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Discretization of the continuity equation for with low compressibility

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Old   April 12, 2012, 07:17
Cool Discretization of the continuity equation for with low compressibility
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Hi all,

I need to know how exactly the terms of the continuity equation are discretized in space. I have searched through books and papers on this but I still don't get the answer I'm looking for so I would really appreciate your help.

The continuity equation reads:
\frac{\partial\rho}{\partial  t}+\underline{v}.\nabla\left(\rho\right)+\rho  div\left(\underline{v}\right)=0

I have used 1st order UDS to approximate \rho and \underline{v} but that leaves my with matrices with terms on the diagonal and its lower or upper lines depending on the direction of the flow and hence information is not passed through between the cells. As far as I know, the terms should lie on the three lines (the diagonal and its lower and upper lines).

I would really appreciate your help asap.


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