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

What is the relationship between \(\frac{\phi_c-\phi_w}{\phi_E-\phi_w}

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

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