Mass conservation


I have a general question regarding conservation of mass in LBM. I have been looking at high Reynolds number flows in corrugated channels. I keep a track of mass by summing over the density on all fluid nodes at each time step. Ideally, this number should remain constant throughout the computation. However, there are truncation errors in the computation of f and feq (distribution functions), and this would introduce some error in the total mass.

I look at the following quantity at each time step: (M-M0)/M0, where M is the mass at the some time t and M0 is the initial mass. This quantity turns out to be O(10^-6) to O(10^-5).
I am not sure how good this is. I use large domains like 2000*218, etc, and my mach number is 0.1, but I use small values of viscosity like 0.003, etc. I use second-order bounce back on walls and periodic conditions along the channel.

Could someone please throw some light on this?

Thanks and best wishes,