Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ANALYTICAL AND NUMERICAL STUDY OF MODE INTERACTIONS IN SHOCK-INDUCED INTERFACIAL INSTABILITY

  • Sohn, Sung-Ik (School of Information Engineering Tongmyong University of Information Technology)
  • Published : 2000.01.01
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Abstract

Mode interactions at Unstable fluid interfaces induced by a shock wave (Richtmyer-Meshkov Instability) are studied both analytically and numerically. The analytical approach is based on a potential flow model with source singularities in incompressible fluids of infinite density ratio. The potential flow model shows that a single bubble has a decaying growth rates at late time and an asymptotic constant radius. Bubble interactions, bubbles of different radii propagates with different velocities and the leading bubbles grow in size at the expense of their neighboring bubbles, are predicted by the potential flow model. This phenomenon is validated by full numerical simulations of the Richtmyer-Meshkov instability in compressible fluids for initial multi-frequency perturbations on the unstable interface.

Keywords

References

  1. Comm. Pure Appl. Math. v.13 Taylor istability in shock acceleration of compressible fluids R. D. Richtmyer
  2. Phys. Fluids v.15 Numercal investigation of the stability of a shock-accelerated interfaces between two fluids K. A. Meyer;P. J. Blewett
  3. Phys. Fluids v.29 Rayeigh-Taylor stability for a normal shock wave-density discontiunity interaction G. Fraley
  4. Fhys. Fluids v.29 Small amplitude theory of Richtmyer-Meshkov instability Y. Yang
  5. Phys. Fluids v.6 Potential flow models of Rayleigh-Taylor and Rich J. Hecht;U. Alon;D. Shvarts
  6. J. Fluid Mech. v.301 A numerical investingation of Richtmyer-Meshkov instability using front tracking R. L. Holmes;J. W. Grove;D. H. Sharp
  7. Phys. Fluids v.9 Nonlinear solutions of unstable fluid mixing diven by shock waves Q. Zhang;S.-I. Sohn
  8. Zeit. angew. Math. Phys. v.50 Quantitiative theory of Richtmyer-Meshkov instability in theree dimensions
  9. SIAM J. Sci. Stat. Comput. v.7 Front tracking for gas dynamics I.-L. Chern;J. Glimm;O. McBryan;B. Plohr;S. Yaniv
  10. Proc. R. Soc. London A v.201 The instability of liquid surfaces when accelerated in an direction perpendicular to their planes Ⅰ G. I. Taylor
  11. Astro-phys. J v.122 On the instability of superimposed fluids in a gravitational field D. Layzer
  12. Proc. R. Soc. London A v.241 On steady-state bubbles generated by Taylor istability P. R. Garabedian
  13. Phys. Rev. A v.33 Nonlinear free-suface Rayleigh-Taylor instability H. J. Kull
  14. Phys. Fluids v.31 Bubble competition in Rayleigh-Taylor instability J. Zufiria
  15. Phys. Fluids v.27 Bubbles rising in a tube and jets falling form a nozzle J.-M. Vanden-Broeck
  16. Theoretical hybrodynamics L. M. Milne-Thompson
  17. Supersonic flow and shock waves R. Courant;K. O. Friedrich
  18. Adv. Appl. Math. v.6 Front tracking and two dimensional Riemann problems J. Glimm;C. Klingenberg;O. McBryan;B. Plohn;D. Sharp;S. Yaniv
  19. Phys. Fluids A v.2 A numerical study of bubble interactions in Rayleigh-Taylor instability for compressible fluids J. Glimm;X. L. Li;R. Menikoff;D. H. Sharp;Q. Zhang
  20. Appl. Num. Math. v.14 Applications of fornt tracking to the simulation of shock refractons and unstable mixing J. Grove
  21. Comm. Kor. Math. Soc. v.13 On the numerical methods for discontinuties and interfaces H.-C. Hwang
  22. J. Comp. Phys. v.32 Towards the ultimate conservation difference scheme. V. A second-order sequet to Godunov's method B. van Leer