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Shock Wave Detection Based on the Theory of Characteristics

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Shock Fitting

Part of the book series: Shock Wave and High Pressure Phenomena ((SHOCKWAVE))

Abstract

Detecting the locations of shock waves in the computational domain of a shock-capturing solution is of a great importance from the viewpoint of the shock-fitting methodology. This paper introduces an algorithm for detecting shock waves from shock-capturing solutions based on the theory of characteristics. A shock wave is easily identified as a collision of characteristics of the same family, and the authors show a method of extracting the shock wave location by introducing local linearization of the vector field of the characteristics. The authors also show the successful extensions of this method to unsteady and three-dimensional flowfields. The following is a brief summary of these topics.

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References

  1. Anderson, J.D.J.: Modern Compressible Flow with Historical Perspective. McGraw-Hill Publishing Company, New York (1990)

    Google Scholar 

  2. Buning, P.G., Steger, J.L.: Graphics and Flow Visualization in Computational Fluid Dynamics. AIAA Paper 85-1507, pp. 162–167 (1985)

    Google Scholar 

  3. Darmofal, D.: Hierarchal visualization of three-dimensional vortical flow calculation. Ph.D. thesis, Massachusetts Institute of Technology (1991)

    Google Scholar 

  4. Darmofal, D.: An image analysis based approach to shock identification in CFD. AIAA Journal 95-0117 (1995)

    Google Scholar 

  5. Glimm, J., Grove, J.W., Kang, Y., Lee, T., Li, X., Sharp, D.H., Yu, Y., Ye, K., Zhao, M.: Statistical Riemann problems and a composition law for errors in numerical solutions of shock physics problems. SIAM J. Sci. Comput. 26, 666–697 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Glimm, J., Grove, J.W., Kang, Y., Lee, T., Li, X., Sharp, D.H., Yu, Y., Ye, K., Zhao, M.: Errors in numerical solutions of spherically symmetric shock physics problems. Contemp. Math. 371, 163–179 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.R.: Uniformly high order accurate essentially non-oscillarory schems, III. J. Comput. Phys. 71, 231–303 (1987)

    Article  ADS  MATH  Google Scholar 

  8. Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems, and an Introduction of Chaos. Academic Press, Cambridge (2003)

    MATH  Google Scholar 

  9. Kanamori, M., Suzuki, K.: Shock wave detection in two-dimensional flow based on the theory of characteristics from CFD data. J. Comput. Phys. 230(8), 3085–3092 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Kanamori, M., Suzuki, K.: Three-dimensional shock wave detection based on the theory of characteristics. AIAA J. 51(9), 2126–2132 (2013)

    Article  ADS  Google Scholar 

  11. Liou, S.P., Mehlig, S., Singh, A., Edwards, D., Davis, R.: An image analysis based approach to shock identification in CFD. AIAA Paper 95-0117 (1995)

    Google Scholar 

  12. Lovely, D., Haimes, R.: Shock detection from computational fluid dynamics results. AIAA Paper 99-3285 (1999)

    Google Scholar 

  13. Ma, K.L., Rosendale, J.V., Vermeer, W.: 3D shock wave visualization on unstructured grids. In: Crawfis, R., Hansen, C. (eds.) Proceedings of the 1996 Symposium on Volume visualization, pp. 87–104 (1999)

    Google Scholar 

  14. Moretti, G.: Computation of flows with shocks. Annu. Rev. Fluid Mech. 19, 313–337 (1987)

    Article  ADS  Google Scholar 

  15. Paciorri, R., Bonfiglioli, A.: Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique. J. Comput. Phys. 230(8), 3155–3177 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Shima, E., Jounouchi, T.: Role of CFD in aeronautical engineering (no.14) - AUSM type upwind schemes. In: Ebihara, M. (ed.) Proceedings of the 14th NAL Symposium on Aircraft Computational Aerodynamics, pp. 7–24 (1999)

    Google Scholar 

  17. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillaroty shock-capturing schemes. J. Comput. Phys. 77, 439–471 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83, 32–78 (1989)

    Article  ADS  MATH  Google Scholar 

  19. Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  20. van Leer, B.: Toward the ultimate conservative difference scheme. 4, a new approach to numerical convection. J. Comput. Phys. 23, 276–299 (1977)

    Google Scholar 

  21. van Leer, B.: Toward the ultimate conservative difference scheme. 5, a second-order sequel to godunov’s method. J. Comput. Phys. 32, 101–136 (1979)

    Google Scholar 

  22. Woodward, P., Colella, P.: The numerical simulation of two-dimensional fluid with strong shock. J. Comput. Phys. 54, 115–173 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Yee, H.C.: Construction of explicit and implicit symmetric TVD schemes and their applications. J. Comput. Phys. 68, 151–179 (1987)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Yee, H.C., Warming, R.F., Harten, A.: Implicit total variation diminishing (TVD) schemes for steady-state calculations. J. Comput. Phys. 57, 327–360 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Yoon, S., Kwak, D.: An implicit three-dimensional Navier-Stokes solver for compressible flow. AIAA J. 30(11), 2635–2659 (1992)

    MATH  Google Scholar 

  26. Zeldovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Publications, Mineola (2002)

    Google Scholar 

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Correspondence to Masashi Kanamori .

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Kanamori, M., Suzuki, K. (2017). Shock Wave Detection Based on the Theory of Characteristics. In: Onofri, M., Paciorri, R. (eds) Shock Fitting. Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-319-68427-7_8

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