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Convergence acceleration of iterative solutions of Euler equations for transonic flow computations

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Abstract

In this paper, two acceleration techniques for Euler calculations are investigated. The first technique is an extrapolation procedure based on the Power Method; it is applicable when the iterative matrix has dominant eigenvalues. Both real and complex conjugate roots are allowed. The second technique is a generalization of the Minimal Residual Method, where the extrapolation step consists of a weighted combination of the corrections at different iteration levels and the weights are chosen to minimize the L 2-norm of the residual. Numerical results, using Jameson's Runge-Kutta Multigrid Code, are presented. The extra computational work to apply either technique is negligible and the extra storage is not a problem on current supercomputers.

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References

  • Boerstoel, A., Kassies, A. (1983) : Integrating multigrid relaxation into a robust fast-solver for transonic potential flows around lifting airfoils. AIAA Paper 83-1855

  • Doria, M. (1985): Private communication

  • Eriksson, L.; Rizzi, A. (1983): Analysis by computer of the convergence to steady state of discrete approximations to the Euler equations. AIAA Paper 83-1951

  • Hafez, M. (1983): Progress in finite element techniques for transonic flows. AIAA Paper 83-1919

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  • Hafez, M.; Whitlow, W.; Osher, S. (1984) : Improved finite difference schemes for transonic potential calculation. AIAA Paper 84-0092

  • Jameson, A. (1983): Solution of the Euler equations for two-dimensional transonic flow by a multigrid method. Applied Math. Comp. 13, 327–356

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  • Jesperson, D. (1983): Design and implementation of a multigrid code for the Euler equations. Applied Math. Comp. 13, 327–356

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  • Kreiss, G.; Kreiss, H.O. (1985) : Convergence to steady state of solutions of Burger's equation. ICASE Rep. No. 85-50

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The reader is referred to two recent papers, where similar ideas can be found

  • Jesperson, D.C.; Buning, P.G. (1985): Accelerating an iterative process by explicit annihilation. SIAM J. Sci. Stat. Comput. 6, 639–651

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  • Wigton, L.B. ; Yu, N.J. ; Young, D.P. (1985) : GMRES acceleration of computational fluid dynamics codes. AIAA Paper 1494

  • The present paper, however, is based on the early work of Hafez and Cheng in 1975 and it was presented at AIAA 18th Fluid and Plasma Dynamics in July 1985 as AIAA Paper 85-1641

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Authors and Affiliations

  1. University of California, Davis, CA, USA

    M. Hafez

  2. Vigyan Research Associates, Inc., Hampton, VA, USA

    E. Parlette

  3. NASA Langley Research Center, Hampton, VA, USA

    M. Salas

Authors
  1. M. Hafez
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  2. E. Parlette
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  3. M. Salas
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Additional information

Communicated by S.N. Atluri, February 26, 1986

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Hafez, M., Parlette, E. & Salas, M. Convergence acceleration of iterative solutions of Euler equations for transonic flow computations. Computational Mechanics 1, 165–176 (1986). https://doi.org/10.1007/BF00272622

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  • DOI: https://doi.org/10.1007/BF00272622

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