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Old   November 10, 2011, 16:24
Question FVM boundary conditions
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Hi there:

I'm solving equations using finite volume methods on an irregular triangular mesh. I construct my control volumes as shown in the attached file. My question is, how do I deal with nodes at boundaries? Nodes on the edge of my domain only have 4 neighbouring nodes, while corners only have 3 neighbouring nodes. Consequently, I cannot construct a control volume like I have for non-boundary nodes. Do I simply construct a "partial" control volume? Any suggestions or advice would be appreciated.
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Old   November 10, 2011, 20:40
Shenren Xu
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Hello Nereus

What you need to look into is something call "ghost cell" or "ghost node" to take care of the flux across the boundary face. I suggest you read the chapters in Blazek's book. It explains node-based FVM in very practical way. Also, you were right that you only need to use the "partial" volume, as the "ghost node/cell" only provides flow variables to allow you to calculate the flux and does not occupy any volume.

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Old   November 11, 2011, 13:35
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Thanks for the reply, Shenren. That book is exactly what I was looking for!
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boundary conditions, finite volume method, irregular triangular mesh

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