Dear all

My question is related to the four-roll mill flow, a simple periodic flow with no-inertial terms. This is flow can be found in the phd thesis of Orestis Malaspinas.

This flow was solver by Orestis Malaspinas for both Newtonian and non-Newtonian fluids. I am exclusively interested in the Newtonian case.

I was already able to implement the flow with LB, which is very simple since boundary conditions are periodic and the eq. distribution function has only linear terms.

Although the numerical solution is qualitatively identical to the analytical one the two are quantitatively distinct by a scale factor. This suggests me that my conversion of units t(from physical to lattice space) is not right.

My problem is that this flow has no inertial terms. A flow with no inertial terms has zero Reynolds number! So I cannot relate the velocity with a spatial length scale and the kinematic viscosity! Is there any non-dimensional parameter that I am missing? This flow must be governed by some non-dimensional number.

What I find strange is that if I apply a standard non-dimensional analysis to the momentum eq. of my problem: gx+1/Re*(d^2(u)/dx^2+d^2(u)/dy^2) and gx+1/Re*(d^2(v)/dx^2+d^2(v)/dy^2)=0, i.e. I find that the diffusive term must be weighted by the inverse of the Reynolds number. But by definition Re=0! Therefore I must be mistaken some definition in the physical parameters! Because when I related this analysis to the analytical solution of the flow I obtain mismatching resulting.

u_analy= sin(x)*cos(y)

v_analy= -cos(x)*sin(y)

gx= 2*niu*sin(x)*cos(y)
gy= -2*niu*cos(x)*sin(y)

Any hints or suggestions will be very much welcomed and appreciated

Thanks in advance.

Goncalo