Consider the following equation representing the temporal integration over the time interval t-$\frac{\Delta t}{2}$ and t+$\frac{\Delta t}{2}$ at the spatial point C.$\int_{t-\Delta t/2}^{t+\Delta t/2}\frac{\partial(\rho_C\phi_C)}{\partial t}V_Cdt+\int_{t-\Delta t/2}^{t+\Delta t/2}L(\phi_C)dt=0$ If the first term is discretized using the difference of fluxes and the second term is evaluated using the midpoint rule, what is the discretized form?

Question

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$V_C (\rho_C\phi_C)^{t-\frac{\Delta t}{2}}+L(\phi_C^t )\Delta t$

TuteeHUB · Answer

$V_C (\rho_C\phi_C)^{t+\frac{\Delta t}{2}}-L(\phi_C^t )\Delta t$

TuteeHUB · Answer

$V_C (\rho_C\phi_C)^t+L(\phi_C^t )\Delta t$

TuteeHUB · Answer

$V_C (\rho_C\phi_C)^{t+\frac{\Delta t}{2}}-V_C(\rho_C \phi_C)^{t-\frac{\Delta t}{2}}+L(\phi_C^t)\Delta t$

1.	Consider the following equation representing the temporal integration over the time interval t-\(\frac{\Delta t}{2}\) and t+\(\frac{\Delta t}{2}\) at the spatial point C.\(\int_{t-\Delta t/2}^{t+\Delta t/2}\frac{\partial(\rho_C\phi_C)}{\partial t}V_Cdt+\int_{t-\Delta t/2}^{t+\Delta t/2}L(\phi_C)dt=0\) If the first term is discretized using the difference of fluxes and the second term is evaluated using the midpoint rule, what is the discretized form?
A.	\(V_C (\rho_C\phi_C)^{t-\frac{\Delta t}{2}}+L(\phi_C^t )\Delta t\)
B.	\(V_C (\rho_C\phi_C)^{t+\frac{\Delta t}{2}}-L(\phi_C^t )\Delta t\)
C.	\(V_C (\rho_C\phi_C)^t+L(\phi_C^t )\Delta t\)
D.	\(V_C (\rho_C\phi_C)^{t+\frac{\Delta t}{2}}-V_C(\rho_C \phi_C)^{t-\frac{\Delta t}{2}}+L(\phi_C^t)\Delta t\)
Answer» E.

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