Is there anyone acknowledging that which one is superior? Many CFD references mentioned both of them but no one explains about the fact that which one is better. Please give me your knowledge about this issue.

Hi Jinwon

I didn't there was a difference between the two. Most of what I know about limiters comes from a book by Hirsch:Numerical computation of internal and external flows.

Cheers Shuo

The reason of my question is the structure of the solution method. The slope limiter in the Euler euqation needs to deal with it in the local characteristic variables based on the eigen-system while the flux limiter does not seem like. Anyway, thanks for your reply.

Jinwon

Flux limiters are typically applied directly to the fluxes, rather than the flow or characteristic variables. Hirsch touches on this in vol. 2 of his books. In using flux limiters, one usually extrapolates the fluxes to the cell face (via MUSCL, QUICK, etc.) and then limits the flux extrapolation. The formulas for limiting and extrapolation are the same between the two approaches, but variable extrapolation and slope-limiting seems to make better use of the built-in dissipation arising from the specific non-linearities of the flow equations (ref. Hirsch, Numerical Computation of Internal and External Flows, V. 2, pp. 508-509).