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)

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).