Question

For three-dimensional flows, what is the approximation of the volume integral using the midpoint rule?

(a) Product of the integrand at the face centre and the volume of the control volume

(b) Product of the integrand at the control volume centre and the volume of the control volume

(c) Product of the integrand at the control volume centre and the surface area of the control volume

(d) Product of the integrand at the face centre and the surface area of the control volume

I had been asked this question in an interview for internship.

My question is from Finite Volume Method in division Finite Volume Methods of Computational Fluid Dynamics

Answer 1

The correct answer is (b) Product of the integrand at the control volume centre and the volume of the control volume

The explanation is: Using the midpoint rule, the volume integral is approximated as the product of the integrand at the centre of the cell (the control volume) and the volume of the cell. Representing it mathematically,

∫VqdV = qP×ΔV.