Question

What is the normalized relationship between Φf and Φc for the FROMM scheme?

(a) \(\tilde{\phi_f}=\tilde{\phi_c}+\frac{1}{4}\)

(b) \(\tilde{\phi_f}=\tilde{\phi_c}-\frac{1}{4}\)

(c) \(\tilde{\phi_f}=\frac{1}{4}-\tilde{\phi_c}\)

(d) \(\tilde{\phi_f}=\frac{1}{4} \tilde{\phi_c}\)

I have been asked this question in an internship interview.

The question is from Convection-Diffusion Problems topic in division Convection-Diffusion Problems of Computational Fluid Dynamics

Answer 1

Correct choice is (a) \(\tilde{\phi_f}=\tilde{\phi_c}+\frac{1}{4}\)

Explanation: The relationship between Φf and Φc is

\(\phi_f=\phi_c+\frac{1}{4}(\phi_D-\phi_U)\)

The normalized forms of Φf, Φc, ΦD and ΦU are \(\tilde{\phi_f}, \tilde{\phi_c},\) 1 and 0 respectively. Therefore,

\(\tilde{\phi_f}=\tilde{\phi_c}+\frac{1}{4}.\)