An efficient four-factored time integration scheme for three-dimensional compressible flow problems

  • Kozo Fujii
Algorithms Numerical Techniques
Part of the Lecture Notes in Physics book series (LNP, volume 490)


A new implicit time integration scheme is presented. The scheme is based on the two-factored relaxation-type scheme. By adopting the approximation of the flux Jacobian matrices in the streamwise direction similarly to the LU-SGS scheme, both the implicit factors are diagonalized by the eigenmatrices for the other two directions. The SGS factorization used in the LU-ADI scheme is next adopted. The resultant scheme has four factors, each of which consists of the simple scalar sweep. The scheme is called FF-SGS (Four-factored symmetric Gauss Seidel) scheme. The implicit operations in the present scheme differs from those of the LU-ADI scheme only at the scalar diagonal elements and therefore can easily developed from the existing code.

Several computations are carried out and the results show the present scheme’s applicability and efficiency as a conventional time marching scheme. For the simulations where most of the flow field is supersonic, local iterations at each streamwise station make the present scheme much more efficient. Some of the computational examples are shown. The results indicate the present FF-SGS scheme can be a versatile tool for a wide variety of the flow fields.


Supersonic Flow AIAA Paper Present Scheme Streamwise Direction Local Iteration 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Kozo Fujii
    • 1
  1. 1.The Institute of Space and Astronautical ScienceSagamihara, KanagawaJapan

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