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51.

The Peclet number is calculated at the ____________(a) control volume(b) cell centres(c) vertices(d) facesThis question was posed to me by my college professor while I was bunking the class.The above asked question is from Convection-Diffusion Problems topic in portion Convection-Diffusion Problems of Computational Fluid Dynamics

Answer»

The correct choice is (d) faces

The best I can explain: The HYBRID differencing SCHEME uses piecewise formulae based on the Peclet NUMBER evaluated at the faces of each control VOLUME. Based on this Peclet number, a scheme is chosen.
Discussion
52.

What is the relationship between \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w}\) and the Peclet number (Pe) when the grid is uniform?(a) \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = \frac{1}{2}(1-\frac{Pe}{2}) \)(b) \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = \frac{1}{2}(1+\frac{Pe}{2}) \)(c) \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = \frac{1}{2}(\frac{Pe}{2}-1) \)(d) \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = (\frac{Pe}{4}) \)This question was posed to me in an international level competition.I need to ask this question from Convection-Diffusion Problems in division Convection-Diffusion Problems of Computational Fluid Dynamics

Answer»

Right choice is (a) \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = \frac{1}{2}(1-\frac{PE}{2}) \)

The explanation is: For the CENTRAL DIFFERENCE scheme applied to the convection-diffusion problems

\(\frac{\phi_c-\phi_w}{\phi_E-\phi_w}=\frac{a_E}{a_W+a_E}\)

APPLYING this to

\(\frac{\phi_c-\phi_w}{\phi_E-\phi_w} = \frac{1}{2}(1-\frac{Pe}{2}) \).
Discussion