This set of Computational Fluid Dynamics online quiz focuses on “Deferred Correction for High-Resolution Schemes”.

1. The coefficients in the deferred correction procedure are based on ___________

a) the downwind scheme

b) the quick scheme

c) the upwind scheme

d) the high-resolution scheme

View Answer

Explanation: Deferred correction procedure is used to overcome problems related to the convergence of a scheme. The coefficients used here are based on the upwind scheme which is suitable for convection.

2. What is added as a source term in the deferred correction method?

a) Difference between the high-resolution and the upwind schemes

b) Constants in the high-resolution schemes

c) Constants in the upwind schemes

d) Difference between the downwind and the upwind schemes

View Answer

Explanation: The source term of the given flow problem is considered. In addition to this, a source term is added in the deferred correction method which is equal to the difference between the high-resolution scheme and the upwind scheme.

3. Difference between the upwind line and the high-resolution scheme line gives __________

a) the difference between the upwind and the downwind nodes

b) the normalized difference between the cell face values

c) the difference between the far upwind and the upwind nodes

d) the difference between the far upwind and the downwind nodes

View Answer

Explanation: The effects of the deferred correction method can be seen in an NVD frame. The normalized difference between the cell face values is given by the difference between the upwind and the high-resolution scheme lines in the NVD.

4. If the normalized difference between the cell face values is high, the convergence rate ___________

a) tends to infinity

b) is undisturbed

c) is low

d) is high

View Answer

Explanation: If the difference between the high-resolution scheme line and the upwind line increases, convergence is affected. The rate of convergence diminishes. This is when the normalized difference between the cell face values is high.

5. Deferred correction procedure for high-resolution schemes leads to __________

a) NVF and TVD

b) NWF and DWF

c) NVF and DWF

d) TVD and NWF

View Answer

Explanation: The convergence problem of the high-resolution schemes paved the way for techniques of implementing high-resolution schemes that are more implicit such as NWF and DWF.

6. What does NWF stand for?

a) Normalized Weighing Factor

b) Northern Weighing Factor

c) Normalized West Factor

d) Normalized Weighted Formulation

View Answer

Explanation: The abbreviation NWF stands for Normalized Weighing Factor. The abbreviation DWF stands for Downwind Weighing Factor. These two are implicit methods of formulating high-resolution schemes.

7. Which of these statements is correct?

a) The DWF method converges faster than the NWF method

b) Both the methods are of the same properties

c) The NWF method is more robust than the DWF method

d) The DWF method is more robust than the NWF method

View Answer

Explanation: The NWF method is created to overcome the shortcomings of the DWF method. In the NWF method, instabilities do not arise. This allows the NWF method to be much more robust than the DWF method.

8. The Downwind Weighing Factor is a function of the flow variables at ___________

a) the face and upwind nodes

b) the far upwind, upwind and downwind nodes

c) the upwind and downwind nodes

d) the face, upwind and downwind nodes

View Answer

Explanation: The Downwind Weighing Factor is given by

\(DWF_f=\frac{\phi_f-\phi_c}{\phi_d-\phi_c}\)

Where,

Φ

_{f}→ Flow variable at the face.

Φ

_{c}→ Flow variable at the upwind node.

Φ

_{f}→ Flow variable at the downwind node.

9. What is the difficulty in the direct use of nodal values without the deferred correction method?

a) Convergence and stability

b) Stability and accuracy

c) Accuracy and Boundedness

d) Boundedness and convergence

View Answer

Explanation: The difficulty arising when explicitly expressing a flow variable in terms of neighbouring values is the convergence rate. They violate one of the basic rules for stability and convergence which is the coefficients should be of the same sign.

10. The NWF method uses __________

a) TVD

b) NVF

c) Both NVF and TVD

d) Neither NVF nor TVD

View Answer

Explanation: The NWF method operates by linearizing the normalized interpolation profile. This uses the simplified form of the TVD framework given by \(\tilde{\phi}_f=a\tilde{\phi}_c+b\). The correction term here is smaller than the one obtained by standard deferred correction methods.

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