FVM boundary conditions

Nereus · November 10, 2011, 16:24

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.

Shenren_CN · November 10, 2011, 20:40

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.

Cheers,
Shenren

Nereus · November 11, 2011, 13:35

Thanks for the reply, Shenren. That book is exactly what I was looking for!

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November 10, 2011, 20:40		#2
Shenren_CN Member Shenren Xu Join Date: Jan 2011 Location: London, U.K. Posts: 67 Rep Power: 15	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. Cheers, Shenren

November 11, 2011, 13:35		#3
Nereus New Member Nereus Join Date: Sep 2011 Posts: 18 Rep Power: 15	Thanks for the reply, Shenren. That book is exactly what I was looking for!