Quick question about including forces

Sukop states on page 54 that F = ma can be reduced to Delta U = tau*F/rho

I understand everything but tau. He says it’s because tau is the elementary time of collisions but I feel that the particle momenta is increased, due to F, by F dt where dt would be the time-step and not tau.

Someone mind shedding some light on this?

Dear ponja,

You are right about it. It needs Delta t, which is 1 in calculations. But it seems to me that Sukop originated the method of Shan-Chen to incorporate force. In that case if you change velocity as Delta U = tau*F/rho - you will restore proper momentum tensor upto the second order. So basically, they just adapt the method of Shan-Chen, and it’s not straightforwardly related to the F=ma.

Hopefully, it will help,