influence of convex or concave control volume in finite volume discretization

openfoammaofnepo · March 23, 2014, 15:34

Dear CFD friends,

When we do the finite volume discretization, if the control volumes are polyhedral, then the feature that the control volumes are convex and concave has any influence on the finite volume discretization? In terms of the Gauss divergence method, convex control volume is not a required condition, but how it affects the discretization? Any hints? Thank you very much.

Thanks,
OFFO

sbaffini · March 24, 2014, 02:13

There are typicaly two aspects to consider (in my knowledge):

1) Geometrical algorithms. These are used to build face and volume related quantities for the FV cell. You have to be sure that these work well for non convex polyhedra. Algorithms related to point search, particle tracking, etc. might also have some requirement.

2) Accuracy for the face flux. In general, when you use a first order Taylor reconstruction and the mid-point rule for the face integrals you might end-up with a severe error for non-convex polyhedra. Consider, for example, a C-shaped 2D cell, would you expect this discretization to work well in this case? However, i suggest to look for geometric multigrid topics. That's possibly the only case where such cells might come out.

March 23, 2014, 15:34	influence of convex or concave control volume in finite volume discretization	#1
openfoammaofnepo Senior Member Join Date: Jan 2013 Posts: 372 Rep Power: 14	Dear CFD friends, When we do the finite volume discretization, if the control volumes are polyhedral, then the feature that the control volumes are convex and concave has any influence on the finite volume discretization? In terms of the Gauss divergence method, convex control volume is not a required condition, but how it affects the discretization? Any hints? Thank you very much. Thanks, OFFO

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March 24, 2014, 02:13		#2
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,152 Blog Entries: 29 Rep Power: 39	There are typicaly two aspects to consider (in my knowledge): 1) Geometrical algorithms. These are used to build face and volume related quantities for the FV cell. You have to be sure that these work well for non convex polyhedra. Algorithms related to point search, particle tracking, etc. might also have some requirement. 2) Accuracy for the face flux. In general, when you use a first order Taylor reconstruction and the mid-point rule for the face integrals you might end-up with a severe error for non-convex polyhedra. Consider, for example, a C-shaped 2D cell, would you expect this discretization to work well in this case? However, i suggest to look for geometric multigrid topics. That's possibly the only case where such cells might come out.