Explore topic-wise MCQs in Computational Fluid Dynamics.

This section includes 9 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.

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