From 3b2cecfe22bb9a7c1af64ca50d0bc60f16c0eee2 Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Mon, 3 Sep 2018 12:59:37 +0200
Subject: [PATCH] lbm phasefield improvements
- 1D benchmark scenario, trying different correction functions
- 2D neumann angle evaluation based on circle fitting
---
phasefield/analytical.py | 6 ++
phasefield/contact_angle_circle_fitting.py | 120 +++++++++++++++++++++
phasefield/phasefieldstep.py | 16 ++-
phasefield/scenarios.py | 1 +
4 files changed, 141 insertions(+), 2 deletions(-)
create mode 100644 phasefield/contact_angle_circle_fitting.py
diff --git a/phasefield/analytical.py b/phasefield/analytical.py
index 2a6ef6e4..2a3854e2 100644
--- a/phasefield/analytical.py
+++ b/phasefield/analytical.py
@@ -78,6 +78,12 @@ def free_energy_functional_n_phases_penalty_term(order_parameters, interface_wid
return bulk + interface + penalty_term_factor * bulk_penalty_term
+def n_phases_correction_function(c, beta, power=2):
+ return sp.Piecewise((-beta * c ** power, c < 0),
+ (-beta * (1 - c) ** 2, c > 1),
+ (c ** 2 * (1 - c) ** power, True))
+
+
def free_energy_functional_n_phases(num_phases=None, surface_tensions=symmetric_symbolic_surface_tension,
interface_width=interface_width_symbol, order_parameters=None,
include_bulk=True, include_interface=True, symbolic_lambda=False,
diff --git a/phasefield/contact_angle_circle_fitting.py b/phasefield/contact_angle_circle_fitting.py
new file mode 100644
index 00000000..fa70e220
--- /dev/null
+++ b/phasefield/contact_angle_circle_fitting.py
@@ -0,0 +1,120 @@
+from collections import namedtuple
+
+import numpy as np
+
+
+def circle_intersections(midpoint0, midpoint1, radius0, radius1):
+ """Returns intersection points of two circles."""
+ midpoint_distance = np.linalg.norm(midpoint0 - midpoint1)
+ x0, y0 = midpoint0
+ x1, y1 = midpoint1
+
+ k1 = (y0 - y1) / (x0 - x1) # slope for the line linking two centers
+ b1 = y1 - k1 * x1 # line equation of the line linking two centers
+
+ k2 = -1 / k1 # slope for the line linking two cross points
+ b2 = (radius0 ** 2 - radius1 ** 2 - x0 ** 2 + x1 ** 2 - y0 ** 2 + y1 ** 2) / (2 * (y1 - y0))
+
+ if midpoint_distance > (radius0 + radius1): # no intersection
+ return []
+
+ if np.abs(radius1 - radius0) == midpoint_distance or midpoint_distance == radius0 + radius1:
+ xx = -(b1 - b2) / (k1 - k2)
+ yy = -(-b2 * k1 + b1 * k2) / (k1 - k2)
+ return [(xx, yy)]
+ elif np.abs(radius1 - radius0) < midpoint_distance < radius0 + radius1:
+ xx1 = (-b2 * k2 + x1 + k2 * y1 - np.sqrt(-b2 ** 2 + radius1 ** 2 + k2 ** 2 * radius1 ** 2 - 2 * b2 *
+ k2 * x1 - k2 ** 2 * x1 ** 2 + 2 * b2 * y1 + 2 * k2 * x1 * y1 - y1 ** 2)) / (1 + k2 ** 2)
+ yy1 = k2 * xx1 + b2
+
+ xx2 = (-b2 * k2 + x1 + k2 * y1 + np.sqrt(-b2 ** 2 + radius1 ** 2 + k2 ** 2 * radius1 ** 2 - 2 * b2 *
+ k2 * x1 - k2 ** 2 * x1 ** 2 + 2 * b2 * y1 + 2 * k2 * x1 * y1 - y1 ** 2)) / (1 + k2 ** 2)
+ yy2 = k2 * xx2 + b2
+
+ return [(xx1, yy1), (xx2, yy2)]
+ else:
+ return []
+
+
+def interface_region(concentration_arr, phase0, phase1, area=3):
+ import scipy.ndimage as sc_image
+
+ area_phase0 = sc_image.morphology.binary_dilation(concentration_arr[..., phase0] > 0.5, iterations=area)
+ area_phase1 = sc_image.morphology.binary_dilation(concentration_arr[..., phase1] > 0.5, iterations=area)
+ return np.logical_and(area_phase0, area_phase1)
+
+
+def contour_line(concentration_arr, phase0, phase1, cutoff=0.05):
+ from skimage import measure
+ concentration_arr = concentration_arr.copy()
