Smith 



Fig. 4 - Geometric representation of the NASA 

 HL-10 reentry vehicle. Each half is represented 

 by 1278 quadrilateral elements 



bodies, although not as obvious for the latter. For the plane quadrilateral ele- 

 ments used with truly three-dimensional bodies, the proper point to use is not 

 obvious at all. For rectangular elements, it seems evident that the point should 

 lie at the center, but there are many possible definitions which reduce to the 

 center for these elements. On each quadrilateral element there is one point 

 where a constant source density on that element gives rise to no velocity in its 

 own plane, i.e., there is a point where the effect of the element is entirely nor- 

 mal to itself. It was decided to evaluate velocities and pressures at this point. 

 For elements that are nearly rectangular this point is located near the centroid 

 of the area of the quadrilateral, but for certain types of quadrilaterals the two 

 points may be a significant distance apart. For all types of body surfaces the 

 point on an element where velocities and pressures are evaluated is designated 

 as the control point of that element. 



Once the body surface has been approximated by elements of the appropriate 

 type, the elements are ordered sequentially and numbered from 1 to N, where N 

 is the total number of elements. The exact order of the sequence is immaterial. 

 It is simply a logical device for keeping track of the elements during the com- 

 putational procedure. Reference will accordingly be made to the ith element 

 and the jth element, where the integers i and j denote the position of the ele- 

 ments in the sequence. 



324 



