Question

Approximate the surface integral ∫Swf d\(\vec{S}\) using the Simpson’s rule.

(a) \(\frac{S_w}{6}\)(2fnw+2fw+2fsw)

(b) \(\frac{S_w}{4}\)(2fnw+2fsw)

(c) \(\frac{S_w}{6}\)(fnw+4fw+fsw)

(d) \(\frac{S_w}{4}\)(fnw+2fw+fsw)

The question was asked in a national level competition.

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

Answer 1

Correct choice is (c) \(\frac{S_w}{6}\)(fnw+4fw+fsw)

To elaborate: The Simpson’s rule uses values of the integrand at three points – centre of the face and the two vertices in the same face. It is given by

\(\frac{S_w}{6}\)(fnw+4fw+fsw).