This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Incompressible Flows – Staggered Grid”.

1. The staggered grid can be used to overcome __________

a) decoupling of pressure and velocities

b) coupling of pressure and velocities

c) interpolation problems

d) boundedness problems

View Answer

Explanation: The uncoupling between pressure and velocities cause a number of problems. Coupling can be enforced if the different flow variables are stored in the staggered grid form. Here, pressure and velocity are stored in different places.

2. Which of these statements is correct when using the staggered grids?

a) Interpolation is enough to find the pressure gradient in the continuity equation

b) No interpolation is needed to find the pressure gradient in the continuity equation

c) No interpolation is needed to find the pressure gradient in the momentum equation

d) Interpolation is enough to find the pressure gradient in the momentum equation

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Explanation: The momentum equation has this pressure gradient term given by \(\frac{\partial p}{\partial x}, \frac{\partial p}{\partial y}\, and \frac{\partial p}{\partial z}\). To find this pressure gradient, there is no need for any interpolation. The pressure gradients can be easily found out.

3. The staggered grid needs no interpolation to get the __________

a) velocity field in the momentum equation

b) velocity field in the continuity equation

c) kinetic energy field in the momentum equation

d) kinetic energy in the continuity equation

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Explanation: In the staggered grid formation, as the pressure is already stored in a different place from the pressure, there is no need of any interpolation to find the velocity field required for the continuity equation.

4. Which of these is not stored at the cell centres in the staggered grids?

a) Density

b) Pressure

c) Temperature

d) Velocity

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Explanation: In the staggered grid, all the scalar flow quantities are stored in the cell centres. Therefore, temperature, pressure and density are all stored in the cell centres. As velocity is a vector quantity, it is not stored here.

5. While using a staggered grid, the velocities are stored in the ___________

a) face centres

b) cell centres

c) edge centres

d) vertices

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Explanation: In the staggered grid arrangement, the velocities are stores in the face centres. This is why there will not be any need for interpolation to get the velocity field for the continuity equation.

6. What is the advantage of the staggered grid arrangement?

a) Helps to avoid stability problems

b) Helps to avoid convergence and consistency problems

c) Helps to avoid convergence problems and oscillations

d) Helps to avoid boundedness problems and oscillations

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Explanation: The biggest advantage of the staggered grid arrangement is the coupling of pressure and velocities. It also helps to avoid convergence problems and oscillations in pressure and velocity fields.

7. Arbitrary Lagrangian-Eulerian method comes under __________

a) Staggered grid arrangements

b) Partially staggered grid arrangements

c) Collocated arrangements

d) Orthogonal arrangement

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Explanation: The Arbitrary Lagrangian-Eulerian method is a partially staggered grid arrangement. It uses different locations to store the velocity and pressure fields but the arrangement varies from the completely staggered arrangement.

8. Which of these statements is correct about the Arbitrary Lagrangian-Eulerian method?

a) It produces non-converging pressure or velocity fields

b) It produces inconsistent pressure or velocity fields

c) It produces erroneous pressure or velocity fields

d) It produces oscillatory pressure or velocity fields

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Explanation: One of the main disadvantages of the Arbitrary Lagrangian-Eulerian method is the possibility of producing oscillatory pressure or velocity fields. It is advantageous only in some special cases.

9. Which of these statements is incorrect about the Arbitrary Lagrangian-Eulerian method?

a) Velocities are stored in the face centres

b) All the components of velocities are stored at the same point

c) Velocities are stored in the vertices

d) Pressures are stored in the cell centres

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Explanation: In the Arbitrary Lagrangian-Eulerian method, the scalar quantities are all stored at the cell centres like the completely staggered arrangement. All the velocity components are stored at the same point which are the vertices.

10. The Arbitrary Lagrangian-Eulerian method is advantageous for ___________

a) Curvilinear grids

b) Non-orthogonal grids

c) Cartesian grids

d) Orthogonal grids

View Answer

Explanation: The Arbitrary Lagrangian-Eulerian method has some advantages for the non-orthogonal grids. One of these advantages is that the pressure at the boundaries need not be specified here.

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