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May 30, 2016, 23:07 
The Coupled System of Equations

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Can somebody explain the notation of the system of equations written in CFX theory guide ?
I don't understand the double notation, subscrit and superscript ... Last edited by MissCFD; May 31, 2016 at 08:28. 

May 30, 2016, 23:15 

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May 31, 2016, 10:50 

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nb stand for (N)eigh(B)ors
i stand for equation_i the equation reads as "sum around the neighbors of its influence coefficients on i times its variable value is equal to b_i" Those coefficients include the advection, diffusion and other physics interacting between "control volume_i" and its neighbors.. Note the equation may be written in multiple forms where phi can be the value of the solved variable, or the iterative correction to the variable. Based on the interpretation of phi, b can be the source or the residual of the equation. Hope the above gives some context. 

May 31, 2016, 14:47 

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Quote:
I'm not sure to visualize, so can you tell me if this notation means the same ? Does this correspond to system equations for one node ? 

May 31, 2016, 21:04 

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Assuming "i" stands for node number, and "nb" includes all the other influencing "i"s (say j) around "i", your are correct.


May 31, 2016, 22:43 

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(1) & (2) And, this equations (1 or 2) is written for all the nodes of mesh, so we obtain i times this equation and this is what forms the matricial system ? 

June 1, 2016, 14:12 

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I would read them as equivalent


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