Question

Consider a two-dimensional flow. If f is the component of the flux vector normal to the control volume faces, which of these terms represent ∫Sfd\(\vec{S}\)?

(a) \(\Sigma_{k=1}^4 \int_{S_k} f d\vec{S}\)

(b) \(\Sigma_{k=1}^2 \int_{S_k} f d\vec{S}\)

(c) \(\Sigma_{k=1}^6 \int_{S_k} f d\vec{S}\)

(d) \(\Sigma_{k=1}^8 \int_{S_k} f d\vec{S}\)

I have been asked this question during a job interview.

This intriguing question originated from Finite Volume Method in chapter Finite Volume Methods of Computational Fluid Dynamics

Answer 1

The correct answer is (a) \(\Sigma_{k=1}^4 \int_{S_k} f d\vec{S}\)

Explanation: In a two-dimensional flow, the number of faces bounding a control volume is four. So, the summation of the integrals along these four faces will be equal to the total flux of the control volume. Here, f may be convective or diffusive flux.