Skip to main content
SpringerLink
Log in

Multigrid algorithms for compressible flow calculations

  • Conference paper
  • First Online:
Multigrid Methods II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1228))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hess, J.L. and Smith, A.M.O., "Calculation of Non-Lifting Potential Flow About Arbitrary Three-Dimensional Bodies", Douglas Aircraft Report, ES 40622, 1962

    Google Scholar 

  2. Rubbert, P.E. and Saaris, G.R., "A General Three Dimensional Potential Flow Method Applied to V/STOL Aerodynamics", SAE Paper 680304, 1968.

    Google Scholar 

  3. Murman, E.M. and Cole, J.D., "Calculation of Plane Steady Transonic Flows", AIAA Journal, Vol. 9, 1971, pp. 114–121.

    Article  MATH  Google Scholar 

  4. Jameson, Antony, "Iterative Solution of Transonic Flows Over Airfoils and Wings, Including Flows at Mach 1", Comm. Pure. Appl. Math, Vol. 27, 1974, pp. 283–309.

    Article  MathSciNet  MATH  Google Scholar 

  5. Jameson, Antony and Caughey, D.A., "A Finite Volume Method for Transonic Potential Flow Calculations", Proc. AIAA 3rd Computational Fluid Dynamics Conference, Albuquerque, 1977, pp. 35–54.

    Google Scholar 

  6. Bristeau, M.O., Pironneau, O., Glowinski, R., Periaux, J., Perrier, P., and Poirier, G., "On the Numerical Solution of Nonlinear Problems in Fluid Dynamics by Least Squares and Finite Element Methods (II). Application to Transonic Flow Simulations", Proc. 3rd International Conference on Finite Elements in Nonlinear Mechanics, FENOMECH 84, Stuttgart, 1984, edited by J. St. Doltsinis, North Holland, 1985, pp. 363–394.

    Google Scholar 

  7. Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes", AIAA Paper 81-1259, AIAA 14th Fluid Dynamics and Plasma Dynamics Conference, Palo Alto, 1981.

    Google Scholar 

  8. Jameson, Antony, and Baker, Timothy J., "Solution of the Euler Equations for Complex Configurations", Proc. AIAA 6th Computational Fluid Dynamics Coference, Danvers, 1983, pp. 293–302.

    Google Scholar 

  9. Pulliam, T.J., and Steger, J.L., "Recent Improvements in Efficiency, Accuracy and Convergence for Implicit Approximate Factorization Algorithms", AIAA Paper 85-0360, AIAA 23rd Aerospace Sciences Meeting, Reno, January 1985.

    Google Scholar 

  10. MacCormack, R.W., "Current Status of Numerical Solutions of the Navier-Stokes Equations", AIAA Paper 85-0032, AIAA 23rd Aerospace Sciences Meeting, Reno, January 1985.

    Google Scholar 

  11. Jameson, A., Baker, T.J., and Weatherill, N.P., "Calculation of Inviscid Transonic Flow Over a Complete Aircraft", AIAA Paper 86-0103, AIAA 24th Aerospace Sciences Meeting, Reno, January 1986.

    Google Scholar 

  12. Fedorenko, R.P., "The Speed of Convergence of One Iterative Process", USSR Comp. Math. and Math. Phys., Vol. 4, 1964, pp. 227–235.

    Article  MATH  Google Scholar 

  13. South, J.C. and Brandt, A., "Application of a Multi-Level Grid Method to Transonic Flow Calculations", Proc. of Workshop on Transonic Flow Problems in Turbomachinery, Monterey, 1976, edited by T.C. Adamson and M.F. Platzer, Hemisphere, 1977, pp. 180–206.

    Google Scholar 

  14. Jameson, Antony, "Acceleration of Transonic Potential Flow Calculations on Arbitrary Meshes by the Multiple Grid Method", Proc. AIAA 4th Computational Fluid Dynamics Conference, Williamsburg, 1979, pp. 122–146.

    Google Scholar 

  15. Caughey, D.A., "Multigrid Calculation of Three-Dimensional Transonic Potential Flows", AIAA Paper 83-0374, AIAA 21st Aerospace Sciences Meeting, Reno, January 1983.

    Google Scholar 

  16. Ni, Ron Ho., "A Multiple Grid Scheme for Solving the Euler Equations", AIAA Journal, Vol. 20, 1982, pp. 1565–1571.

    Article  MATH  Google Scholar 

  17. Jameson, A., "Solution of the Euler Equations by a Multigrid Method", Applied Math. and Computation, Vol. 13, 1983, pp. 327–356.

