Robust FVM for compressible flow without Riemann solvers
 

Please provide, the name of the algorithm or good paper for algorithms that avoid Reinamm solvers for flux calculation in FVM in compressible flows. Algorithms that can handle a variety of flow condition, stable (high CFL number), monotone, good convergence rate are preferred.
Thank you.

If you are focusing on compressible inviscid flows, where singularity can appear, I suggest to have a look to the book of Leveque about FVM for hyperbolic equations. You will find description and references of many hystorical and modern flux reconstructions.