Question

Approximate the surface integral ∫Snfd\(\vec{S}\) using the midpoint rule.

(a) fn  Sn

(b) Sn (fne+fnw)

(c) \(\frac{S_n}{2}\) (fne+fnw)

(d) \(\frac{S_n}{2}\) fn

I have been asked this question in examination.

Query is from Finite Volume Method topic in portion Finite Volume Methods of Computational Fluid Dynamics

Answer 1

Correct choice is (a) fn  Sn

The explanation is: For surface integral, the value of the integrand at the face centre is used in the midpoint approximation. The neighbouring values are not used. So,

∫Snfd\(\vec{S}\)=fnS