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Journal of Scientific Computing

, Volume 34, Issue 3, pp 247–259 | Cite as

Positive Scheme Numerical Simulation of High Mach Number Astrophysical Jets

  • Youngsoo Ha
  • Carl L. Gardner
Article

Abstract

High Mach number astrophysical jets are simulated using a positive scheme, and are compared with WENO-LF simulations. A version of the positive scheme has allowed us to simulate astrophysical jets with radiative cooling up to Mach number 270 with respect to the heavy jet gas, a factor of two times higher than the maximum Mach number attained with the WENO schemes and ten times higher than with CLAWPACK. Such high Mach numbers occur in many settings in astrophysical flows, so it is important to develop a scheme that can simulate at these Mach numbers.

Keywords

Astrophysical jets Radiative cooling Positive scheme simulations 

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References

  1. 1.
    Hester, J.J., Stapelfeldt, K.R., Scowen, P.A.: Hubble space telescope wide field planetary camera 2 observations of HH 1–2. Astron. J. 116, 372–395 (1998) CrossRefGoogle Scholar
  2. 2.
    Ha, Y., Gardner, C.L., Gelb, A., Shu, C.-W.: Numerical simulation of high Mach number astrophysical jets with radiative cooling. J. Sci. Comput. 24, 29–44 (2005) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Gardner, C.L., Ha, Y., Hester, J.J., Krist, J.E., Shu, C.-W., Stapelfeldt, K.R.: Numerical simulation of high Mach number astrophysical jets. In: Analysis, Modeling and Computation of Hyperbolic PDE and Multiphase Flow. SUNY, Stony Brook (2005) Google Scholar
  4. 4.
    Liu, X.-D., Lax, P.D.: Positive schemes for solving multi-dimensional hyperbolic systems of conservation laws. J. Comput. Fluid Dyn. 5, 133–156 (1996) Google Scholar
  5. 5.
    Lax, P.D., Liu, X.-D.: Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM J. Sci. Comput. 19, 319–340 (1998) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Shu, C.-W.: High order ENO and WENO schemes for computational fluid dynamics. In: High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering, vol. 9, pp. 439–582. Springer, New York (1999) Google Scholar
  8. 8.
    LeVeque, R.J.: CLAWPACK website. http://www.amath.washington.edu/~claw/
  9. 9.
    LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002) MATHGoogle Scholar
  10. 10.
    Schmutzler, T., Tscharnuter, W.M.: Effective radiative cooling in optically thin plasmas. Astron. Astrophys. 273, 318–330 (1993) Google Scholar
  11. 11.
    Lax, P.D., Wendroff, B.: Systems of conservation laws. Commun. Pure Appl. Math. 13, 217 (1960) MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Borice, J.P., Book, D.L.: Flux corrected transport I, SHASTA, a fluid transport algorithm that works. J. Comput. Phys. 11, 38–69 (1973) CrossRefGoogle Scholar
  13. 13.
    Harten, A., Zwas, G.: Self-adjusting hybrid schemes for shock computations. J. Comput. Phys. 9, 568–583 (1973) CrossRefMathSciNetGoogle Scholar
  14. 14.
    Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357–372 (1981) MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Harten, A.: On a class of high resolution total-variation-stable finite-difference schemes. SIAM J. Numer. Anal. 21, 1–23 (1984) MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sweby, P.K.: High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21, 995–1011 (1984) MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Shu, C.-W.: Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9, 1073–1084 (1988) MATHCrossRefGoogle Scholar
  18. 18.
    Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes II. J. Comput. Phys. 83, 32–78 (1989) MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Shu, C.-W.: Private communication Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Division of Applied MathematicsKorean Advanced Institute of Science and TechnologyTaejonSouth Korea
  2. 2.Department of Mathematics and StatisticsArizona State UniversityTempeUSA

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