APPENDIX B 



Lateral Stretching of the Coordinates 



In the lateral stretching of the coordinates, the x grid and the y grid 

 are treated independently. Grid in each direction is divided into several 

 regions, each with a certain number of non-uniformly spaced grid points. 

 These points are then mapped into a uniformly spaced computational grid with 

 equal number of points via Eq. (2.22). The coefficients in the equations are 

 determined by matching the functional as well as their derivatives at the 

 boundaries between regions. Derivatives in the original coordinates (x,y) are 

 related to those in the stretched coordinates {'^, ^) as: 



(B-1) 



3 



3a 



3 . 



. 1 3 



3x 



3x 



3a 



U^ 3a 



2 

 3 



1 



3 



/i A 



_3_ _ 3y J_ _ _1_ _3_ 

 3y ~ 3y 3y " y 3y 



2 



3 Xi_ 



i7 ^ 3y ^^ 



w y 



(B-2) 



(B-3) 



(B-4) 



where v^ and y are stretching coefficients which vary from region to region. 

 Details of determination of the lateral stretching coefficients can be found 

 in Schmalz (1983). 



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