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I've been exploring the CFL (Courant-Friedrichs-Lewy) condition in polar coordinates and have observed that previous inquiries haven't yielded a satisfactory answer. I've come across this paper which appears to provide a more compelling explanation for the CFL condition in polar coordinates. However, I'm uncertain about the implementation, especially with regard to the M term. I'm not sure how to obtain it—do I need to utilize the wave solution and compute the derivatives?

cfl condition

I'd appreciate any insights or guidance on this matter. Thank you!

These are the other questions about CFL condition that I found in stack exchange CFL CONDITION IN POLAR COORDINATES and CFL condition in polar coordinates

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