Numerical modeling of multidimensional problems of gravitational gas dynamics with high resolution schemes
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2010), pp. 92-99.

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The aim of this paper is to implement and analyze a nonoscillatory high-resolution scheme for multudimensional hyperbolic conservation laws. Using methods of Nessyahu and Tadmor for solving three-dimensional equations of gravitational gas dynamics we provide a central two-step (predictor and corrector) scheme.
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Boris Rybakin; Natalia Shider. Numerical modeling of multidimensional problems of gravitational gas dynamics with high resolution schemes. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2010), pp. 92-99. https://geodesic-test.mathdoc.fr/item/BASM_2010_1_a7/

[1] Matsumoto T., Self-gravitational Magnetohydrodynamics with Adaptive Mesh Refinement for Protospellar Collapse, Publ. Astron. Soc. Japan, 59, 2007, October 25

[2] Gheller C., Pantano O., Moscardini L., A cosmological hydrodynamic code based on the Piecewise Parabolic Method, Mon. Not. R. Astron. Soc., 5 October 2006

[3] Jiang G.-S., Levy D., Lin C.-T., Osher S., Tadmor E., “High-Resolution Nonoscillatory Central Schemes With Nonstaggered Grids For Hyperbolic Conservation Laws”, SIAM J. NUMER. ANAL., 35:6, December (1998), 2147–2168 | DOI | MR | Zbl

[4] Rybakin B., Shider N., “Computer modeling of multidimensional problems of gravitational gas dynamics on multiprocessor computers”, Computer Science Journal of Moldova, 17:1(49) (2009), 3–13

[5] Nessyahu H., Tadmor E., “Non-oscillatory central differencing for hyperbolic conservation laws”, J. Comp. Phys., 87 (1990), 408–448 | DOI | MR

[6] Balbras J., Qian Xin, “Non-oscillatory Central Schemes for 3D Hyperbolic Conservation Laws”, Hyperbolic Partial Differential Equations, Theory, Numerics and Applications, Proceedings of the 12th international conference, University of Maryland, 2009

[7] Levy D., Puppo G., Russo G., “A Fourty-Order Weno Scheme for Multidimensional Hyperbolic System of Conservation Laws”, Mathematical Modelling and Numerical Analysis, 33:3 (1999), 547–571 | DOI | MR | Zbl

[8] Kurganov A., Chi-Tien Lin, “On the Reduction of Numerical Dissipation in Central-Upwind Schemes”, Communications in Computational Physics, 2:1 (2007), 141–163 | MR | Zbl

[9] Toth G., Odstrcil D., “Comparision of Some Flux Corrected Transport and Total Variation Diminishing Numerical Schemes for Hydrodynamic and Magnetohydrodynamic Problems”, Journal of Comp. Phys., 128 (1996), 82–100 | DOI | Zbl

[10] Liska R., Wendroff B., “Comparison of Several Difference Schemes on 1d and 2d Test Problems for the Euler Equations”, SIAM J. SCI. COMPUT, 25:3 (2003), 995–1017 | DOI | MR | Zbl

[11] Kulikov I., Lazareva G., Snytnikov A., Vshivkov V., “Supercomputer Simulation of an Astrophysical Object Collapse by the Fluids-in-Cell Method”, PaCT, LNCS, 5698, ed. V. Malyshkin, Springer-Verlag, Berlin–Heidelberg, 2009, 414–422