Which of these statements is correct regarding the Adams-Moulton scheme used on the non-uniform grids?

The current central coefficient for the uniform and the non-uniform grid is the same

The current central coefficient for the finite difference and the finite volume schemes are the same

The current central coefficient for the uniform and the non-uniform grid is the same

The variation in time-steps does not result in any change

There is no variation in the values when the grid is uniform

The general discretised form of the transient term using the finite volume approach isFluxT=FluxC C+FluxC C +FluxV.

(- frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

nThe superscript o indicates the older time step. If the Crank-Nicolson method is used with non-uniform grids, what is FluxV?

(- frac{ Delta t^{oo}}{ Delta t^o} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

( frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

(- frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

( frac{ Delta t^{oo}}{ Delta t^o} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

Which of these is correct for the non-uniform time-steps?(Note: t is the distance between the centroids of two temporal elements. t is the size of a temporal element. The superscript o indicates the older time step).

( delta t= frac{( Delta t- Delta t^o)}{2} )

( delta t= frac{( Delta t+ Delta t^o)}{2} )

If the Adams-Moulton scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the current time-step?(Note: is the density and V the volume).

(( frac{1}{ Delta t^o}+ frac{1}{ Delta t+ Delta t^o}) rho_C V_C )

(( frac{1}{ Delta t}+ frac{1}{ Delta t^{oo}+ Delta t^o}) rho_C V_C )

(( frac{1}{ Delta t}+ frac{1}{ Delta t+ Delta t^{oo}}) rho_C V_C )

(( frac{1}{ Delta t}+ frac{1}{ Delta t+ Delta t^o}) rho_C V_C )

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the second previous time-step?(Note: is the density and V the volume).

( frac{ Delta t^o}{ Delta t( Delta t+ Delta t^o)} rho_C^{oo}V_C )

( frac{ Delta t( Delta t+ Delta t^o)}{ Delta t Delta t^o} rho_C^{oo}V_C )

( frac{ Delta t+2 Delta t^o}{( Delta t+ Delta t^o)} rho_C^{oo}V_C )

( frac{ Delta t}{ Delta t^o( Delta t+ Delta t^o)} rho_C^{oo}V_C )

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the previous time-step?(Note: is the density and V the volume).

( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o )

( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C V_C )

( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o V_C )

( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o )

( frac{ Delta t+ Delta t^o}{ Delta t- Delta t^o} rho_C^o V_C )

Which of these statements is correct about the variable time-steps?

The finite volume scheme yields equivalent algebraic equations irrespective of the non-uniformity

The finite volume and finite difference schemes do not yield equivalent algebraic equations

The finite volume scheme yields equivalent algebraic equations irrespective of the non-uniformity

The finite difference scheme yields equivalent algebraic equations irrespective of the non-uniformity

All the second-order schemes result in the same algebraic equation when the grid is non-uniform

10 + Mcqs in Approaches for Non-uniform Time Steps in Computational Fluid Dynamics Page 1 McqOptions

1.	Which of these statements is correct regarding the Adams-Moulton scheme used on the non-uniform grids?
A.	The current central coefficient for the finite difference and the finite volume schemes are the same
B.	The current central coefficient for the uniform and the non-uniform grid is the same
C.	The variation in time-steps does not result in any change
D.	There is no variation in the values when the grid is uniform
Answer» B. The current central coefficient for the uniform and the non-uniform grid is the same

Discussion

2.	The general discretised form of the transient term using the finite volume approach is FluxT=FluxC _C+FluxC _C +FluxV.
A.	nThe superscript o indicates the older time step. If the Crank-Nicolson method is used with non-uniform grids, what is FluxV?
B.	(- frac{ Delta t^{oo}}{ Delta t^o} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )
C.	( frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )
D.	(- frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )
E.	( frac{ Delta t^{oo}}{ Delta t^o} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )
Answer» D. (- frac{ Delta t^{oo}}{ Delta t^o+ Delta t^{oo}} frac{ rho_c^{oo} V_C phi_c^{oo}}{ Delta t} )

Discussion

3.	Which of these is correct for the non-uniform time-steps? (Note: t is the distance between the centroids of two temporal elements. t is the size of a temporal element. The superscript o indicates the older time step).
A.	( delta t= frac{( Delta t- Delta t^o)}{2} )
B.	( delta t= frac{( Delta t+ Delta t^o)}{2} )
C.	t= t
D.	t= t
Answer» C. t= t

Discussion

4.	If the Adams-Moulton scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the current time-step? (Note: is the density and V the volume).
A.	(( frac{1}{ Delta t^o}+ frac{1}{ Delta t+ Delta t^o}) rho_C V_C )
B.	(( frac{1}{ Delta t}+ frac{1}{ Delta t^{oo}+ Delta t^o}) rho_C V_C )
C.	(( frac{1}{ Delta t}+ frac{1}{ Delta t+ Delta t^{oo}}) rho_C V_C )
D.	(( frac{1}{ Delta t}+ frac{1}{ Delta t+ Delta t^o}) rho_C V_C )
Answer» E.

