# Incompressibility and high particle count simulation

Hello guys!

@Alex sorry for tagging you, but think I really need you to help out here.

I need some advice here. I am doing some simulation in a relative small domain, with a lot of particles, imagine 12 million particles in a rectangle of a volume of 1.125 m^3, so a very dense simulation. Because of this the simulation of course takes a large amount of time to run - the initial speed of the fluid is 0.8 m/s and I have made it so that cs0 = 24 m/s - this means that the maximum speed of a particle should be 2.4 m/s according to the Github wiki, (cs0 > 10 times larger than max particle speed), but now my question arises.

Due to the fact I need to simulate so many particles and I know that cs0 controls the solver speed, I have been quite aggressive and only given it a factor of 2 between initial (0.8 m/s) and theoretical max of a particle (2.4 m/s) - so about 50k particles have a speed of sound above this value, so this means that:

npFluid = 12e6

npAbove = 50e3

FracCs0 = npAbove/npFluid = 0.0042 = 0.42 %

So when 0.42 % of my particles are above this limit, I assume that for engineering purposes that the general solution would not differ too much from an ideal case?

Kind regards