Question

The deferred correction source term of the NWF method using he normalized interpolation profile \(\tilde{\phi_f}=l\tilde{\phi_c}+k\) is _________

(a) (1-l-k)Φu

(b) (k)Φu

(c) (-l)Φu

(d) (l-k)Φu

I had been asked this question in exam.

I'm obligated to ask this question of High Resolution Schemes in division High Resolution Schemes of Computational Fluid Dynamics

Answer 1

The correct answer is:

(a) (1 - l - k)Φu

Explanation:

The deferred correction method in numerical schemes is a technique that improves the accuracy of a solution by iteratively refining an approximation. In the context of the Normalized Weighted Flux (NWF) method, the source term of the deferred correction can be expressed as a combination of the interpolated values and corrections made using the normalized interpolation profile.

The term (1 - l - k) is derived from the relationship between the corrected and the uncorrected values in the NWF method, with l and k being constants related to the scheme's correction parameters. This formulation reflects how the source term is adjusted during the correction process.

Thus, the deferred correction source term is typically represented as (1 - l - k)Φu, where Φu is the value at the uncorrected grid points.

Correct Answer: (a) (1 - l - k)Φu