M. Kulikova, E. I. Vorobyovb, I. G. Chernykha, V. G. Elbakyanc

a 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
Full-text PDF (678 kB) Citations (3)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.406
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. .
Funding agency Grant number
Russian Foundation for Basic Research 19-51-14002 АНФ
Austrian Science Fund I4311
The authors were supported by the Russian Foundation for Basic Research (project no. 19-51-14002) and the Austrian Science Fund (FWF) (project no. I-4311).
Received: 14.02.2020
Revised: 28.04.2020
Accepted: 10.09.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 4, Pages 672–680
DOI: https://doi.org/10.1134/S1990478920040067
Bibliographic databases:
Document Type: Article
UDC: 519.4
Language: Russian
Citation: I. M. Kulikov, E. I. Vorobyov, I. G. Chernykh, V. G. Elbakyan, “Application of geodesic grids for modeling the hydrodynamic processes in spherical objects”, Sib. Zh. Ind. Mat., 23:4 (2020), 77–87; J. Appl. Industr. Math., 14:4 (2020), 672–680
Citation in format AMSBIB
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\by I.~M.~Kulikov, E.~I.~Vorobyov, I.~G.~Chernykh, V.~G.~Elbakyan
\paper Application of geodesic grids for modeling the hydrodynamic processes in spherical objects
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 4
\pages 77--87
\mathnet{http://mi.mathnet.ru/sjim1110}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.406}
\elib{https://elibrary.ru/item.asp?id=44752281}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 4
\pages 672--680
\crossref{https://doi.org/10.1134/S1990478920040067}
\elib{https://elibrary.ru/item.asp?id=44961232}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85100319601}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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