Order of accuracy m means _____________

as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m times of the grid size

as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m powers of the grid size

as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m times of the grid size

as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m powers of the grid size

as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m times of the grid size

Find the central second difference of u in y-direction using the Taylor series expansion.

( frac{u_{i,j+1}-2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )

( frac{u_{i,j+1}+2u_{i,j}+u_{i,j-1}}{( Delta y)^2} )

( frac{u_{i,j+1}-2u_{i,j}+u_{i,j-1}}{( Delta y)^2} )

( frac{u_{i,j+1}-2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )

( frac{u_{i,j+1}+2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )

Using the Taylor series expansion, What is the first term of the truncation error of the finite difference equation (( frac{ partial u}{ partial x})_{i,j}= frac{u_{i+1,j}-u_{i,j}}{ Delta y} )?

(( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )

(-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2} )

(( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )

(-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )

(( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2} )

Find the first-order forward difference approximation of (( frac{ partial u}{ partial x})_{i,j} ) using the Taylor series expansion.

( frac{u_{i,j+1}-u_{i,j}}{2 Delta x} )

( frac{u_{i+1,j}-u_{i,j}}{2 Delta x} )

( frac{u_{i,j+1}-u_{i,j}}{ Delta x} )

( frac{u_{i+1,j}-u_{i,j}}{ Delta x} )

Find the second-order accurate finite difference approximation of the first derivative of the velocity component (u) in the x-direction using the Taylor series expansion. (Note: i and j are in the x and y-direction respectively).

( frac{u_{i,j+1}-u_{i,j-1}}{2 Delta x} )

( frac{u_{i,j+1}-u_{i,j-1}}{ Delta x} )

( frac{u_{i+1,j}-u_{i-1,j}}{ Delta x} )

( frac{u_{i+1,j}-u_{i-1,j}}{2 Delta x} )

( frac{u_{i,j+1}-u_{i,j-1}}{2 Delta x} )

Consider the equation (( frac{ partial u}{ partial y})_{i,j}=( frac{u_{i,j}-u_{i,j-1}}{ Delta y}) ) formulated using the Taylor series expansion. Find the type of equation.

second-order forward difference

first-order rearward difference

second-order forward difference

second-order rearward difference

9 + Mcqs in Finite Difference Method in Computational Fluid Dynamics Page 1 McqOptions

1.	Order of accuracy m means _____________
A.	as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m powers of the grid size
B.	as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m times of the grid size
C.	as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m powers of the grid size
D.	as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m times of the grid size
Answer» B. as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m times of the grid size

Discussion

2.	What is the least order of accuracy for the second derivatives?
A.	first-order
B.	third-order
C.	fourth-order
D.	second-order
Answer» E.

Discussion

3.	What is the order of the central difference for the mixed derivative ( frac{ partial^2 u}{ partial x partial y} ) while approximated using the Taylor series expansion?
A.	1
B.	2
C.	3
D.	4
Answer» C. 3

Discussion

4.	Find the central second difference of u in y-direction using the Taylor series expansion.
A.	( frac{u_{i,j+1}+2u_{i,j}+u_{i,j-1}}{( Delta y)^2} )
B.	( frac{u_{i,j+1}-2u_{i,j}+u_{i,j-1}}{( Delta y)^2} )
C.	( frac{u_{i,j+1}-2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )
D.	( frac{u_{i,j+1}+2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )
Answer» C. ( frac{u_{i,j+1}-2u_{i,j}-u_{i,j-1}}{( Delta y)^2} )

Discussion

5.	Using the Taylor series expansion, What is the first term of the truncation error of the finite difference equation (( frac{ partial u}{ partial x})_{i,j}= frac{u_{i+1,j}-u_{i,j}}{ Delta y} )?
A.	(-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2} )
B.	(( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )
C.	(-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )
D.	(( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2} )
Answer» B. (( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{3} )

Discussion

6.	Find the first-order forward difference approximation of (( frac{ partial u}{ partial x})_{i,j} ) using the Taylor series expansion.
A.	( frac{u_{i,j+1}-u_{i,j}}{2 Delta x} )
B.	( frac{u_{i+1,j}-u_{i,j}}{2 Delta x} )
C.	( frac{u_{i,j+1}-u_{i,j}}{ Delta x} )
D.	( frac{u_{i+1,j}-u_{i,j}}{ Delta x} )
Answer» E.

Discussion

7.	Find the second-order accurate finite difference approximation of the first derivative of the velocity component (u) in the x-direction using the Taylor series expansion. (Note: i and j are in the x and y-direction respectively).
A.	( frac{u_{i,j+1}-u_{i,j-1}}{ Delta x} )
B.	( frac{u_{i+1,j}-u_{i-1,j}}{ Delta x} )
C.	( frac{u_{i+1,j}-u_{i-1,j}}{2 Delta x} )
D.	( frac{u_{i,j+1}-u_{i,j-1}}{2 Delta x} )
Answer» D. ( frac{u_{i,j+1}-u_{i,j-1}}{2 Delta x} )

Discussion

8.	Consider the equation (( frac{ partial u}{ partial y})_{i,j}=( frac{u_{i,j}-u_{i,j-1}}{ Delta y}) ) formulated using the Taylor series expansion. Find the type of equation.
A.	first-order forward difference
B.	first-order rearward difference
C.	second-order forward difference
D.	second-order rearward difference
Answer» C. second-order forward difference

Discussion

9.	The truncation error in a finite difference expansion is (-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2}-( frac{ partial^3 u}{ partial x^3})_{i,j} frac{( Delta x)^3}{6} ). What is the order of accuracy of the finite difference equation?
A.	1
B.	2
C.	-2
D.	-1
Answer» B. 2

Discussion

Explore topic-wise MCQs in Computational Fluid Dynamics.

Order of accuracy m means _____________

What is the least order of accuracy for the second derivatives?

What is the order of the central difference for the mixed derivative ( frac{ partial^2 u}{ partial x partial y} ) while approximated using the Taylor series expansion?

Find the central second difference of u in y-direction using the Taylor series expansion.

Using the Taylor series expansion, What is the first term of the truncation error of the finite difference equation (( frac{ partial u}{ partial x})_{i,j}= frac{u_{i+1,j}-u_{i,j}}{ Delta y} )?

Find the first-order forward difference approximation of (( frac{ partial u}{ partial x})_{i,j} ) using the Taylor series expansion.

Find the second-order accurate finite difference approximation of the first derivative of the velocity component (u) in the x-direction using the Taylor series expansion. (Note: i and j are in the x and y-direction respectively).

Consider the equation (( frac{ partial u}{ partial y})_{i,j}=( frac{u_{i,j}-u_{i,j-1}}{ Delta y}) ) formulated using the Taylor series expansion. Find the type of equation.

The truncation error in a finite difference expansion is (-( frac{ partial^2 u}{ partial x^2})_{i,j} frac{ Delta x}{2}-( frac{ partial^3 u}{ partial x^3})_{i,j} frac{( Delta x)^3}{6} ). What is the order of accuracy of the finite difference equation?