I find that the number of tracers is $2\times 1820^3$ in TNG100-1. Does it mean the number of galaxies here ?
And I also find that the number of gas particles is $1820^3$, the number of DM particles is $1820^3$. So the number of
total particles is $4\times 1820^3$, is that right?
"Tracers" are PartType3, they are just another type of particle. We usually don't include them in the count, so the total number of particles would be 2x1820^3 or, yes, if you include them, then 4x1820^3.
The number of galaxies is much smaller, ~50,000 for TNG100 and ~400,000 for TNG300, for example.
Are "tracers" used to tracing the evolution of the fluid with time ?
That's right, how they work is described in Genel+2013, and the first time they were used in an example application was Nelson+2013.
Thank you so much, Dylan.