Mathematical Modeling of the Evolution of Compact Astrophysical Gas Objects

  • Alexander V. Babakov
  • Alexey Yu. Lugovsky
  • Valery M. Chechetkin
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 133)


In the current study, the vortex structures that occur in one of the most common astrophysical objects such as massive stars and accretion disks are investigated using mathematical modeling methods. Modeling of convective processes with the formation of vortex structures in massive stars of various masses, rotating and being possessed in the self-gravitation conditions is carried out. Modeling uses a gas-dynamic model of an inviscid perfect gas. The numerical technique is based on the finite-difference approximation of the conservation laws for the additive characteristics of the environment for a finite volume. Direct calculation of gravitational forces is used by summing up the interaction between all the finite volumes in the area of integration. For the objects with different mass and rotation speed, visualized pictures of the vortex structure are given. Modeling of the processes of formation of large-scale vortex structures in accretionary stellar disks with different disk thickness is also carried out. Self-gravitation of the matter of a disk rotating in the field of the gravity of a compact central object is not taken into consideration. The numerical technique is based on the explicit, conservative, and monotone in the linear approximation Godunov-type Roe-Einfeldt-Osher scheme, which approximates with order no higher than the third the conservation laws of the characteristics of the environment. For the disks with different thicknesses, visualized pictures of the vortex structure are given. Evolutionary calculations are carried out on the basis of parallel algorithms implemented on the computational complex of the cluster architecture.


Mathematical simulation Conservative difference schemes Numerical methods Parallel algorithms Gas dynamics Astrophysics Massive stars Gravity Convection Vortex structures Supernovae Accretion disks 



The authors are grateful to A.G. Aksenov for helpful discussions of the setting of the initial field for the modeling of rotating massive stellar objects.


