An efficient four-factored time integration scheme for three-dimensional compressible flow problems
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.
KeywordsSupersonic Flow AIAA Paper Present Scheme Streamwise Direction Local Iteration
Unable to display preview. Download preview PDF.
- 1.S. R. Chakravarthy: AIAA Paper 84-0165, 1984.Google Scholar
- 2.R. W. Walters and D. L. Dwoyer: AIAA Paper 85-1529CP, 1985.Google Scholar
- 3.R. W. Newsome, R. W. Walters and J. L. Thomas: AIAA Paper 87-1113CP, 1987.Google Scholar
- 5.T. H. Pulliam and D. S. Chaussee: J. C. P. Vol. 39, pp. 372–397, 1977.Google Scholar
- 6.S. Obayashi, K. Matsushima, K. Fujii and K. Kuwahara: AIAA Paper 86-338, 1986.Google Scholar
- 7.S. Yoon and A. Jameson: AIAA Paper 87-0600, 1987.Google Scholar
- 8.S. Obayashi: AIAA Paper 88-4360, 1988.Google Scholar
- 9.S. Ying and J. L. Steger: AIAA Paper 86-2179, 1986.Google Scholar