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The MacCormack finite-difference "predictor-corrector" method is well known to generate spurious oscillations near solution discontinuities such as shock waves in gas dynamics equations. Or even in simpler case of scalar advection equation, when advected function contains jumps.

For teaching purposes, I'd like to find a simplest way to make it work with such discontinuities, so that it wouldn't be too complex for students to implement. I'm aware of such methods as adding Davis artificial viscosity or applying Boris-and-Book-like "monotonizators". But are there simpler ways to dampen oscillations to some acceptable values?

omican
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    Acceptable is quite vague. Do you simply want to prevent code crashing? – ConvexHull Sep 27 '22 at 22:03
  • I mean that achieving TVD property is not neccessary, it would be enough to bound oscillations by some percentage of the jump magnitude or some constant value. – omican Sep 28 '22 at 06:10
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    Back in the 1980s I wrote a Royal Aircraft Establishment report on this. Very simple and effective. Of course no online version but I do still have a paper copy somewhere that I will try to dig out. – Philip Roe Sep 30 '22 at 00:44
  • @PhilipRoe Dear Professor, did you have any success finding that report? Also, on an irrelevant note: I often refer to Jacobian averaging named after you in my presentations, but never got to know how to pronounce your name correctly :-) What is the proper way? – omican Oct 05 '22 at 21:14

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