def test_stokes(self):
# System setup
agrid = 1
radius = 5.5
box_width = 54
real_width = box_width + 2 * agrid
box_length = 54
system = espressomd.System(box_l=[real_width, real_width, box_length])
system.box_l = [real_width, real_width, box_length]
system.time_step = 0.4
system.cell_system.skin = 0.4
# The temperature is zero.
system.thermostat.set_lb(kT=0)
# LB Parameters
v = [0, 0, 0.01] # The boundary slip
kinematic_visc = 5.0
# Invoke LB fluid
lbf = lb.LBFluidGPU(visc=kinematic_visc,
dens=1,
agrid=agrid,
tau=system.time_step,
fric=1)
system.actors.add(lbf)
# Setup walls
walls = [None] * 4
walls[0] = lbboundaries.LBBoundary(shape=shapes.Wall(
normal=[-1, 0, 0], dist=-(1 + box_width)),
velocity=v)
walls[1] = lbboundaries.LBBoundary(shape=shapes.Wall(normal=[1, 0, 0],
dist=1),
velocity=v)
walls[2] = lbboundaries.LBBoundary(shape=shapes.Wall(
normal=[0, -1, 0], dist=-(1 + box_width)),
velocity=v)
walls[3] = lbboundaries.LBBoundary(shape=shapes.Wall(normal=[0, 1, 0],
dist=1),
velocity=v)
for wall in walls:
system.lbboundaries.add(wall)
# setup sphere without slip in the middle
sphere = lbboundaries.LBBoundary(
shape=shapes.Sphere(radius=radius,
center=[real_width / 2] * 2 + [box_length / 2],
direction=1))
system.lbboundaries.add(sphere)
def size(vector):
tmp = 0
for k in vector:
tmp += k * k
return np.sqrt(tmp)
system.integrator.run(800)
stokes_force = 6 * np.pi * kinematic_visc * radius * size(v)
print("Stokes' Law says: f=%f" % stokes_force)
# get force that is exerted on the sphere
for i in range(5):
system.integrator.run(200)
force = sphere.get_force()
print("Measured force: f=%f" % size(force))
self.assertLess(abs(1.0 - size(force) / stokes_force), 0.06)
## A script to simulate planar Poisseuille flow in Espresso
from espressomd import lb, shapes, lbboundaries
import numpy as np
# System setup
system = espressomd.System(box_l=[1.0, 1.0, 1.0])
system.time_step = 0.01
system.cell_system.skin = 0.2
box_l = 16
system.box_l = [box_l] * 3
lbf = lb.LBFluidGPU(agrid=1, dens=1, visc=1, tau=0.01, ext_force=[0, 0.001, 0])
system.actors.add(lbf)
system.thermostat.set_lb(kT=0)
# Setup boundaries
walls = [lbboundaries.LBBoundary() for k in range(2)]
walls[0].set_params(shape=shapes.Wall(normal=[1,0,0], dist = 1.5))
walls[1].set_params(shape=shapes.Wall(normal=[-1,0,0], dist = -14.5))
for wall in walls:
system.lbboundaries.add(wall)
## Perform enough iterations until the flow profile
## is static (5000 LB updates):
system.integrator.run(5000)
## Part of the solution
