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Solving schemes for computational magneto-aerodynamics

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Abstract

The electromagnetic force introduces a new physics dimension for enhancing aerodynamic performance of aerospace vehicles. In order to simulate interdisciplinary phenomena, the Navier-Stokes and Maxwell equations in the time domain must be integrated on a common frame of reference. For a wide range of applications from subsonic unmanned vehicles to hypersonic flight control, the resultant nonlinear partial differential equations offer a formidable challenge for numerical analysis. The experience and physical insight using the approximate Riemann and compact-differencing formulation as well as several temporal discritizations will be shared. The most recent development and advancement in numerical procedures for solving this system of governing equations are delineated.

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References

  1. Resler, E. L., and Sears, W. R. (1958). The prospect for magneto-aerodynamics,J. Aero. Science 1958 25, 235–245 and 258.

    MathSciNet  Google Scholar 

  2. Shang, J. S. (2001). Recent research in magneto-aerodynamics,Progress in Aerospace Sciences 31, 1–20.

    Article  Google Scholar 

  3. Shang, J. S. (2003).Historical Perspective of Magneto-Fluid-Dynamics, VKI Lecture Series on Introduction to Magneto-Fluid-Dynamics, von Karman Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium, pp. 27–30.

    Google Scholar 

  4. Shang, J. S. (2003).MFD Research in US Toward Aerospace Applications, VKI Lecture Series on Introduction to Magneto-Fluid-Dynamics, von Karman Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium, pp. 27–30.

    Google Scholar 

  5. Mitchner, M., and Kruger, C. (1973).Partial Ionized Gases, John Wiley, New York.

    Google Scholar 

  6. Brio, M., and Wu, C. C. (1988). An upwind differencing scheme for the equations of ideal magnetohydrodynamics,JCP 75, 400–422.

    MATH  MathSciNet  Google Scholar 

  7. Powell, K. G., Roe, P. L. Linde, T. J. Gombosi, T. I. and De Zeeuw, D. (1999). A solution adaptive upwind scheme for ideal magnetohydrodynamics,JCP 154 284–309.

    MATH  Google Scholar 

  8. Gaitonde, D. V. (2003). Three-dimensional flow-through scramjet simulation with MGD energy-bypass,AIAA 2003–0172.

  9. Surzhikov, S. T. and Shang, J. S. (2003). Glow discharge in magnetic field,AIAA 2003–1054, Reno NV, 6–9.

  10. Surzhikov, S. T. and Shang, J. S. (2003). Glow discharge in magnetic field with heating of neutral gas,AIAA 2003–3654, Orlando FL., 23–26.

  11. Raizer, Yu. P., and Surzhikov, S. T. (1988). Two-dimensional structure of the normal glow discharge and the role of diffusion in forming of cathode and anode current spots,High Temperatures 26(3).

  12. Menart, J., Shang, J., Kimmel, R., and Hayes, J. (2003). Effects of magnetic fields on plasmas generated in a Mach 5 wind tunnel,AIAA 2003–4165, Orlando FL.

  13. Shang, J. S. (2002). Plasma injection for hypersonic blunt body drag reduction,AIAA J. 40(6), 1178–1186.

    Article  Google Scholar 

  14. Shang, J. S. (2002). Shared knowledge in computational fluid dynamics, electromagnetics, and magneto-aerodynamics,Progress in Aerospace Sciences,38, 449–467.

    Article  Google Scholar 

  15. Gottlieb, D., and Orsag, S., (1997).Numerical analysis of Spectral Methods, SIAM, Philadelphia, PA.

    Google Scholar 

  16. Colatz, L. (1966).The Numerical Treatment of Differential Equations, Springer-Verlag, New York.

    Google Scholar 

  17. Lele, S. K. (1992). Compact finite difference schemes with spectral-like resolution,JCP 103, 16–42.

    MATH  MathSciNet  Google Scholar 

  18. Tam, C. K. W., and Weber, J. C. (1993). Dispersion-relation-preserving finite different schemes for computational acoustics,JCP 262–281.

  19. Carpenter, M. K., Gottlieb, D., and Abarbanel, S. (1994). Time stable boundary conditions for finite-difference scheme solving hyperbolic systems: methodology and application to high-order compact schemes,JCP 111, 220–236.

    MATH  MathSciNet  Google Scholar 

  20. Gaitonde, D., and Shang, J. S. (1997). Optimized compact-difference-based finite-volume schemes for linear wave phenomena,JCP 138, 617–643.

    MATH  MathSciNet  Google Scholar 

  21. Shang, J. S. (1999). High-order compact-difference schemes for time-dependent maxwell equations,JCP 153, 312–333.

    MATH  MathSciNet  Google Scholar 

  22. Gaitonde, D., and Visbal, M. (2003). Advances in the application of high-order techniques in simulation of multi-disciplinary phenomena,Inter. J. Comp. Fluid Dynamics 17, 95–1006.

    Article  MATH  MathSciNet  Google Scholar 

  23. Shang, J. S. (1995). A fractional-step method for solving 3-D, time-domain maxwell equations,JCP 118, 109–119.

    MATH  Google Scholar 

  24. Steger, J. L. and Warming, R. F. (1981). Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,JCP 40, 263–293.

    MATH  MathSciNet  Google Scholar 

  25. van Leer, B. (1982).Flux-Vector Splitting for the Euler Equations, Inst. for Computer Applications in Science and Engineering, TR 82-30, NASA Langley.

  26. MacCormack, R. W. (1999). An upwind conservation form method for the ideal magnetohydrodynamics equations,AIAA 99–3609, Norfolk VA.

  27. Shang, J. S., Canupp, P. W., and Gaitonde, D. V. (1999). Computational magnetoaerodynamic hypersonics,AIAA 99–4903, Norfolk VA.

  28. von Engel, A., and Steenbeck, M. (1932)Elektrische Gasentladungen, Vol. 2, Journal Springer, Berlin.

    Google Scholar 

  29. Hayes, W., and Probstein, R. (1959).Hypersonic Flow Theory, Academic Press, New York, pp. 333–365.

    MATH  Google Scholar 

  30. Harten, A. (1983). High-resolution schemes for hyperbolic conservation laws,J. CP 49, 375–385.

    Google Scholar 

  31. Gustafsson, B. (1975). The convergent rate for difference approximations to mixed initial boundary value problems,Math. Comp. 29, 396–401.

    Article  MATH  MathSciNet  Google Scholar 

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  1. Mechanical and Materials Engineering, Wright State University, Dayton, OH, USA

    J. S. Shang

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  1. J. S. Shang
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Correspondence to J. S. Shang.

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Shang, J.S. Solving schemes for computational magneto-aerodynamics. J Sci Comput 25, 289–306 (2005). https://doi.org/10.1007/BF02728992

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  • DOI: https://doi.org/10.1007/BF02728992

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