  1. 1.
    Sawada, K., Matsuda, T., Hachisu, I.: Spiral shocks on a Roche lobe overflow in a semi-detached binary system. Mon. Not. Roy. Astron. Soc. 219, 75–88 (1986)Google Scholar
  2. 2.
    Velikhov, Y.P., Lugovsky, A.Y., Mukhin, S.I., Popov, Y.P., Chechetkin, V.M.: The impact of large-scale turbulence on the redistribution of angular momentum in stellar accretion disks. Astron. Rep. 51(2), 154–160 (2007)Google Scholar
  3. 3.
    Lugovsky, A.Y., Mukhin, S.I., Popov, Y.P., Chechetkin, V.M.: The development of large-scale instability in stellar accretion disks and its influence on the redistribution of angular momentum. Astron. Rep. 52(10), 811–814 (2008)Google Scholar
  4. 4.
    Lugovskii, A.Y., Chechetkin, V.M.: The development of large-scale instability in Keplerian stellar accretion disks. Astron. Rep. 56(2), 96–103 (2012)Google Scholar
  5. 5.
    Pudritz, R.E., Norman, C.A.: Bipolar hydromagnetic winds from disks around protostellar objects. Astrophysical J. 301, 571–586 (1986)Google Scholar
  6. 6.
    Velikhov, E.P., Sychugov, K.R., Chechetkin, V.M., Lugovskii, AYu., Koldoba, A.V.: Magneto-rotational instability in the accreting envelope of a protostar and the formation of the large-scale magnetic field. Astron. Rep. 56(2), 84–95 (2012)Google Scholar
  7. 7.
    Chakrabarti, S., Laughlin, G., Shu, F.H.: Branch, Spur, and Feather Formation in Spiral Galaxies. Astrophys. J. 596(1), 220–239 (2003)Google Scholar
  8. 8.
    Lugovskii, A.Y., Filistov, E.A.: Numerical modeling of transient structures in the disks of spiral galaxies. Astron. Rep. 58(2), 48–62 (2014)Google Scholar
  9. 9.
    Mingalev, I.V., Rodin, A.V., Orlov, K.G.: Numerical simulations of the global circulation of the atmosphere of Venus: Effects of surface relief and solar radiation heating. Sol. Syst. Res. 49(1), 24–42 (2015)Google Scholar
  10. 10.
    Couch, S.M., Ott, C.D.: The role of turbulence in neutrino-driven core-collapse supernova explosions. Astroph. J. 799, 5–15 (2015)Google Scholar
  11. 11.
    Wongwathanarat, A., Muller, E., Janka, H.-T.: Three-dimensional simulations of core-collapse supernovae: from shock revival to shock breakout. Astron. Astrophycs. 577(A48), 1–20 (2015)Google Scholar
  12. 12.
    Mingalev, I.V., Astaf’eva, N.M., Orlov, K.G., Chechetkin, V.M., Mingalev, V.S., Mingalev, O.V.: Numerical simulation of formation of cyclone vortex flows in the intratropical zone of convergence and their early detection. Cosm. Res. 50(3), 233–248 (2012)Google Scholar
  13. 13.
    Belotserkovskii, O.M., Mingalev, I.V., Mingalev, V.S., Mingalev, O.V., Oparin, A.M., Chechetkin, V.M.: Formation of large-scale vortices in shear flows of the lower atmosphere of the earth in the region of tropical latitudes. Cosm. Res. 47(6), 466–479 (2009)Google Scholar
  14. 14.
    Schwab, J., Martínez-Rodríguez, H., Piro, A.L., Badenes, C.: Exploring the carbon simmering phase: Reaction rates, mixing, and the convective Urca process. Astrophys. J. 851(2), 105 (2017)Google Scholar
  15. 15.
    Melson, T., Heger, A., Janka, H.T.: Supernova simulations from a 3D progenitor model—Impact of perturbations and evolution of explosion properties. Mon. Not. R. Astron. Soc. (MNRAS) 472(1), 491–513 (2017)Google Scholar
  16. 16.
    Dolence, J.C., Burrows, A., Zhang, W.: Two-dimensional core-collapse supernova models with multi-dimensional transport. Astroph. J. 800, 10 (2015)Google Scholar
  17. 17.
    Lugovsky, A.Y., Popov, Y.P.: Roe–Einfeldt–Osher scheme as applied to the mathematical simulation of accretion disks on parallel computers. Comput. Math. Math. Phys. 55(8), 1407–1418 (2015)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Babakov, A.V., Popov, M.V., Chechetkin, V.M.: Mathematical Simulation of a Massive Star Evolution Based on a Gasdynamical Model. Math. Models Comput. Simul. 10(3), 357–362 (2018)MathSciNetGoogle Scholar
  19. 19.
    Belotserkovskii, O.M., Severinov, L.I. (1973) The conservative “flow” method and the calculation of the flow of a viscous heat-conducting gas past a body of finite size. U.S.S.R. Comput. Math. Math. Phys. 13(2), 141–156Google Scholar
  20. 20.
    Belotserkovskii, O.M., Babakov, A.V.: The simulation of the coherent vortex structures in the turbulent flows. Adv. Mech. Pol. 13(3–4), 135–169 (1990)Google Scholar
  21. 21.
    Babakov, A.V.: Numerical simulation of spatially unsteady jets of compressible gas on a multiprocessor computer system. U.S.S.R. Comput. Math. Math. Phys. 51(2), 235–244 (2011)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Babakov, A.V., Novikov, P.A.: Numerical simulation of unsteady vortex structures in near wake of poorly streamlined bodies on multiprocessor computer system. U.S.S.R. Comput. Math. Math. Phys. 51(2), 245–250 (2011)zbMATHGoogle Scholar
  23. 23.
    Babakov, A.V.: Program package FLUX for the simulation of fundamental and applied problems of fluid dynamics. U.S.S.R. Comput. Math. Math. Phys. 56(6), 1151–1161 (2016)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Belotserkovskii, O.M., Babakov, A.V., Beloshitskii, A.V., Gaidaenko, V.I., Dyadkin, A.A.: Numerical simulation of some problems of recovery capsule aerodynamics. Math. Models Comput. Simul. 8(5), 568–576 (2016)Google Scholar
  25. 25.
    Aksenov, A.G.: Numerical solution of the Poisson equation for the three-dimensional modeling of stellar evolution. Astron. Lett. 25, 185–190 (1999)Google Scholar
  26. 26.
    Aksenov, A.G., Blinnikov, S.I.: A Newton iteration method for obtaining equilibria of rapidly rotating stars. Astron. Astrophys. 290, 674–681 (1994)Google Scholar
  27. 27.
    Osher, S., Solomon, F.: Upwind difference schemes for hyperbolic systems of conservations laws. Math. Comput. 38, 339–374 (1982)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Chakravarthy, S., Osher, S.: A new class of high accuracy TVD schemes for hyperbolic conservation laws. AIAA Papers 85(0363), 1–11 (1985)Google Scholar
  29. 29.
    Einfeldt, B.: On Godunov_type methods for gas dynamics. SIAM J. Numer. Anal. 25, 294–318 (1988)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Kuznetsov, O.A.: Preprint No. 43. IPM RAN (Keldysh Inst. of Applied Mathematics of Russian Academy of Sciences), Moscow (1998)Google Scholar
  31. 31.
    Abakumov, M.V.: Construction of flux difference schemes and their application to the computation of gas flows in accretion disks. MAKS Press, Moscow (2012)Google Scholar
  32. 32.
    Abakumov, M.V., Mukhin, S.I., Popov, Y.P., Chechetkin, V.M.: Studies of equilibrium configurations for a gaseous cloud near a gravitating center. Astron. Rep. 40(3), 366–377 (1996)zbMATHGoogle Scholar
  33. 33.
    Abakumov, M.V., Mukhin, S.I., Popov, Y.P., Chechetkin, V.M.: Comparison between two and three dimensional modeling of the structure of an accretion disk in a binary system. Astron. Rep. 47(1), 11–19 (2003)Google Scholar
  34. 34.
    Belotserkovskii, O.M., Oparin, A.M.: Numerical experiment in turbulence: from order to chaos. Nauka, Moscow (2001)zbMATHGoogle Scholar
  35. 35.
    Belotserkovskii, O.M., Chechetkin, V.M., Fortova, S.V., Oparin, A.M., Popov, Y.P., Lugovsky, A.Y., Mukhin, S.I.: The turbulence in free shear flows and in accretion discs. Astron. Astrophys. Trans. 25, 419–434 (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander V. Babakov
    • 1
  • Alexey Yu. Lugovsky
    • 2
  • Valery M. Chechetkin
    • 2
  1. 1.Institute for Computer Aided Design of the RASMoscowRussian Federation
  2. 2.Keldysh Institute of Applied Mathematics of the RASMoscowRussian Federation

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