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Implementation of theta BC in cylindrical coordinate system FVM |
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June 2, 2016, 06:01 |
Implementation of theta BC in cylindrical coordinate system FVM
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#1 |
New Member
Abhi
Join Date: Dec 2014
Posts: 28
Rep Power: 11 |
I am working on cylindrical coordinate system using FVM. I am solving the 3d unsteady diffusion equation using r,theta and z coordinates. Whereas I am able to apply the r and z BC's, I am unable to understand how to correctly apply the theta boundary condition. The equation is
c =++ P.S.: The equation has partial differentials, couldn't find out how to write them here.... The theta BC is T(r,0,z,t)=T(r,2,z,t) and (r,0,z,t)= (r,2,z,t) Please help me in understanding how to implement this BC in the above equation using FV Method. Also if u guys need it u can assume the wall temperatures as fixed temperatures (Dirichlet BC, since my problem is implementation of theta BC.) Any help is appreciated. |
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June 2, 2016, 11:28 |
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#2 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,768
Rep Power: 71 |
First, in a FV formulation you have to work with the conservative form of the equation in such a matter to discretize the fluxes of the balanced varables.
Then, the azimuthal direction has the natural periodic condition f(0)=f(2*pi), if you work in the physical domain you see easily this fact. |
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June 2, 2016, 11:56 |
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#3 | |
New Member
Abhi
Join Date: Dec 2014
Posts: 28
Rep Power: 11 |
Quote:
aT= a T+ ap0*T_{old} What I mean is how to put the theta BC in conservation form of above diffusion equation, (similar to r and z???) , but i'm unable to understad how to do that. Thank you for your help and any suggestion is appreciated. |
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