Convection-Diffusion Problems MCQ

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• Numerical dispersion is a result of __________
  ক

  higher-order interpolation profile

  খ

  unphysical behaviour of assumed interpolation profile

  গ

  first-order interpolation profile

  ঘ

  quadratic interpolation profile
• What is the problem of numerical diffusivity?
  ক

  The simulated model has a higher diffusivity than the actual flow

  খ

  The simulated model has a lower diffusivity than the actual flow

  গ

  The simulated model has a different diffusivity than the actual flow

  ঘ

  The simulated model has a zero diffusivity
• Which of these is correct for the central difference scheme?
  ক

  Neither numerical dispersion nor numerical diffusion error arises

  খ

  Only numerical diffusion error arises

  গ

  Both numerical dispersion and numerical diffusion errors arise

  ঘ

  Only numerical dispersion error arises
• Which is correct regarding the upwind scheme?
  ক

  Neither numerical dispersion nor numerical diffusion error arises

  খ

  Only numerical diffusion error arises

  গ

  Both numerical dispersion and numerical diffusion errors arise

  ঘ

  Only numerical dispersion error arises
• Which of these methods can be used to evaluate the errors in convection-diffusion schemes?
  ক

  Using the exact solution of the source-free problem

  খ

  Using the exact solution of the source and diffusion-free problem

  গ

  Using the exact solution of the diffusion-free problem

  ঘ

  Using the first-order schemes
• Numerical dispersion error causes __________
  ক

  convergence problems

  খ

  accuracy problems

  গ

  boundedness problems

  ঘ

  stability problems
• Which of these methods cannot be used to reduce the errors due to cross-stream numerical diffusion?
  ক

  Interpolation in the direction of flow

  খ

  Higher order interpolation profile

  গ

  Multi-dimensional interpolation profiles

  ঘ

  Changing the direction of interpolation
• What is the cause of cross-stream numerical diffusion?
  ক

  One-dimensional nature of the assumed profiles

  খ

  Multi-dimensional nature of the assumed profiles

  গ

  Higher order of accuracy

  ঘ

  Higher order of interpolation
• Which of these ways can be used to overcome stream-wise numerical diffusion?
  ক

  Decreasing the order of interpolation

  খ

  Increasing the order of interpolation

  গ

  Increasing the number of neighbours considered

  ঘ

  Decreasing the number of neighbours considered
• Numerical diffusion causes __________
  ক

  smearing of sharp gradients

  খ

  oscillations

  গ

  undershoots and overshoots

  ঘ

  inaccuracy
• Which of these is correct about the FROMM scheme?
  ক

  A linear profile is obtained between the immediate upwind and the far downwind nodes

  খ

  A linear profile is obtained between the far upwind and the immediate downwind nodes

  গ

  A linear profile is obtained between the far upwind and the immediate upwind nodes

  ঘ

  A linear profile is obtained between the far upwind and the far downwind nodes
• FROMM scheme ____________
  ক

  gives weighted importance to the upwind and downwind schemes

  খ

  gives equal importance to upwind and downwind scheme

  গ

  is downwind biased

  ঘ

  is upwind biased
• What is the order of accuracy of the FROMM scheme?
  ক

  First-order

  খ

  Second-order

  গ

  Third-order

  ঘ

  Fourth-order
• Which of these is correct for a QUICK scheme?
  ক

  False diffusion is zero

  খ

  False diffusion is small

  গ

  False diffusion is big

  ঘ

  False diffusion is infinity
• Which of these is correct about the QUICK scheme?
  ক

  Stable and bounded

  খ

  Stable and unbounded

  গ

  Unstable and bounded

  ঘ

  Unstable and unbounded
• What is the first term of the truncation error of the QUICK scheme?
  ক

  \(\frac{1}{16} (\Delta x)^2 \phi_C”’\)

  খ

  \(\frac{1}{16} (\Delta x)^3 \phi_C”’\)

  গ

  \(\frac{1}{16} (\Delta x)^3 \phi_C^{iv}\)

  ঘ

  \(\frac{1}{16} (\Delta x)^2 \phi_C^{iv}\)
• How many terms does the discretized form of source-free 1-D convection problem modelled using the QUICK scheme has?
  ক

  3

  খ

  5

  গ

  2

  ঘ

  4
• What is the order of accuracy of the QUICK scheme?
  ক

  second-order

  খ

  first-order

  গ

  fourth-order

  ঘ

  third-order
• Which is correct about the QUICK scheme?
  ক

  A two-point upwind biased interpolation

  খ

  A three-point upwind biased interpolation

  গ

  A three-point downwind biased interpolation

  ঘ

  A two-point downwind biased interpolation
• What does QUICK stand for?
  ক

  Quadratic Upstream Interpolation for Convective Kinetics

  খ

  Quadratic Upstream Interval for Convective Kinetics

  গ

  Quadratic Upwind Interval for Convective Kinetics

  ঘ

  Quadratic Upwind Interpolation for Convective Kinetics
• Which statement is correct?
  ক

  The second-order upwind scheme is never stable

  খ

  The second-order upwind scheme is always stable

  গ

  The second-order upwind scheme is conditionally stable

  ঘ

  The second-order upwind scheme is always unstable
• The second-order upwind scheme is ___________ than the general upwind scheme.
  ক

  less diffusive

  খ

  more diffusive

  গ

  less accurate

  ঘ

  less stable
• The value at the face in the second order upwind scheme is calculated using _____________
  ক

  interpolation

  খ

  extrapolation

  গ

  weighted average

  ঘ

  geometric mean
• The Second Order Upwind (SOU) scheme uses ____________
  ক

  asymmetric linear profile

  খ

  symmetric linear profile

  গ

  asymmetric quadratic profile

  ঘ

  symmetric quadratic profile
• In which of these ranges is the central differencing scheme used?
  ক

  -2≤Pe≤2

  খ

  -1≤Pe≤1

  গ

  -0.5≤Pe≤0.5

  ঘ

  -5≤Pe≤5
• The Peclet number is calculated at the ____________
  ক

  control volume

  খ

  cell centres

  গ

  vertices

  ঘ

  faces
• What is the advantage of the hybrid differencing scheme compared to the QUICK scheme?
  ক

  Transportiveness

  খ

  Accuracy

  গ

  Stability

  ঘ

  Conservativeness
• Which of these is correct about the hybrid differencing scheme?
  ক

  It is conservative but not transportive

  খ

  It is conservative and transportive

  গ

  It is transportive but not conservative

  ঘ

  It is neither transportive nor conservative
• What is the order of accuracy of the hybrid differencing scheme?
  ক

  Fourth-order

  খ

  Third-order

  গ

  Second-order

  ঘ

  First-order
• The hybrid differencing scheme is ____________
  ক

  never bounded

  খ

  bounded unconditionally

  গ

  bounded in the low Peclet number

  ঘ

  bounded in the high Peclet number