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 )

Question

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 )

TuteeHUB · Accepted 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  )

TuteeHUB · Answer

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?

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  )

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