Discussion

5.	If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the second previous time-step? (Note: is the density and V the volume).
A.	( frac{ Delta t^o}{ Delta t( Delta t+ Delta t^o)} rho_C^{oo}V_C )
B.	( frac{ Delta t( Delta t+ Delta t^o)}{ Delta t Delta t^o} rho_C^{oo}V_C )
C.	( frac{ Delta t+2 Delta t^o}{( Delta t+ Delta t^o)} rho_C^{oo}V_C )
D.	( frac{ Delta t}{ Delta t^o( Delta t+ Delta t^o)} rho_C^{oo}V_C )
Answer» E.

Discussion

6.	If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the previous time-step? (Note: is the density and V the volume).
A.	( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C V_C )
B.	( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o V_C )
C.	( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o )
D.	( frac{ Delta t+ Delta t^o}{ Delta t- Delta t^o} rho_C^o V_C )
Answer» C. ( frac{ Delta t- Delta t^o}{ Delta t+ Delta t^o} rho_C^o )

Discussion

7.	Which of these statements is correct about the variable time-steps?
A.	The finite volume and finite difference schemes do not yield equivalent algebraic equations
B.	The finite volume scheme yields equivalent algebraic equations irrespective of the non-uniformity
C.	The finite difference scheme yields equivalent algebraic equations irrespective of the non-uniformity
D.	All the second-order schemes result in the same algebraic equation when the grid is non-uniform
Answer» B. The finite volume scheme yields equivalent algebraic equations irrespective of the non-uniformity

Discussion

8.	Which of these characteristics of the Crank-Nicolson scheme is affected by the non-uniform transient grids?
A.	Consistency
B.	Convergence
C.	Stability
D.	Accuracy
Answer» E.

Discussion

9.	For which of these schemes is the interpolation profile need not be modified for the non-uniform transient grid?
A.	Downwind scheme
B.	Upwind scheme
C.	Crank-Nicolson scheme
D.	second-order schemes
Answer» D. second-order schemes

Discussion

10.	Discretization of the transient term is not affected by uniform or non-uniform grids when _________
A.	the scheme is downwind
B.	the scheme is upwind
C.	the scheme is first-order
D.	the scheme is second-order
Answer» D. the scheme is second-order

Discussion

Explore topic-wise MCQs in Computational Fluid Dynamics.

Which of these statements is correct regarding the Adams-Moulton scheme used on the non-uniform grids?

The general discretised form of the transient term using the finite volume approach isFluxT=FluxC C+FluxC C +FluxV.

Which of these is correct for the non-uniform time-steps?(Note: t is the distance between the centroids of two temporal elements. t is the size of a temporal element. The superscript o indicates the older time step).

If the Adams-Moulton scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the current time-step?(Note: is the density and V the volume).

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the second previous time-step?(Note: is the density and V the volume).

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the previous time-step?(Note: is the density and V the volume).

Which of these statements is correct about the variable time-steps?

Which of these characteristics of the Crank-Nicolson scheme is affected by the non-uniform transient grids?

For which of these schemes is the interpolation profile need not be modified for the non-uniform transient grid?

Discretization of the transient term is not affected by uniform or non-uniform grids when _________

The general discretised form of the transient term using the finite volume approach is
FluxT=FluxC _C+FluxC _C +FluxV.

Which of these is correct for the non-uniform time-steps?
(Note: t is the distance between the centroids of two temporal elements. t is the size of a temporal element. The superscript o indicates the older time step).

If the Adams-Moulton scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the current time-step?
(Note: is the density and V the volume).

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the second previous time-step?
(Note: is the density and V the volume).

If the Crank-Nicolson scheme is used with the finite difference approach to get the discretized equation of the transient term with the non-uniform grid, what is the central coefficient of the previous time-step?
(Note: is the density and V the volume).