Sparse Quasi- Newton Method for Navier- Stokes Solution

  • Ning Qin
  • Bryan E. Richards
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


A sparse finite difference Newton method and a sparse quasi-Newton method have been applied to the Navier-Stokes solution. Much faster convergence to the steady state has been achieved compared to the conventional time marching method. For multidimensional applications, a block line Gauss-Seidel iterative method has been used for the solution of the resulting linear system. The methods have been demonstrated for hypersonic flow solution around a sharp cone using Osher’s flux difference splitting scheme for spatial discretization.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Qin and B.E. Richards, Notes on Numer. Fluid Mech. 20(1988), 310.Google Scholar
  2. 2.
    L.K. Schubert, Math. Comp. 24(1970), 27.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    C.G. Broyden, Math. Comp. 25(1971), 285.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    B. Van Leer, J.L. Thomas, P. Roe and R.W. Newsome, AIAA-87-1104.Google Scholar
  5. 5.
    N. Qin and B.E. Richards, Proc. Int. Conf. on Hypersonic Aerodynamics, Sept. 1989, Manchester, paper 26.Google Scholar
  6. 6.
    S. Osher and F. Solomon, Math. Comp. 38(1982), 339.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    S. Osher and S.R. Chakravarthy, J. Comp. Phys. 50(1983), 447.MathSciNetADSCrossRefzbMATHGoogle Scholar
  8. 8.
    S.P. Spekreijse, Ph.D. thesis, CWI, Amsterdam, (1987).Google Scholar
  9. 9.
    R.R. Tracy, Aero. Lab. Memo. No.69, CIT, (1963)Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • Ning Qin
    • 1
  • Bryan E. Richards
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of GlasgowGlasgowScotland, UK

Personalised recommendations