Numerical Solutions 

 REFERENCES 



Arakawa, A., (1966), J. Comp. Phys. 1, 119 



Cooley, J.W. and Tukey, J.W,, (1965), Math, of Comput. 19, 297 



Douglas, J., (1962), Numer. Mathem. 4, 41 



Douglas, J. and Rachford, H.H., (1956), Trans. Am. Math. Soc. 82, 421 



Hockney, R.W. (1965), J. Assoc. Comp. Mach. 12, 95 



Orszag, S.A., (1968), International Symposium on High-Speed Computers in 

 Fluid Dynamics, Monterey, Calif., Aug. 1968 



Varga, R.S., (1962), "Matrix Iterative Analysis," Prentice-Hall 



Williams, G.P., (1967), Geophysical Fluid Dynamics Lab., ESSA, Washington, 

 D.C., private communication 



DISCUSSION 



R. Barakat (Itek Corp., Lexington, Mass.) has stated that, to his knowledge, 

 an algorithm similar to that of Cooley -Tukey has been developed by Lanczos 

 (1943) for real sine functions. The author replied that he has not read that 

 paper, but will look into it. Barakat also questioned whether the Fourier- 

 transform method would be accurate for functions which do not vanish outside 

 a certain region. Piacsek indicated that his procedure was of the nature of 

 "curve-fitting" by means of a discrete set of Fourier harmonics, so that the 

 criticism did not apply. 



Numerical Solutions of the Two-Dimensional 

 Navier-Stokes Equations 



M. Gauthier 



Societe Sogreah 



Grenoble, France 



I shall discuss briefly two numerical problems we have met for the solution 

 of the Navier-Stokes (NS) equations for the two-dimensional case. 



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