Question

The Downwind Weighing Factor in the normalized form is given by __________

(a) \(\frac{\tilde{\phi_f}-\tilde{\phi_c}}{1-\tilde{\phi_c}}\)

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

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

(d) \(\frac{\tilde{\phi_c}-\tilde{\phi_f}}{1-\tilde{\phi_f}}\)

I got this question in an online quiz.

I'm obligated to ask this question of High Resolution Schemes in division High Resolution Schemes of Computational Fluid Dynamics

Answer 1

Correct choice is (a) \(\frac{\tilde{\phi_f}-\tilde{\phi_c}}{1-\tilde{\phi_c}}\)

Best explanation: The Downwind Weighing Factor is given by

DWFf=\(\frac{\phi_f-\phi_c}{\phi_d-\phi_c}\)

Normalizing this, we get

DWFf=\(\frac{\tilde{\phi_f}-\tilde{\phi_c}}{\tilde{\phi_d}-\tilde{\phi_c}}\)

But, the value of \(\tilde{\phi_d}\) is 1. So,

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