Finite Difference Methods MCQ

Test your knowledge with important Finite Difference Methods MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Finite Difference Methods MCQs at Bissoy

• I am using forward differences in the predictor step. Which method would you suggest me to use in the corrector step?
  ক

  Rearward differences

  খ

  Central differences

  গ

  Forward differences

  ঘ

  Second-order differences
• Which value is predicted in the predictor step of the MacCormack’s technique?
  ক

  Variable at the average time-step

  খ

  Variable at the upcoming time-step

  গ

  Time derivative of the variable at the upcoming time-step

  ঘ

  Time derivative of the variable at the average time-step
• Which of these methods is used for finding the average time derivative in MacCormack’s technique?
  ক

  Trial and error method

  খ

  Predictor-corrector method

  গ

  Genetic algorithm

  ঘ

  Relaxation method
• Which of these terms of the Taylor series expansion is used in the MacCormack’s technique?
  ক

  (Δ t)1 and (Δ t)2

  খ

  (Δ t)1

  গ

  (Δ t)0 and (Δ t)1

  ঘ

  (Δ t)0
• What is the order of accuracy of the MacCormack’s technique?
  ক

  Fourth-order

  খ

  Third-order

  গ

  First-order

  ঘ

  Second-order
• Which series expansion is used by the MacCormack’s technique?
  ক

  Taylor Series

  খ

  Fourier series

  গ

  McLaurin series

  ঘ

  Laurent series
• MacCormack’s technique is __________
  ক

  explicit, finite-difference method

  খ

  implicit, finite-difference method

  গ

  explicit, finite volume method

  ঘ

  implicit, finite volume method
• Which is the technique used to overcome the disadvantages of the Lax-Wendroff technique?
  ক

  Upwind scheme

  খ

  MacCormack’s technique

  গ

  Downwind scheme

  ঘ

  Richtmeyer method
• Which of these is wrong for the Lax-Wendroff technique?
  ক

  Linearization is needed

  খ

  Simultaneous equations are not required

  গ

  It is simple to solve

  ঘ

  It uses the finite difference method
• What is the disadvantage of the Lax-Wendroff technique?
  ক

  Stability

  খ

  Explicit

  গ

  Order of accuracy

  ঘ

  \((\frac{\partial ^2 \rho}{\partial t^2 })_{i,j}^t\)
• How many terms of the Taylor series expansion is used in the Lax-Wendroff technique?
  ক

  (Δ t)1 and (Δ t)2

  খ

  (Δ t)0, (Δ t)1 and (Δ t)2

  গ

  (Δ t)0 and (Δ t)1

  ঘ

  (Δ t)0
• Which series expansion is used by the Lax-Wendroff Technique?
  ক

  Taylor Series

  খ

  Fourier series

  গ

  McLaurin series

  ঘ

  Laurent series
• What is the order of accuracy of the Lax-Wendroff technique?
  ক

  fourth-order

  খ

  third-order

  গ

  first-order

  ঘ

  second-order
• The Lax-Wendroff technique is ____________
  ক

  explicit, finite-difference method

  খ

  implicit, finite-difference method

  গ

  explicit, finite volume method

  ঘ

  implicit, finite volume method
• To make the spectral method advantageous _____________
  ক

  Function must be periodic but grids can be non-uniform

  খ

  Grids should be uniform and function must be periodic

  গ

  Grids should be uniform but function can be non-periodic

  ঘ

  Grids should be structured and function must be periodic
• What is the cost of computation of FFT? (Note: ‘N’ is the number of grid points).
  ক

  N

  খ

  log ⁡N

  গ

  N log ⁡N

  ঘ

  \(\frac{N^2}{2} \)
• The cost of computation for Fourier coefficients can be reduced by ___________
  ক

  FFT

  খ

  DFT

  গ

  IDFT

  ঘ

  IFT
• The cost of computing the Fourier coefficients is ___________ (Note: ‘N’ is the number of grid points).
  ক

  N3

  খ

  N2

  গ

  \(\frac{N^2}{2} \)

  ঘ

  \(\frac{N^3}{3} \)
• Spectral methods are much more accurate than the Finite Difference methods ___________
  ক

  unconditionally

  খ

  conditionally depending on the problem taken

  গ

  conditionally when the number of grid points is small

  ঘ

  conditionally when grid size is small
• For higher order derivatives, spectral methods ___________
  ক

  can be easily generated

  খ

  are not suitable

  গ

  difficult to generate

  ঘ

  become invalid
• What is the advantage of using fourier series in the spectral method?
  ক

  Less grid size

  খ

  Large number of grid points

  গ

  Continuous results

  ঘ

  Flexibility
• What causes aliasing in Spectral methods?
  ক

  Small grid sizes

  খ

  Fourier series

  গ

  Arbitrary values for Fourier series

  ঘ

  Periodic nature
• Spectral methods use ___________
  ক

  Fourier series

  খ

  Taylor series

  গ

  McLaurin series

  ঘ

  Laurent series
• Spectral methods are particularly suitable for __________
  ক

  Subsonic flows

  খ

  Boundary layer flows

  গ

  Compressible flows

  ঘ

  Turbulence modelling