    Article  MathSciNet  MATH  Google Scholar 

  18. Jameson, A., and Schmidt, W., "Recent Developments in Numerical Methods for Transonic Flows", Proc. 3rd International Conference on Finite Elements in Nonlinear Mechanics, FENOMECH 84, Stuttgart, 1984, edited by J.St. Doltsinis, North-Holland, 1985, pp. 467–493.

    Google Scholar 

  19. Jameson, A., and Mavriplis, D., "Finite Volume Solution of the Two dimensional Euler Equations on a Regular Triangular Mesh", AIAA Paper 85-0435, AIAA 23rd Aerospace Sciences Meeting, Reno, January 1985.

    Google Scholar 

  20. Hall, M.G., "Cell Vertex Multigrid Schemes for Solution of the Euler Equations", IMA Conference on Numerical Methods for Fluid Dynamics", Reading, April 1985.

    Google Scholar 

  21. Hemker, P.W., and Spekreijse, S.P., "Multigrid Solution of the Steady Euler Equations", Proc. Oberwolfach Meeting on Multigrid Methods, December 1984.

    Google Scholar 

  22. Godunov, S.K., "A Difference Method for the Numerical Calculation of Discontinous Solutions of Hydrodynamic Equations", Mat. Sbornik, 47, 1959, pp. 271–306, translated as JPRS 7225 by U.S. Dept. of Commerce, 1960.

    MathSciNet  MATH  Google Scholar 

  23. Boris, J.P., and Book, D.L., "Flux Corrected Transport. 1. SHASTA, A Fluid Transport Algorithm that Works", J. Comp. Phys. Vol. 11, 1973, pp. 38–69.

    Article  MATH  Google Scholar 

  24. Van Leer, B., "Towards the Ultimate Conservative Difference Scheme. II, Monotonicity and Conservation Combined in a Second Order Scheme," J. Comp. Phys. Vol. 14, 1974, pp. 361–370.

    Article  MATH  Google Scholar 

  25. Steger, J.L., and Warming, R.F., "Flux Vector Splitting of the Inviscid Gas Dynamics Equations with Applications to Finite Difference Methods," J. Comp. Phys., Vol. 40, 1981, pp. 263–293.

    Article  MathSciNet  MATH  Google Scholar 

  26. Roe, P.L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes", J. Comp. Phys., Vol. 43, 1981, pp. 357–372.

    Article  MathSciNet  MATH  Google Scholar 

  27. Osher, S., and Solomon, F., "Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws", Math. Comp., Vol. 38, 1982, pp. 339–374.

    Article  MathSciNet  MATH  Google Scholar 

  28. Harten, A., "High Resolution Schemes for Hyperbolic Conservation Laws", J. Comp. Phys., Vol. 49, 1983, pp. 357–393.

    Article  MathSciNet  MATH  Google Scholar 

  29. Osher, Stanley, and Chakravarthy, Sukumar, "High Resolution Schemes and the Entropy Condition", SIAM J. Num. Analysis, Vol. 21, 1984, pp. 955–984.

    Article  MathSciNet  MATH  Google Scholar 

  30. Sweby, P.K., "High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws", SIAM J. Num. Analysis, Vol. 21, 1984, pp. 995–1011.

    Article  MathSciNet  MATH  Google Scholar 

  31. Anderson, B.K., Thomas, J.L., and Van Leer, B., "A Comparison of Flux Vector Splittings for the Euler Equations", AIAA Paper 85-0122, AIAA 23rd Aerospace Sciences Meeting, Reno, January, 1984.

    Google Scholar 

  32. Yee, H.C., "On Symmetric and Upwind TVD Schemes", Proc. 6th GAMM Conference on Numerical Methods in Fluid Mechanics, Göttingen, September 1985.

    Google Scholar 

  33. Jameson, A., "A Nonoscillatory Shock Capturing Scheme Using Flux Limited Dissipation", Lectures in Applied Mathematics, Vol. 22, Part 1, Large Scale Computations in Fluid Mechanics, edited by B.E. Engquist, S. Osher and R.C.J. Sommerville, AMS, 1985, pp. 345–370.

    Google Scholar 

  34. Lax, P.D., "Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves", SIAM Regional Series on Applied Mathematics, Vol. 11, 1973.

