InterviewSolution
Saved Bookmarks
| 1. |
Which of these equations is the discretized form of the transient term using the first-order implicit Euler scheme?(a) \(\frac{(\rho_C\phi_C)^t-(\rho_C\phi_C)^{t+\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)(b) \(\frac{(\rho_C\phi_C)^t-(\rho_C\phi_C)^{t-\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)(c) \(\frac{(\rho_C\phi_C)^t+(\rho_C\phi_C)^{t+\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)(d) \(\frac{(\rho_C\phi_C)^t+(\rho_C\phi_C)^{t-\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)I got this question in an internship interview.This key question is from Transient Flows topic in chapter Transient Flows of Computational Fluid Dynamics |
|
Answer» RIGHT CHOICE is (b) \(\frac{(\rho_C\phi_C)^t-(\rho_C\phi_C)^{t-\Delta t}}{\Delta t} V_C+L(\phi_C^t)\) The EXPLANATION is: The first-order implicit Euler scheme GIVES its terms using the older terms. Before using this scheme, the terms are \(\frac{V_C(\rho_C \phi_C )^{t+\frac{\Delta t}{2}}}{\Delta t}-\frac{V_C(\rho_C\phi_C)^{t-\frac{\Delta t}{2}}}{\Delta t}+L(\phi_C^t)\) When the scheme is applied to these equations, \(\frac{(\rho_C\phi_C)^t-(\rho_C\phi_C)^{t-\Delta t}}{\Delta t} V_C+L(\phi_C^t)\). |
|