5. Advanced Finite-Difference Methods for Computational Fluid Dynamics (CFD)

This video is devoted to advanced finite-difference methods. Shown is the derivation of 3rd and 4th-order finite-difference approximations for the first and second derivative, based on polynomial fitting, as well as the compact high-order schemes. Another important topic is the deferred-correction approach, which allows easier implementation of high-order schemes in implicit solution methods for steady-state flows and also saves memory and computing effort. At the end, numerical experiments are conducted to verify the order of the described approximations.
You can download this video, the transcript of its soundtrack, the PowerPoint presentation file, and other supplementary material (computer codes for numerical experiments) from this site:
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[istvantamasjozsa]

At 13:50 and at 17:35, it remains unexplained "why for the smallest grid spacing the slope reduces". This behaviour is caused by number precision as shown in the truncation_vs_round_off_error github repository.

I found that this phenomenon often causes frustration when grid/time-step convergence studies are carried out because when round-off errors start to dominate then convergence cannot be demonstrated anymore.