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lost.identity October 6, 2010 09:54

1-D spherical finite volume discretisation
 
I'm trying to discretise the conservative equations using FVM for a 1-D spherical geometry (i.e. spherical symmetry).

After applying the Gaus's theorem I get the following for spatial discretisation of the diffusive terms

\boldsymbol{\Gamma_f}\cdot\boldsymbol{A}_f

I know that for 1-D Cartesian the face area vector is simply \boldsymbol{A}=\boldsymbol{i} where i is the unit vector in the x-direction.

However, what will be the face area vector for a spherical geometry? Surely it can't just be the unit vector.

I know that the area element in spherical coordinates is given by

d\boldsymbol{A} = r^2\sin\theta{d}\theta{d}\phi\boldsymbol{e}_r symbol. So in 1-D can I assume it to be just r^2?

Thanks.

david_e October 7, 2010 15:36

You can take it to be r^2, because to get the conservative formulation one usually integrates over \theta and \phi.


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