Panel Discussion 



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Dp 

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Figure 3 



Several comments pertained to the stability of the calculations. One sug- 

 gestion, by P. Fink (University of New South Wales, Australia), based on Dr. 

 Hirt's paper in the session on Fundamental Hydrodynamics (paper No. 11 of 

 these Proceedings), was that the mesh size for stability could be investigated ' 

 analytically, rather than empirically by numerical trial, by carrying addi- 

 tional terms in the Taylor- series expansions used to express the Navier- 

 Stokes equations in finite-difference form. Another suggestion, based on nu- 

 merical calculations of flow about a cylinder, was that the results are sensitive 

 to the assumed upstream and downstream boundary conditions. This is contrary 

 to the experience of Macagno and Hung in the case of an abrupt expansion, who 

 found that the development of the vortex structure was insensitive to the as- 

 sumed upstream velocity profile, a uniform stream in one case and parabolic 

 velocity profile in another; furthermore they found that the downstream flow 

 pattern eventually became parabolic without the necessity of any assumption. 

 It appears that the sensitivity of the computed flow to the assumed boundary 

 conditions depends on the boundary geometry. 



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