Streetj Chan and Fromm 



- ^ (- ^i+lj + 2uij - Uj.ij 



Equation (19) must be solved for all i simultaneously for a given j. 

 The matrix of coefficients of the unknowns in Eq, (19) is tridiagonal 

 and is quickly and easily solved by a tridigonal-matrix equation 

 solver employing Gaussian Elimination. The process is repeated for 

 each j until the u^j are known. Appropriate boundary conditions 

 are introduced at the ends of the j**' row in each computation. 



Third, the y-momentum Eq, (5) is used to obtain a difference 

 equation for the v values at the n+1 level. The result is entirely 

 equivalent to that for the u values, viz, , the third-order terms on 

 the right-hand side create a naturally implicit system so time -splitting 

 is used. Now, however, we use v^ and r\P values for all i-1 and 

 i+1 points along a given column of implicit equations (i = constant, 

 3 ^ j :S N-2) and we use the u"*' values just computed. The result, 

 when rearranged for computation, is 



Avi;:; + Bv;';' + ev,";; =s, j = 3,4,... ,n-2 (20) 



where 



^ = -|s-ii^^(¥-^iiM 



B = l +^ 

 3^^ 



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At . V 



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158 



