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

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