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 )

• A. 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?
• 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+ frac{ Delta t}{2}}-L( phi_C^t ) Delta t )
• D. (V_C ( rho_C phi_C)^t+L( phi_C^t ) Delta t )
• E. (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 )