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In the wiki page of Flux limiter, it writes:

If these edge fluxes can be represented by low and high resolution schemes, then a flux limiter can switch between these schemes depending upon the gradients close to the particular cell, as follows, $$ F\left(u_{i+{\frac {1}{2}}}\right)=f_{i+{\frac {1}{2}}}^{low}-\phi \left(r_{i}\right)\left(f_{i+{\frac {1}{2}}}^{low}-f_{i+{\frac {1}{2}}}^{high}\right),\\{\displaystyle F\left(u_{i-{\frac {1}{2}}}\right)=f_{i-{\frac {1}{2}}}^{low}-\phi \left(r_{i-1}\right)\left(f_{i-{\frac {1}{2}}}^{low}-f_{i-{\frac {1}{2}}}^{high}\right)},\\\\$$ where $f^{{low}}=$ low resolution flux, $f^{{high}}=$ high resolution flux, $ \phi(r)=$flux limiter function,$r_{{i}}={\frac {u_{{i}}-u_{{i-1}}}{u_{{i+1}}-u_{{i}}}}.$

I'm new to this area, my question is, what is the definition of low resolution schemes? I can only find definition about high resolution schemes. Most importantly, how do we know if a flux can be represented by low and high resolution schemes? If it can, then what are the explicit expressions of $f^{low}$ and $f^{high}$? For example, the Godunov flux is $$f^{God}(u_l,u_r):=\begin{cases}\max_{u\in[u_l,u_r]}f(u)~~\text{if }u_l> u_r\\\min_{u\in[u_r,u_l]}f(u)~~\text{if }u_l\le u_r\end{cases},$$ given that $f$ is convex, then can it be represented by low and high resolution schemes? What about other fluxes such as the Lax-Friedrichs flux or the Engquist-Osher flux? Many thanks advance!

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    $\begingroup$ This isn't a research question, so it's probably not appropriate for MO. You could ask on scicomp.SE. But if you're new to the area and want to learn more, I recommend starting with this book or this book. $\endgroup$ Jun 9, 2022 at 6:44

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