    Google Scholar 

  35. Jameson, A., and Lax, P.D., "Conditions for the Construction of Multi-Point Total Variation Diminishing Difference Schemes", Princeton University Report MAE 1650, April 1984.

    Google Scholar 

  36. Yoon, S., Private Communication.

    Google Scholar 

  37. Gilles, M., Drela, M., and Thompkins, W.T., "Newton Solution of Direct and Inverse Transonic Euler Equations", AIAA Paper 85-1530, Proc, AIAA 7th Computational Fluid Dynamics Conference, Cincinnati, 1985, pp. 394–402.

    Google Scholar 

  38. Kinmark, I.P.E., "One Step Integration Methods with Large Stability Limits for Hyperbolic Partial Differential Equations", Advances in Computer Methods for Partial Differential Equations, V, edited by R. Vichnevetsky and R.S. Stepleman, IMACS, 1984, pp. 345–349.

    Google Scholar 

  39. Jameson, A., "Transonic Flow Calculations for Aircraft", Lecture Notes in Mathematics, Vol. 1127, Numerical Methods in Fluid Dynamics, edited by F. Brezzi, Springer Verlag, 1985, pp. 156–242.

    Google Scholar 

  40. Gourlay, A.R., and Mitchell, A.R., "A Stable Implicit Difference Scheme for Hyperbolic Systems in Two Space Variables", Numer. Math., Vol. 8, 1966, pp. 367–375.

    Article  MathSciNet  MATH  Google Scholar 

  41. Beam, R.W., and Warming, R.F., "An Implicit Finite Difference Algorithm for Hyperbolic Systems in Conservation Form", J. Comp. Phys., Vol. 23, 1976, pp. 87–110.

    Article  MathSciNet  MATH  Google Scholar 

  42. Jameson, A., and Turkel E., "Implicit Schemes and LU Decompositions", Math. Comp. Vol. 37, 1981, pp. 385–397.

    MathSciNet  MATH  Google Scholar 

  43. Obayashi, S., and Kuwakara, K., "LU Factorization of an Implicit Scheme for the Compressible Navier Stokes Equations", AIAA Paper 84-1670, AIAA 17th Fluid Dynamics and Plasma Dynamics Conference, Snowmass, June 1984.

    Google Scholar 

  44. Obayashi, S., Matsukima, K., Fujii, K., and Kuwakara, K., "Improvements in Efficiency and Reliability for Navier-Stokes Computations Using the LU-ADI Factorization Algorithm", AIAA Paper 86-0338, AIAA 24th Aerospace Sciences Meeting, Reno, January 1986.

    Google Scholar 

  45. Chakravarthy, S.R., "Relaxation Methods for Unfactored Implicit Upwind Schemes", AIAA Paper 84-0165, AIAA 23rd Aerospace Sciences Meeting, Reno, January 1984.

    Google Scholar 

  46. Jameson, A., and Yoon, S., "Multigrid Solution of the Euler Equations Using Implicit Schemes", AIAA Paper 85-0293, AIAA 23rd Aerospace Sciences Meeting, Reno, January, 1985.

    Google Scholar 

  47. Jameson, A., and Yoon, S., "LU Implicit Schemes with Multiple Grids for the Euler Equations", AIAA Paper 86-0105, AIAA 24th Aerospace Sciences Meeting, Reno, January, 1986.

    Google Scholar 

  48. Anderson, W.K., Thomas, J.L., and Whitfield, D.L., "Multigrid Acceleration of the Flux Split Euler Equations", AIAA Paper 86-0274, AIAA 24th Aerospace Sciences Meeting, Reno, January 1986.

    Google Scholar 

  49. Berger, M., and Jameson, A., "Automatic Adaptive Grid Refinement for the Euler Equations", AIAA Journal, Vol. 23, 1985, pp. 561–568.

    Article  Google Scholar 

  50. Dannenhoffer, J.F., and Baron, J.R., "Robust Grid Adaption for Complex Transonic Flows", AIAA Paper 86-0495, AIAA 24th Aerospace Sciences Meeting, Reno, January 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Princeton University, 08544, Princeton, N.J.

    Antony Jameson

Authors
  1. Antony Jameson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Wolfgang Hackbusch Ulrich Trottenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Jameson, A. (1986). Multigrid algorithms for compressible flow calculations. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods II. Lecture Notes in Mathematics, vol 1228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072647

Download citation

  • DOI: https://doi.org/10.1007/BFb0072647

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17198-0

  • Online ISBN: 978-3-540-47372-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation