Consistency law at Lattice Boltzmann

I am a student PhD at this moment I work with palabos for modeling a channel rectangular tridimensional, whose initial condition is V=0cm/s, and affected for a force. I used a model D3Q19, and did several cases.

My question is, when I modified resolution number’s without changed my problem physical (physical velocity, Reynolds number and characteristic length) my velocity profile changed.

According to consistency of problem, this doesn’t must change the solution because I would to change the resolution number, but that the effect of this change is increasing accuracy.

Please community someone can tell me why do it happen this, or where can I found literature about of this topic.

Thank you