8.2.3 Lees and Edwards

[Lees+Edwards, J.Phys.C 5(1972)1921; Evans-Morriss Mol.Phys. 37(1979)1745; Comp.Phys.Rep. 1(1984)297]

Lees and Edwards suggested a method to combine laminary flow with periodic boundaries in the direction:

Here are in language-independent form, the appropriate code parts for PBC and NIC:

// Periodic boundary conditions:
// round(float) is the integer next to float
// L is the cell side length; note that x,y,z vary between -L/2 and L/2
// t is the elapsed time
// gamma is the shear rate

cz=round(z/L)
cx=x-cz*gamma*L*t
x=cx-round(x/L)*L
y=y-round(y/L)*L
z=z-cz*L
.....


// Nearest image convention:

delx=x(j)-x(i)
...
cz=round(dz/L)
cdelx=delx-cz*gamma*L*t
delx=cdelx-round(cdelx/L)*L
dely=dely-round(dely/L)*L
delz=delz-cz*L
...


This is the procedure for a single time step:
• Compute all forces, applying the nearest image convention
• Integrate the equs. of motion for
• Perform a least squares fit to a linear velocity profile, determining and such that
 (8.19)

where is the thermal velocity of the particle.
• Apply a simple thermostat by adjusting all such that
 (8.20)

• Compute the stress tensor element
 (8.21)

From the average stress we find :
 (8.22)

F. J. Vesely / University of Vienna