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The Godunov Schemes

  • Maurice Holt
Part of the Springer Series in Computational Physics book series (SCIENTCOMP)

Abstract

In one of his earliest papers concerned with numerical schemes for solving equations of Gas Dynamics Godunov (1959) seeks an alternative to the Method of Characteristics. He proposes three main requirements for such schemes. Firstly, they should retain the simplicity of Characteristics Methods while overcoming the inconveniences introduced by shearing and distortion of characteristics networks. Secondly, they should be able to include consideration of surfaces of discontinuity such as shock waves and fluid interfaces. Thirdly, when applied to linearized equations they should predict a solution for physical variables which is in qualitative agreement with analytical solutions.

Keywords

Riemann Problem Contact Discontinuity Riemann Solution Direct Sweep Network Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alalykin, G. B., Godunov, S. K., Kireeva, I. L., Pliner, L. H.: Solutions of One Dimensional Problems in Gas Dynamics in Moving Networks. Moscow: NAUKA 1970.Google Scholar
  2. Chorin, A. J.: J. Comp. Phys. 22, 517–533 (1976).CrossRefMATHADSMathSciNetGoogle Scholar
  3. Chorin, A. J.: J. Comp. Phys. 25, 253–272 (1977).CrossRefMATHADSMathSciNetGoogle Scholar
  4. Colella, P.: SIAM J. Sci. Comput. 3, 76–110 (1982).CrossRefMATHMathSciNetGoogle Scholar
  5. Concus, P., Proskurowski, W.: J. Comp. Phys. 30, 153–166 (1979).CrossRefMATHADSMathSciNetGoogle Scholar
  6. Flores, J., Holt, M.: J. Comp. Phys. 44, 377–387 (1981).CrossRefMATHADSMathSciNetGoogle Scholar
  7. Glimm, J.: Comm. Pure Appl. Math. 18, 697–715 (1955).CrossRefMathSciNetGoogle Scholar
  8. Godunov, S. K.: Mat. Shorn. 47, 271 (1959).MathSciNetGoogle Scholar
  9. Godunov, S. K., Zabrodin, A. V., Prokopov, G. P.: USSR Comp. Math. Math. Phys. 6, 1020–1050 (1961).MathSciNetGoogle Scholar
  10. Godunov, S. K., Deribas, A. A., Zabrodin, A. V., Kozin, N. S.: J. Comp. Phys. 5, 517–539 (1970).CrossRefADSGoogle Scholar
  11. Godunov, S. K., Ryabenkii, V. W.: The Theory of Difference Schemes. New York: Wiley 1964.Google Scholar
  12. Holt, M., Li, K.-M.: Phys. Fluids 24, 816 (1981).CrossRefMATHADSGoogle Scholar
  13. Masson, B. S., Taylor, T. D., Foster, R. M.: AIAA J, 7, 694 (1969).CrossRefMATHADSGoogle Scholar
  14. Masson, B. S., Taylor, T. D.: Polish Fluid Dynamic Transactions 5 (1971).Google Scholar
  15. Moretti, G.: AIAA J, 5 (1967).Google Scholar
  16. Rozhdestvenskii, B. L., Yanenko, N. N.: Theory of Quasilinear Hyperbolic Partial Differential Equations. Moscow: NAUKA 1970.Google Scholar
  17. Sod, G. A.: J. Fluid Mech. 83, 785–794 (1977).CrossRefMATHADSGoogle Scholar
  18. Sod, G. A.: J. Comp. Phys. 27, 1–31 (1978).CrossRefMATHADSMathSciNetGoogle Scholar
  19. Taylor, T. D., Masson, B. S.: J. Comp. Phys. 5 (1970).Google Scholar
  20. Taylor, T. D.: AGARDograph No. 187, 1974.Google Scholar
  21. Vasiliev, O. F.: Lecture Notes in Physics No. 8 (Ed. M. Holt), p. 410. Berlin-Heidelberg-New York: Springer 1971.Google Scholar
  22. Whitham, G. B.: Linear and Non-linear Waves. New York: Wiley 1974.Google Scholar
  23. Wigton, L.: Term paper, Course ME 266, University of California, Berkeley, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1984

Authors and Affiliations

  • Maurice Holt
    • 1
  1. 1.College of Engineering, Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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