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.

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.

Find \(\frac{\partial u}{\partial r}\) at point 1 using forward difference method.

A. 1000
B. 100
C. 500
D. 5000
Answer» B. 100
Discussion
4.

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
5.

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
6.

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
7.

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
8.

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
9.

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
10.

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