Skip to main content
Springer Nature Link
Log in

A Multigrid Parallel Program for Protoplanetary Disc Simulation

  • Conference paper
Parallel Computing Technologies (PaCT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3606))

Included in the following conference series:

  • 512 Accesses

Abstract

In this paper we present a program for simulation of the two-component protoplanetary disc evolution. The model includes gas dynamics and collisionless solid body dynamics. Multigrid method for solution of Poisson equation in cylindrical coordinate system is described. An essentially parallel Poisson equation solver is constructed by means of applying Fast Fourier Transform along the angular direction. Processor workload rearrangement is performed in order to increase the speedup. The results of computational experiments are given to demonstrate the physical validity of the program.

The present work was supported by SB RAS integration project number 148, Subprogram 2 of RAS Presidium Program ”Biosphere genesis and evolution”, and RFBR (grant 05-01-00665), Dutch-Russian NWO-GRID project, contract NWO-RFBS 047.016.007 and Dutch-Russian NWO-Plasma project, contract NWO-RFBS 047.016.018.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Barranco, J., Marcus, P.: Vortices in Protoplanetary Disks and the Formation of Planetesimals. In: DPS 2001 meeting BAAS, p. 33 (2001)

    Google Scholar 

  2. Belotserkovsky, O.M., Davydov, Y.M.: Fluids-in-cells method in gas dynamics. Nauka Publishers, Moscow (1982) (in Russian)

    Google Scholar 

  3. Chan, T.F., Wan, W.L.: Robust multigrid methods for nonsmooth coefficient elliptic linear systems. Journal of Computational and Applied Mathematics 123, 323–352 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Demmel, J.W.: Applied Numerical Linear Algebra. SIAM, Philadelphia (1997)

    MATH  Google Scholar 

  5. De la Fuente Marcos, C., Barge, P.: The effect of long-lived vortical circulation on the dynamics of dust particles in the mid-plane of a protoplanetary disc. MNRAS 323, 601 (2001b)

    Article  Google Scholar 

  6. Grigoryev, Y.N., Vshivkov, V.A., Fedoruk, M.P.: Numerical “Particle-in-Cell” Methods. Theory and Applications. VSP (2002)

    Google Scholar 

  7. Hockney, R.W., Eastwood, J.W.: Computer Simulation Using Particles. IOP Publishing, Bristol (1988)

    Book  MATH  Google Scholar 

  8. Kornet, K., Stepinski, T., Rozyczka, M.: Diversity of planetary systems from evolution of solids in protoplanetary disks. Astronomy and Astrophysics 378, 180 (2001)

    Article  Google Scholar 

  9. Kuksheva, E.A., Malyshkin, V.E., Nikitin, S.A., Snytnikov, A.V., Snytnikov, V.N., Vshivkov, V.A.: Numerical Simulation of Self-Organisation in Gravitationally Unstable Media on Supercomputers. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 354–368. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Pickett, B.K., Durisen, R.H., Davis, G.A.: The Dynamic Stability of Rotating Protostars and Protostellar Disks. I. The Effects of Angular Momentum Distribution. Astrophysical Journal 458, 714–738 (1996)

    Google Scholar 

  11. Snytnikov, A.V.: A Parallel Program for Simulation of Disc-Shaped Self-Gravitating Systems. Bull. Nov. Comp. Center, Comp. Science 19, 73–81 (2003)

    Google Scholar 

  12. Snytnikov, V.N., Dudnikova, G.I., Gleaves, J.T., Nikitin, S.A., Parmon, V.N., Stoyanovsky, V.O., Vshivkov, V.A., Yablonsky, G.S., Zakharenko, V.S.: Space chemical reactor of protoplanetary disk. Adv. Space Res. 30(6), 1461–1467 (2002)

    Article  Google Scholar 

  13. Snytnikov, V.N., Vshivkov, V.A.: Three-Dimensional Numerical Simulation of a Nonstationary Gravitating N-Body System with Gas. Astronomy Letters 30(2), 124–138 (2004)

    Article  Google Scholar 

  14. Toomre, A.: On the gravitational stabilty of a disc of stars. Astrophys. J. 139, 1217 (1964)

    Article  Google Scholar 

  15. Wesseling, P.: An Introduction to Multigrid Methods. John Wiley & Sons, Chichester (1992)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Lavrientieva av. 6, Novosibirsk, 630090, Russia

    Alexey V. Snytnikov & Vitaly A. Vshivkov

Authors
  1. Alexey V. Snytnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vitaly A. Vshivkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Novosibirsk State Technical University,  

    Victor Malyshkin

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Snytnikov, A.V., Vshivkov, V.A. (2005). A Multigrid Parallel Program for Protoplanetary Disc Simulation. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2005. Lecture Notes in Computer Science, vol 3606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11535294_41

Download citation

  • DOI: https://doi.org/10.1007/11535294_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28126-9

  • Online ISBN: 978-3-540-31826-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics