Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Papers : Analysis of Numerical Instability of AUSM - type Schemes

논문 : AUSM 계열 수치기법의 수치적 불안정성에 대한 분석

  • Published : 2002.05.31
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Abstract

Numerical stability is studied based on numerics and mathematics. It is frequently observed in the region where velocity is zero. In that region, the Euler equation have numerous solutions and, thus, it is impossible to determine a unique solution with only governing equations. However, a unique solution can be determined by additional outer flow conditions or outer numerical discontinuity calculation since the information or a unique solution under undisturbed conditions is lost by disturbances. In this reason, the numerical scheme comsistent with Euler equations cannot remove shock instability completely.

AUSM계열 수치기법의 수치적 불안정성에 대한 원인과 해결방안에 대한 연구를 수행하였다. Euler 유동에서 수치적 불안정성은 제어면에 수직한 방향의 유동속도가 영인 영역에서 발생하며 이 영역에서 Eule r 방정식은 근본적으로 부정해를 가지게 되어 무수히 많은 해를 가지게 된다. 지배방정식 자체로는 유일해를 찾는 것이 불가능하고 주위의 유동조건이나 외부교란에 의해 유일해를 결정하게 된다. 이러한 특징은 충격파 영역에서 교란이 존재할 경우 초기 상태에 대한 정보를 상실하게 되어 충격파 불안정성을 유발하게 된다. slip유동을 정확히 계산할 수 있는, 즉 유일해를 결정할 수 없는, 수치기법은 충격파 불안정성을 근본적으로 제거할 수 없다.

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References

  1. P. L. Roe, "Approximate Riemann Solvers, Parameter Vectors and Difference Schemes," J. of Computational Physics, 43, 357-372 (1981). https://doi.org/10.1016/0021-9991(81)90128-5
  2. J. J. Quirk, "A Contribution to the Great Riemann Solver Debate," Int. J. for Numerical Methods in Fluids, 18, 555, (1994). https://doi.org/10.1002/fld.1650180603
  3. M. S. Liou, and C. J. Steffen Jr., "A New Flux Splitting Scheme," J. of Computational Physics, 107, 23-39 (1993). https://doi.org/10.1006/jcph.1993.1122
  4. M. S. Liou, and Y. Wada, "A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities," AIAA Paper 94-0083, (1994).
  5. M. S. Liou, "A Sequel to AUSM: AUSM+," J. of Computational Physics, 129, 364-382 (1996). https://doi.org/10.1006/jcph.1996.0256
  6. K. H. Kim, J. H. Lee, and O. H. Rho, "An Improvement of AUSM Schemes by Introducing the Pressure-based Weight Functions," Computers & Fluids, 27(3), 311-346 (1998). https://doi.org/10.1016/S0045-7930(97)00069-8
  7. K. H. Kim, C. Kim, and O. H. Rho, "Methods for the Accurate Computations of Hypersonic Flows, PART I: AUSMPW+ Scheme," accepted to J. of Computational Physics, (2001). https://doi.org/10.1006/jcph.2001.6873
  8. M. S. Liou, "Mass Flux Schemes and Connection to Shock Instability," J. of Computational Physics, 160, 623-648, (2000). https://doi.org/10.1006/jcph.2000.6478
  9. K. H. Kim, C. Kim, and O. H. Rho, "Methods for the Accurate Computations of Hypersonic Flows, PART II: Shock aligned Grid Technique," accepted to J. of Computational Physics, (2001). https://doi.org/10.1006/jcph.2001.6896
  10. B. Van Leer, "Flux-vector Splitting for the Euler Equation," Lecture Notes in physics, 170, 507-512 (1982). https://doi.org/10.1007/3-540-11948-5_66