This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Incompressible Flows – Rhie-Chow Interpolation”.

1. The checkerboard problem arises due to __________

a) linear interpolation in a staggered grid

b) quadratic interpolation in a staggered grid

c) linear interpolation in a collocated grid

d) quadratic interpolation in a collocated grid

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Explanation: The decoupling between the pressure and velocity values at the cell level happens due to linear interpolation used in the collocated grid. This gives rise to the checkerboard problem in the collocated grids.

2. Which of these methods use Rhie-Chow interpolation?

a) QUICK scheme

b) NVF method

c) TVD method

d) SIMPLE algorithm

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Explanation: Rhie-Chow interpolation is used in the collocated grid without leading to the uncoupled pressure and velocity fields. Rhie-Chow interpolation leads to the formulation of the SIMPLE algorithm.

3. Which of these terms is extra while using the Rhie-Chow interpolation?

a) Diffusion term

b) Dissipative term

c) Advection term

d) Source term

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Explanation: Two different grid stencils are used in the Rhie-Chow interpolation method. The difference between the values obtained from these two grid stencils is added as a dissipative term in the result.

4. The Rhie-Chow interpolation is equivalent to __________

a) pseudo-momentum equation with the coefficients linearly interpolated

b) pseudo-momentum equation with the coefficients quadratically interpolated

c) pseudo-continuity equation with the coefficients linearly interpolated

d) pseudo-continuity equation with the coefficients quadratically interpolated

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Explanation: The Rhie-Chow interpolation is used on collocated grids. It is equivalent to constructing a pseudo-momentum equation at the face. It has coefficients which are obtained using linear interpolation of the momentum equations at the centroids.

5. The Rhie-Chow interpolation mimics __________

a) pressure-velocity coupling of the collocated grid arrangement

b) pressure-velocity coupling of the staggered grid arrangement

c) pressure-velocity decoupling of the staggered grid arrangement

d) pressure-velocity decoupling of the collocated grid arrangement

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Explanation: The pressure gradients in the Rhie-Chow interpolation are calculated using small grid stencil with two different stencils. This resembles the pressure-velocity coupling of the staggered grid arrangement.

6. The coefficients of the equation formed in the Rhie-Chow interpolation is obtained using ___________

a) Weighted average

b) Quadratic interpolation

c) Rhie-Chow interpolation

d) Linear interpolation

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Explanation: The Rhie-Chow interpolation forms momentum equations. The coefficients of this new momentum equation cannot be directly computed. They are assumed using interpolation of the values in the neighbouring nodes.

7. The coefficient approximation in the Rhie-Chow interpolation is ___________

a) fourth-order accurate

b) third-order accurate

c) second-order accurate

d) first-order accurate

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Explanation: The coefficient approximation in the Rhie-Chow interpolation results in an equation which is the same as the one obtained using the staggered grids. This coefficient approximation is of second-order accuracy.

8. The collocated arrangement with Rhie-Chow interpolation will result in an equation which is dependent on the ___________

a) staggered grid

b) linear interpolation

c) average

d) under-relaxation factor

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Explanation: When a collocated grid arrangement is used with the Rhie-Chow interpolation to get the momentum equation at the faces, the resulting solution becomes dependent on the under-relaxation factor present in the momentum equation.

9. The Rhie-Chow interpolation needs a redistribution of the _________

a) source term

b) pressure gradient term

c) viscous force term

d) body force term

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Explanation: The body force in the staggered grid term has the exact stencil of the pressure gradients. Therefore, a redistribution of the body force term in the Rhie-Chow interpolation is needed to match the staggered grids.

10. When the transient term in the Rhie-Chow interpolation is not accounted for separately, the result will ___________

a) be oscillatory

b) be stable

c) have overshoots

d) have undershoots

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Explanation: When the transient term in the Rhie-Chow interpolation is not properly accounted, the result will be time step-dependent and will lead to an oscillatory solution for small time-steps.

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