Which collisioon model is best for high Re supercritical fluid?

My problem is considering the charge process of supercritical fluid into a vessel.
The Re is about 400,000.

I tested SRT, MRT and Smagorinsky model with SRT and MRT.
Only MRT Smagorinsky could give stable simulation result, but the accuracy is somewhat implausible. The different Omega values (adjusting time unit to reproduce the consistent physical viscosity) give different results.

Recently i have looked up a paper about comparison of collision operators for High Re flow such as central moment, cumulant, (recursive) regularized, kbc etc. but i am not sure which one is optimal (for my case and also in general) and implemented in Palabos.

In addition, isn’t any extra model (equation of state) required for supercritical fluid?

Have some idea?