This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Transient SIMPLE and PISO Algorithms”.

1. The SIMPLE algorithm used for transient problems is __________

a) implicit and iterative

b) implicit and direct

c) explicit and iterative

d) explicit and direct

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Explanation: For the implicit solution of transient flow problems, the SIMPLE, SIMPLER and SIMPLEC algorithms can be used to get the solution at each time-step. The solution is iterated until we get them converged at one time-step.

2. Which of these statements is correct about the transient SIMPLE algorithm?

a) No additional terms are needed in the continuity and pressure-correction equations

b) No additional terms are needed in the continuity equation

c) An additional term is needed in the continuity and pressure-correction equations

d) No additional terms are needed in the pressure-correction equation

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Explanation: The transient (unsteady) terms are added to the continuity equation. As the transient SIMPLE algorithm derives its pressure-correction equation from the continuity equation, the pressure-correction equation also gets some additional terms.

3. The PISO algorithm for the transient problem is _________

a) iterative

b) non-iterative

c) never converging

d) fast converging

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Explanation: The PISO algorithm was actually developed for transient problems. When taken for the steady-state problems, it was made iterative. In the original form, the PISO algorithm does not involve iterations.

4. Which of these techniques is used by the PISO algorithm?

a) Neighbour splitting

b) Source splitting

c) Coefficient splitting

d) Operator splitting

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Explanation: The temporal accuracy of the PISO algorithm depends on the differencing scheme used. This includes the operator splitting technique used. Operator splitting uses different methods to calculate different variables.

5. Which of these terms of the momentum equations are altered by the transient term in the PISO algorithm?

a) neighbouring coefficients

b) central coefficients

c) weighted average of the neighbouring coefficients

d) velocity correction term

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Explanation: A term with the initial density, change in volume and change in time is added to the central coefficients of the momentum equations in all the directions. The neighbouring coefficients are not altered.

6. Which of these terms is added to the source term of the momentum equations of the transient PISO algorithm?

a) product of the latest central coefficient and latest velocity

b) product of the current central coefficient and previous velocity

c) product of the previous central coefficient and previous velocity

d) product of the initial central coefficient and current velocity

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Explanation: To the source term of the u-momentum equation, the term \(a_P^0 \, u_P^0\) is added. Where, \(a_P^0\) is the initial central coefficient and \(u_P^0\) is the initial velocity in u-direction. A similar term is added to the sources of the other momentum equations also.

7. Which of these equations are altered by the transient term in the PISO algorithm?

a) both the first and second pressure-correction equations

b) only the first pressure-correction equation

c) only the second pressure-correction equation

d) neither the first nor the second pressure-correction equations

View Answer

Explanation: The transient PISO algorithm has two corrector steps and hence two pressure-correction equations. Both of these equations are affected by the transient term. The source terms of these equations are altered.

8. The order of temporal accuracy achieved by the PISO algorithm for pressure and momentum are ___________ and ___________ respectively.

a) four, three

b) two, three

c) three, four

d) four, two

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Explanation: The PISO procedure is repeated at each time-step to calculate the velocity and pressure values. This algorithm results in third-order temporally accurate pressure values and fourth-order temporally accurate momentum values.

9. Which of these is a disadvantage of the PISO algorithm?

a) memory required

b) small time-steps

c) computational cost

d) time required

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Explanation: The PISO algorithm is advantageous compared to the SIMPLE algorithm that they do not need an iterative process at each time step. But the disadvantage is that they need the time steps to be small enough to produce accurate results.

10. To overcome the performance issues of the PISO algorithm, which of these methods is used?

a) Time-steps based on temporal schemes are used

b) Large time-steps are used

c) First-order temporal differencing is used

d) Higher-order temporal differencing is used

View Answer

Explanation: The need for a small time-step in the PISO algorithm is overcome by using higher-order temporal differencing schemes. For example, a second-order implicit scheme with three time levels can be used.

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