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October 28, 1998, 13:03 
grid generation

#1 
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I am a biginner of CFD. Currently, I am taking a course of CFD. I had a problem with the grid generation. The Thompson method (Differential Equation Method) is used. However, the two elliptic equations in the computational domain are very complicated. My question is how to numerically solve these two equations. I am looking for the answer from the expext. I hope I can get into this wonderful area.


October 28, 1998, 13:49 
Re: grid generation

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Joe F. Thompson's old book on "Numerical Grid Generation" has Fortran listings of various methods for grid generation in the Appendix section ( working condition ). The book is now online. Look for the home page address in the Resources Section, cfdonline, this site. (so, you can read the book from Internet directly)


October 29, 1998, 08:10 
Re: grid generation

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I am also a beginner. What I do not understand in this issue is how to derive the following interative equation: XTEMP=.5*(G22*(P(I,J)*XXI+XXIXI)+G11*(Q(I,J)*XETA+ XETA2) & 2.*G12*XXIETA)/(G11+G22) Could somebody tell me how to get this? Thanks a lot.


October 29, 1998, 18:40 
Re: grid generation

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(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.


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