Question

The centroid of the faces of a 3-D element is obtained by _________

(a) Area-weighted average of the sub-elements

(b) Average of the sub-elements

(c) Area-weighted average of the centroid of the sub-elements

(d) Volume-weighted average of the centroid of the sub-elements

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I would like to ask this question from The Geometry of FVM Elements topic in division Finite Volume Methods of Computational Fluid Dynamics

Answer 1

The correct choice is (c) Area-weighted average of the centroid of the sub-elements

Easiest explanation: The centroid of each of the sub-elements are first located. The weighted average of these centroids is the centroid of the whole face. Areas of the triangles are used as the weight for this average.