Panel Discussion 



SOLUTION OF THE POISSON EQUATION . . . : 



To solve the NS equation we have to solve at each step a Poisson equation 

 which consumes much computing time. It would be very useful to have a sys- 

 tematic study of all the algorithms to solve this problem. According to our own 

 experience, however, it is preferable to use iterative methods to solve a problem 

 with a free surface. For fixed boundaries we have had better success by using 

 properties of symmetric band matrices. Actually, we plan to use a modified 

 algorithm based on chain- matrix properties. 



NUMERICAL DIFFUSION OF TRANSPORT EQUATION - / .. r. 



The problem of numerical treatment of transport terms is a very difficult 

 one. We tested about twelve different schemes in both one- and two-dimensional 

 cases. Because of the numerical diffusion we found it necessary to retain 

 second-order terms in the time scheme. The use of staggered mesh gives 

 rather good results but introduces difficulties with the boundary conditions. 



We have also studied nonanalytical algorithms which give very good results, 

 in particular for steady flow. This fact has facilitated the solution of the steady 

 case even for high-Reynolds-number turbulent flow. 



DISCUSSION 



S. Piacsek inquired about the details of the staggered- mesh procedure in the 

 numerical treatment of the transport equation and the coupling of solutions at odd 

 and even time levels. The author emphasized that the major difficulty encoun- 

 tered is with the boundary conditions, because there are two different expressions 

 of these conditions for the two levels. It is necessary to couple the two levels 

 because otherwise there would be a discrepancy between the two solutions, as 

 was discussed in a 1966 paper. 



Parametric Equations of Ship Forms 

 by Conformal Mapping of Ship Sections 



L. Landweber 



INTRODUCTION 



In a previous paper [Ij, a modification of the Bieberbach method of con- 

 formal mapping has been applied to obtain added masses of ship sections. When 

 a note by Kerczek and Tuck [2j appeared, suggesting that the coefficients of the 

 mapping functions could be made to yield parametric equations of the entire ship 

 hull, an attempt was made to apply the Bieberbach method for this purpose. 



1619 



