Question

Approximate the surface integral in the eastern face ∫Sefd\(\vec{S}\) of a two-dimensional problem using the trapezoidal rule.

(a) \(\frac{3}{2}\)(fne+fse)

(b) 3 \(\frac{S_e}{2}\)(fne+fse)

(c) \(\frac{1}{2}\)(fne+fse)

(d) \(\frac{S_e}{2}\) (fne+fse)

The question was asked in a national level competition.

The above asked question is from Finite Volume Method in portion Finite Volume Methods of Computational Fluid Dynamics

Answer 1

Right choice is (c) \(\frac{1}{2}\)(fne+fse)

For explanation I would say: The trapezoidal rule is a second-order accurate approximation. It needs the values of the integrand at two points. Here, as we need the surface integral in the eastern face, the value is approximated using the northern and the southern nodes of the eastern face.

∫Sefd\(\vec{S}=\frac{1}{2}\) (fne+fse).