MCQOPTIONS

Explore topic-wise MCQs in Computational Fluid Dynamics.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics knowledge and support exam preparation. Choose a topic below to get started.

1.	The numerical diffusion and numerical anti-diffusion terms are equal for the first-order Euler scheme are equal in magnitude when __________
A.	the courant number of diffusion is equal to one
B.	the courant number of diffusion is equal to two
C.	the courant number of convection is equal to one
D.	the courant number of convection is equal to two
Answer» D. the courant number of convection is equal to two

2.	According to the first-order explicit Euler scheme, the value at time-step t-\(\frac{\Delta t}{2}\) is approximated to be equal to the value at __________
A.	t+\(\frac{\Delta t}{2}\)
B.	t
C.	t-Δt
D.	t+Δt
Answer» C. t-Δt

3.	The extra term added while discretizing the transient term of a flow with density ρ and flow variable φ using the first-order explicit Euler scheme is _________
A.	\(\Delta t\frac{\partial^2(\rho\phi)}{\partial t^2}\)
B.	\(-\Delta t\frac{\partial^2(\rho\phi)}{\partial t^2}\)
C.	\(\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\)
D.	\(-\frac{\Delta t}{2}\frac{\partial^2(\rho\phi)}{\partial t^2}\)
Answer» E.

4.	When the first-order implicit Euler scheme is unconditionally stable, the solution is ________
A.	stationary for large time-steps
B.	oscillatory for large time-steps
C.	stationary for small time-steps
D.	oscillatory for small time-steps
Answer» B. oscillatory for large time-steps

5.	The first-order implicit Euler schemes to discretize the transient term creates ________
A.	cross-flow diffusion
B.	cross-diffusion
C.	numerical anti-diffusion
D.	numerical diffusion
Answer» E.

6.	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.	\(\frac{(\rho_C\phi_C)^t+(\rho_C\phi_C)^{t-\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)
Answer» C. \(\frac{(\rho_C\phi_C)^t+(\rho_C\phi_C)^{t+\Delta t}}{\Delta t} V_C+L(\phi_C^t)\)

7.	If the first-order implicit Euler scheme is used, the value at t+Δt/2 is replaced by the value at _________
A.	t
B.	t-\(\frac{\Delta t}{2}\)
C.	t+Δt
D.	t-Δt
Answer» D. t-Δt

8.	Which of these changes should be made in the semi-discretized equation to get the fully discretized equation?
A.	Express the face values in terms of the neighbouring face values
B.	Express the face values in terms of the cell values
C.	Express the cell values in terms of the face values
D.	Express the cell values in terms of the neighbouring cell values
Answer» C. Express the cell values in terms of the face values

9.	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.

10.	The discretization of the transient term using the finite volume approach is more like the spatial discretization of __________
A.	the convection term
B.	the diffusion term
C.	the source term
D.	the anti-diffusion term
Answer» B. the diffusion term