Cell vertex V.S Cell centered for FVM
Could you please briefly summarize comparison between cell vertex and cell centered?
I tried to look for the answer online but failed. Thanks!
First you have to undertstand how we derive them.
Let's assume you know....
Each of these two approaches has advantages and drawbacks. Generally the advantage of one is the drawback of the other.
For example for cell vertex (or node centered) approach in case of non regular grids
the faces of a control volume are always half way between two nodes. It's not the case for cell centered. The consequence of that is the first derivative phi_e=(phi_E-phi_P)/d(P,E) where d(P,E) is the distance between node P and E is necessarly second order For cell centred approach the same discretization of the first derivative will be first order only.
In case of non regular grids the interpolation factor will be 0.5 and interpolation at face center will then be easier. It won't be the case for cell centred and interpolations will be more cumbersome to perform.
For cell vertex, grid points fall on the boundaries and the distance between a boundary node and the next interior node remains the same than for all interior nodes. It is easier for boundary conditions treatments.
The only drawback that I see for cell vertex approach is that for very skewed grids the node P may be outside from its control volume. In cell centred approach this pathologic situation can never happen...
However even if cell vertex seems to present some advantages over cell centred approach the latter is more widely used but it is really a question of choice.
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