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Having trouble writing a coupled differential equation in OpenFOAM 

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December 1, 2015, 08:42 
Having trouble writing a coupled differential equation in OpenFOAM

#1 
New Member
Adkar
Join Date: Apr 2015
Posts: 18
Rep Power: 3 
Is someone willing to help me write this equation in OpenFOAM?
I want to write this coupled differential equation. // x = x coordinate. // Ax = partial derivative of A with ONLY x (1/x)*Laplacian A  (1/(x*x))*Ax = (B)/x (1/x)*Laplacian B  (1/(x*x))*Bx = (A)/x I have two problems here. 1. How do I write the derivative of A and B only with x and not write it as div(B)? 2. How can I multiply 1/x or 1/x*x to the matrix which is the derivative of A and B only with respect to x? I have to solve this using a steadystate solver without any time derivative like simpleFoam. Please Help me. Thank you. 

December 1, 2015, 09:57 

#2 
Senior Member
Michael Prinkey
Join Date: Mar 2009
Location: Pittsburgh PA
Posts: 306
Rep Power: 16 
I haven't worked in OpenFOAM for a while, but these are my first shot at them. My apologies if my OpenFOAM syntax is a little rusty.
(1) You would have to take the gradient of A and B and then dot with the xdirection unit vector. Something like: fvc::grad(A) & vector(1,0,0) (2) fvMesh has a volume vector field C that contains the cell centroids. Again, dot with the xdirection unit vector to get the x component. I would multiply through by 1/x^2 to avoid division by zero. I do this reflexively. There is a coupled solver in the openfoam water supply. You could investigate how to make that work if performance is absolutely critical, but honestly, you are better off by building a segregated iterative solver. Start by fixing B, and solving the first equation for A. Then fixing that result for A and solve the second equation for B. And then iterate until convergence. 

December 2, 2015, 01:37 

#3 
New Member
Adkar
Join Date: Apr 2015
Posts: 18
Rep Power: 3 
Thank you so much Mr. Prinkey for your reply.
Taking the dot product after computing the gradient is a very good idea. I will try that. And thanks for letting me know the tutorial case. I will take a deeper look into it. 

Tags 
basic, equation, syntax error 
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