A Composite Explicit-Implicit Godunov Method for Unsteady Problems on Highly Stiff Grids

  • Igor Men’shov
  • Yoshiaki Nakamura
Conference paper


The present paper is devoted to the development of a composite explicit-implicit method for computing the unsteady Navier-Stokes equations on grids with a high ratio between maximal and minimal grid spacings, here referred to as stiff grids. The method implements a smooth switching between the explicit and implicit modes. In the explicit mode, which is realized in regions of a large grid spacing, the method is represented by a second order Godunov/MUSCL sceme. As a whole, the method satisfies the Max Norm Diminishing (MND) property in the linear case and is stable for any value of the time step in the case of non-linear equations


Hybrid Scheme Implicit Scheme Explicit Scheme Unsteady Problem Exact Linearization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Collins, P. Colella, and H. Glaz: Jour. Comp. Phys. 116, 195 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    P. O’Rourke, M. Sahota: Jour. Comp. Phys. 143, 312 (1998)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    B. van Leer: Jour. Comp. Phys. 32, 101 (1979)ADSCrossRefGoogle Scholar
  4. 4.
    S. Godunov: Math. Sb. 47, 3 (1959)MathSciNetGoogle Scholar
  5. 5.
    A. Jameson: AIAA Tech. report 91-1596 (1991)Google Scholar
  6. 6.
    A. Jameson, S. Yoon: AIAA Journal 25, 929 (1987)ADSGoogle Scholar
  7. 7.
    I. Men’shov, Y. Nakamura: Proceed. of 8th Japan Conference on CFDGoogle Scholar
  8. 8.
    A. Jameson, E. Turkel: Mathematics of Computation 37, 385 (1981)MathSciNetMATHGoogle Scholar
  9. 9.
    I. Men’shov, Y. Nakamura: Computers and Fluids 29, 595 (2000)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Igor Men’shov
    • 1
  • Yoshiaki Nakamura
    • 1
  1. 1.Nagoya UniversityNagoyaJapan

Personalised recommendations