Consider the following stencil. Give the relationship between $\frac{\phi_C-\phi_W}{\phi_E-\phi_W}$ and Peclet number (Pe) for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).

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TuteeHUB · Accepted Answer

for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).a) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big|Pe\big|} $ b) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big|Pe\big|} $ c) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big|Pe\big|} $ d) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big|Pe\big|} $

TuteeHUB · Answer

$\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big|Pe\big|} $

TuteeHUB · Answer

$\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big|Pe\big|} $

TuteeHUB · Answer

$\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big|Pe\big|} $

TuteeHUB · Answer

$\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big|Pe\big|} $

TuteeHUB · Answer

for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).a) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big|Pe\big|} $ b) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big|Pe\big|} $ c) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big|Pe\big|} $ d) $\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big|Pe\big|} $

1.	Consider the following stencil. Give the relationship between \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W}\) and Peclet number (Pe) for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).
A.	\(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big\|Pe\big\|} \)
B.	\(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big\|Pe\big\|} \)
C.	\(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big\|Pe\big\|} \)
D.	\(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big\|Pe\big\|} \)
E.	for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).a) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big\|Pe\big\|} \) b) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big\|Pe\big\|} \) c) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big\|Pe\big\|} \) d) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big\|Pe\big\|} \)
Answer» E. for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).a) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(Pe,0)}{4+\big\|Pe\big\|} \) b) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2-max⁡(-Pe,0)}{4+\big\|Pe\big\|} \) c) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(Pe,0)}{4+\big\|Pe\big\|} \) d) \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W} = \frac{2+max⁡(-Pe,0)}{4+\big\|Pe\big\|} \)

Consider the following stencil. Give the relationship between \(\frac{\phi_C-\phi_W}{\phi_E-\phi_W}\) and Peclet number (Pe) for the upwind scheme while used for the convection term.(Note: Φ is the flow variable).

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