John C. Chien

October 29, 1998 18:40 
Re: grid generation
(1). equation18a,18b,18c define coordinate transformation factors between (X,Y) and (XI,ETA) coordinate systems.(2). equation20 is a vector equation for vectorr, which need to be written in two separate equations, one for X and one for Y. (3). for Xequation, it now takes the form: g22*(X,xi,xi + P * X,xi ) + g11 * ( X,eta,eta + Q * X,eta )  2.0* g12 * X,xi,eta =0. (4). the first order derivatives ( or the transformation factors ) can be evaluated during the iteration as, say, X,xi = ( X(i+1,j)X(i1,j) )/ ( xi(i+1,j) xi(i1,j) ). if we assume the transformed mesh ( XI, YI ) is divided into one unit square, then (xi(i+1,j)xi(i1,j))=2 units. and the first order derivative X,xi = 0.5 * ( X(i+1,j)  X(i1,j) ). (5). for the second order derivatives, such as X,xi,xi= ( X(i+1,j)  2.0 * X(i,j) + X(i1,j) ), it is a second order central difference. (6). the mixed derivative is done is two steps, first find the first order derivatives at j+1 and j1 locations, then use these two to find the second order mixed derivatives. (7). when you substitute these finitedifference form of the transformation factors into the equation in step3 above, you are going to get an equation with a lot of X(i,j), X(i+1,j), X(i1,j),......So, it is very important to group terms with X(i,j) into one group, and keep the rest of the terms in another group. (8). rearrange the equation into the form: X(i,j) = ( the rest of the terms which include X(i+1,j), X(i1,j),...etc...), (9). the S.O.R. method says that you can update the field point ( X(i,j) ) onebyone in a loop ( loop 750) by using "old neighboring point values ( X(i+1,j),.. just calculated )". (10). the newly calculated value of X(i,j) is stored at XTEMP and the O.R. (overrelaxation) part is carried out using the orverelaxation factor w (set equal to 1.8).(11). there are a couple of typo in the code such as YTENP, XTENP. (12). time's up , I have to go now.
