[wavee]

One model I'm using uses a 4th-order reconstruction scheme, and I'm having serious trouble understanding how this works. I understand how third-order reconstructions work overall, but I can't seem to find any good resources for going to higher orders.



The relevant paper is Yamamoto et al (1993) (link below) in equations 36-41. I feel like I'm losing my mind- a ton of papers cite Yamamoto, but I can't find a single explanation anywhere on why these equations have the form they do. I understand flux limiters just fine. It's that third order correction term that gets thrown in that's throwing me for a loop. I'd appreciate any resources available that could explain these high-order MUSCL schemes, even if it's not directly related to this.



I'm really trying to understand how to view these MUSCL schemes as interpolation onto the interfacial values, but I'm struggling to keep everything straight between cell averaged, non-cell averaged, and all the difference terms


https://pdf.sciencedirectassets.com/...5c4032cc&cc=us

[jayhawk21]

Were you able to figure this out? Also, I couldnt see the paper but I am curious about high order schemes