Consider the following stencil. Assume a uniform grid. What is the convective flux at the western face ($\dot{m_w}\phi_w$) using the FROMM scheme?

Question

TuteeHUB · Accepted Answer

$(\phi_P-\frac{\phi_W}{4}+\frac{\phi_E}{4})  max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4})  max⁡(-\dot{m_w},0)$

TuteeHUB · Answer

$(\phi_P-\frac{\phi_E}{4}+\frac{\phi_W}{4})  max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4})  max⁡(-\dot{m_w},0)$

TuteeHUB · Answer

$(\phi_P-\frac{\phi_W}{4}+\frac{\phi_E}{4})  max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4})  max⁡(-\dot{m_w},0)$

TuteeHUB · Answer

$(\phi_P\frac{-\phi_E}{4}+\frac{\phi_W}{4})  max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_C}{4}+\frac{\phi_{WW}}{4})  max⁡(-\dot{m_w},0)$

TuteeHUB · Answer

$(\phi_P\frac{-\phi_W}{4}+\frac{\phi_E}{4})  max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_C}{4}+\frac{\phi_{WW}}{4})max⁡(-\dot{m_w},0)$

1.	Consider the following stencil. Assume a uniform grid. What is the convective flux at the western face (\(\dot{m_w}\phi_w\)) using the FROMM scheme?
A.	\((\phi_P-\frac{\phi_E}{4}+\frac{\phi_W}{4}) max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4}) max⁡(-\dot{m_w},0)\)
B.	\((\phi_P-\frac{\phi_W}{4}+\frac{\phi_E}{4}) max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4}) max⁡(-\dot{m_w},0)\)
C.	\((\phi_P\frac{-\phi_E}{4}+\frac{\phi_W}{4}) max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_C}{4}+\frac{\phi_{WW}}{4}) max⁡(-\dot{m_w},0)\)
D.	\((\phi_P\frac{-\phi_W}{4}+\frac{\phi_E}{4}) max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_C}{4}+\frac{\phi_{WW}}{4})max⁡(-\dot{m_w},0)\)
Answer» B. \((\phi_P-\frac{\phi_W}{4}+\frac{\phi_E}{4}) max⁡(\dot{m_w},0)-(\phi_W\frac{-\phi_{WW}}{4}+\frac{\phi_C}{4}) max⁡(-\dot{m_w},0)\)

Consider the following stencil. Assume a uniform grid. What is the convective flux at the western face (\(\dot{m_w}\phi_w\)) using the FROMM scheme?