Computational Fluid Dynamics Multiple Choice Questions on “Incompressible Flows – SIMPLE Algorithm”.
1. What does SIMPLE stand for?
a) Semi-Implicit Method for Pressure-Linked Equations
b) Simple Implicit Method for Pressure-Linked Equations
c) Solution in Iterative Method for Pressure-Links Explicitly
d) Simple Iterative Method for Pressure-Links Explicitly
Answer: a
Clarification: The SIMPLE in SIMPLE algorithm expands as “Semi-Implicit Method for Pressure-Linked Equations”. This method was introduced by Suhas Patankar and Brian Spalding in the year 1972 at Imperial College.
2. The SIMPLE algorithm is a ____________
a) Weighted average method
b) Predictor-corrector method
c) Euler method
d) Heun’s method
Answer: b
Clarification: The algorithm is a guess and correct method used to calculate the pressure values in a staggered grid arrangement. It involves continuous iterations of predicting the values and correcting them.
3. In the momentum equation for the correction field, which of these terms are neglected?
a) Neighbouring correction terms
b) All the coefficients
c) The source terms
d) The velocity terms
Answer: a
Clarification: The discretized momentum equation is rewritten for the initial guesses. Now, the correction is introduced into this equation and the correction equations are formed. In these correction equations, the corrections for the neighbouring terms are omitted. This is applicable as it does not make any changes globally.
4. Which of these equations are used in the SIMPLE algorithm?
a) Momentum and energy equations
b) Energy equation and equation of state
c) Equation of state and continuity equation
d) Continuity and momentum equations
Answer: d
Clarification: The SIMPLE algorithm involves the calculations for pressure and velocity. It uses both the continuity and momentum equations. The momentum equation is used for the initial guesses. While applying the constraints, the continuity equation is also needed.
5. Which of these equations is/are obtained from the continuity equation?
a) Both the pressure and velocity-correction equations
b) Velocity-correction equation
c) Pressure-correction equation
d) Density-correction equation
Answer: c
Clarification: The equation for the pressure correction arises from the discretized continuity equation. It contains a source term which is the result of the continuity imbalance from the incorrect velocity field.
6. Which of these statements is correct about the pressure correction equation?
a) An over-relaxation factor is used to avoid divergence
b) An under-relaxation factor is used to avoid divergence
c) An under-relaxation factor is used to avoid undershoots
d) An over-relaxation factor is used to avoid undershoots
Answer: b
Clarification: The pressure correction equation may diverge if an under-relaxation factor is not used. So, an under-relaxation factor is used with the correction term which is added to the guessed term to get the correct value.
7. The range of the relaxation factor in the pressure correction equation is ____________
a) 0 ≤ factor < 1
b) 0 < factor < 1
c) 0 < factor ≤ 1
d) 0 ≤ factor ≤ 1
Answer: b
Clarification: An under-relaxation factor equal to 1 leads to no relaxation. The whole correction factor is taken into account. An under-relaxation factor equal to 0 leads to no correction. The guessed value is taken as the correct value. So, the value should lie in between these two.
8. Which of these statements is correct about a small relaxation factor?
a) Computation is unstable but convergence is fast
b) Computation is stable and convergence is fast
c) Computation is stable but convergence is slow
d) Computation is unstable and convergence is slow
Answer: c
Clarification: When the under-relaxation factor is small, the speed of computation is very slow. Because, to get the solutions converged, a large number of iterations are needed. But, this small under-relaxation factor will lead to a stable computation.
9. A large relaxation factor will lead to ____________
a) large and oscillatory iteration steps
b) large and stable iteration steps
c) small and oscillatory iteration steps
d) small and stable iteration steps
Answer: a
Clarification: The under-relaxation factor should be large enough to move the iteration steps forward at a fast rate. But, if it is too large, the iteration steps will be unstable and oscillatory or even divergent at times.
10. Which of these is correct about the SIMPLE algorithm?
a) It is a looped algorithm
b) It is iterative
c) It is sequential
d) It is simultaneous
Answer: d
Clarification: The SIMPLE algorithm is sequential. The final solution of each iteration satisfies both the continuity and the momentum equations. Only when these two are satisfied, the algorithm moves forward for the next iteration.