testsuite: Check planar shear profile of LB

testsuite/CMakeLists.txt

@@ -165,6 +165,7 @@ python_test(FILE simple_pore.py MAX_NUM_PROC 1)
 python_test(FILE field_test.py MAX_NUM_PROC 1)
 python_test(FILE lb_boundary.py MAX_NUM_PROC 2)
 python_test(FILE lb_streaming.py MAX_NUM_PROC 4)
+python_test(FILE lb_shear.py MAX_NUM_PROC 2)
 
 if(PY_H5PY)
   python_test(FILE h5md.py MAX_NUM_PROC 2)

testsuite/lb_shear.py

@@ -0,0 +1,152 @@
+# Copyright (C) 2010-2018 The ESPResSo project
+#
+# This file is part of ESPResSo.
+#
+# ESPResSo is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# ESPResSo is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+import unittest as ut
+import numpy as np
+
+import espressomd.lb
+import espressomd.lbboundaries
+import espressomd.shapes
+
+"""
+Check the Lattice Boltzmann lid driven shear flow in a slab system
+by comparing to the analytical solution.
+
+"""
+
+
+AGRID = 0.5
+VISC = 1.4
+DENS = 2.3
+TIME_STEP = 0.01
+H = 30.
+SHEAR_RATE = 0.3
+
+LB_PARAMS = {'agrid': AGRID,
+             'dens': DENS,
+             'visc': VISC,
+             'fric': 1.0,
+             'tau': TIME_STEP}
+
+
+def shear_flow(x, t, nu, v, h, k_max):
+    """
+    Analytical solution for driven shear flow between two plates.
+
+    Parameters
+    ----------
+    x : :obj:`float`
+        Position from the left plane.
+    t : :obj:`float`
+        Time since start of the shearing.
+    nu : :obj:`float`
+        Kinematic viscosity.
+    v : :obj:`float`
+        Shear rate.
+    h : :obj:`float`
+        Distance between the plates.
+    k_max : :obj:`int`
+        Maximum considered wave number.
+
+    Returns
+    -------
+    :obj:`double` : Analytical velocity
+
+    """
+
+    u = x / h - 0.5
+    for k in np.arange(1, k_max + 1):
+        u += 1.0 / (np.pi * k) * np.exp(
+            -4 * np.pi ** 2 * nu * k ** 2 / h ** 2 * t) * np.sin(2 * np.pi / h * k * x)
+    return v * u
+
+
+class LBShearCommon(object):
+
+    """Base class of the test that holds the test logic."""
+    lbf = None
+    system = espressomd.System(box_l=[H + 2. * AGRID,
+                                      3.0,
+                                      3.0])
+    system.time_step = TIME_STEP
+    system.cell_system.skin = 0.4 * AGRID
+
+    def test_profile(self):
+        """
+        Integrate the LB fluid and regularly compare with
+        the exact solution.
+
+        """
+        self.system.lbboundaries.clear()
+        self.system.actors.clear()
+        self.system.actors.add(self.lbf)
+
+        wall_shape1 = espressomd.shapes.Wall(normal=[1, 0, 0], dist=AGRID)
+        wall_shape2 = espressomd.shapes.Wall(
+            normal=[-1, 0, 0], dist=-(self.system.box_l[0] - AGRID))
+        wall1 = espressomd.lbboundaries.LBBoundary(
+            shape=wall_shape1, velocity=[0, 0, -0.5 * SHEAR_RATE])
+        wall2 = espressomd.lbboundaries.LBBoundary(
+            shape=wall_shape2, velocity=[0, 0, +0.5 * SHEAR_RATE])
+
+        self.system.lbboundaries.add(wall1)
+        self.system.lbboundaries.add(wall2)
+
+        t0 = self.system.time
+        sample_points = int(H / AGRID)
+
+        for i in range(10):
+            self.system.integrator.run(100)
+
+            v_measured = np.zeros(sample_points)
+            x = np.zeros(sample_points)
+            for j in range(1, sample_points + 1):
+                v_measured[j - 1] = self.lbf[j, 1, 1].velocity[2]
+                x[j - 1] = (j - 1 + 0.5) * AGRID
+
+            v_expected = shear_flow(x=x,
+                                    t=self.system.time - t0,
+                                    nu=VISC,
+                                    v=SHEAR_RATE,
+                                    h=H,
+                                    k_max=100)
+
+            rmsd = np.sqrt(np.sum(np.square(v_expected - v_measured)))
+            self.assertLess(rmsd, 1.e-4 * AGRID / TIME_STEP)
+
+
+@ut.skipIf(not espressomd.has_features(
+    ['LB', 'LB_BOUNDARIES']), "Skipping test due to missing features.")
+class LBCPUShear(ut.TestCase, LBShearCommon):
+
+    """Test for the CPU implementation of the LB."""
+
+    def setUp(self):
+        self.lbf = espressomd.lb.LBFluid(**LB_PARAMS)
+
+
+@ut.skipIf(not espressomd.has_features(
+    ['LB_GPU', 'LB_BOUNDARIES_GPU']), "Skipping test due to missing features.")
+class LBGPUShear(ut.TestCase, LBShearCommon):
+
+    """Test for the GPU implementation of the LB."""
+
+    def setUp(self):
+        self.lbf = espressomd.lb.LBFluidGPU(**LB_PARAMS)
+
+
+if __name__ == '__main__':
+    ut.main()