+
+ mask = interface_region(concentration_arr, phase0, phase1)
+ concentration_arr = concentration_arr[..., phase0]
+ concentration_arr[np.logical_not(mask)] = np.nan
+ contours = measure.find_contours(concentration_arr, 0.5)
+
+ contours = [c for c in contours if len(c) > 8]
+
+ if len(contours) != 1:
+ raise ValueError("Multiple or non contour lines (%d) found" % (len(contours),))
+
+ contour = contours[0]
+ absolute_cutoff = int(len(contour) * cutoff) + 1
+ return contour[absolute_cutoff:-absolute_cutoff]
+
+
+def fit_circle(points):
+ # see https://scipy-cookbook.readthedocs.io/items/Least_Squares_Circle.html
+ from scipy import optimize
+
+ def point_distances(xc, yc):
+ """ calculate the distance of each 2D points from the center (xc, yc) """
+ return np.sqrt((points[:, 0]-xc)**2 + (points[:, 1]-yc)**2)
+
+ def f(c):
+ """ calculate the algebraic distance between the data points and the mean circle centered at c=(xc, yc) """
+ ri = point_distances(*c)
+ return ri - ri.mean()
+
+ center_estimate = np.mean(points, axis=0)
+ center, _ = optimize.leastsq(f, center_estimate)
+ radius = point_distances(*center).mean()
+
+ circle = namedtuple('Circle', ['center', 'radius'])
+ return circle(center, radius)
+
+
+def neumann_angles_from_surface_tensions(surface_tensions):
+ g = surface_tensions
+ angles = [
+ np.arccos(-(g(0, 1) * g(0, 1) + g(0, 2) * g(0, 2) - g(1, 2) * g(1, 2)) / 2 / g(0, 1) / g(0, 2)),
+ np.arccos(-(g(0, 1) * g(0, 1) + g(1, 2) * g(1, 2) - g(0, 2) * g(0, 2)) / 2 / g(0, 1) / g(1, 2)),
+ np.arccos(-(g(1, 2) * g(1, 2) + g(0, 2) * g(0, 2) - g(0, 1) * g(0, 1)) / 2 / g(1, 2) / g(0, 2)),
+ ]
+ return [np.rad2deg(a) for a in angles]
+
+
+def liquid_lens_neumann_angles(concentration, drop_phase_idx=2, enclosing_phase1=0, enclosing_phase2=1):
+ circles = [fit_circle(contour_line(concentration, enclosing_phase1, drop_phase_idx)),
+ fit_circle(contour_line(concentration, enclosing_phase2, drop_phase_idx))]
+
+ intersections = circle_intersections(circles[0].center, circles[1].center, circles[0].radius, circles[1].radius)
+
+ y1, y2 = (i[1] for i in intersections)
+ assert np.abs(y1 - y2) < 0.1, "Liquid lens is not aligned in y direction (rotated?)"
+ y_horizontal = (y1 + y2) / 2
+
+ xs = np.sqrt(circles[0].radius ** 2 - (y_horizontal - circles[0].center[1]) ** 2)
+ angle = np.rad2deg(np.arctan(-xs / np.sqrt(circles[0].radius ** 2 - xs ** 2))) % 180
+ angle = 180 - angle
+ neumann3_upper = angle
+ neumann1 = 180 - neumann3_upper
+
+ xs = np.sqrt(circles[1].radius ** 2 - (y_horizontal - circles[1].center[1]) ** 2)
+ angle = np.rad2deg(np.arctan(-xs / np.sqrt(circles[1].radius ** 2 - xs ** 2))) % 180
+ angle = 180 - angle
+ neumann3_lower = angle
+ neumann2 = 180 - neumann3_lower
+
+ neumann3 = neumann3_upper + neumann3_lower
+ return neumann1, neumann2, neumann3
diff --git a/phasefield/phasefieldstep.py b/phasefield/phasefieldstep.py
index a5f48169..45a0fba8 100644
--- a/phasefield/phasefieldstep.py
+++ b/phasefield/phasefieldstep.py
@@ -169,7 +169,6 @@ class PhaseFieldStep:
if op == density_order_parameter:
continue
- print("CH Gamma", cahn_hilliard_gammas[i])
ch_method = cahn_hilliard_lb_method(self.hydro_lbm_step.method.stencil, self.mu_field(i),
relaxation_rate=cahn_hilliard_relaxation_rates[i],
gamma=cahn_hilliard_gammas[i])
@@ -295,8 +294,21 @@ class PhaseFieldStep:
return self._get_slice(self.phi_field_name, slice_obj)
def concentration_slice(self, slice_obj=None):
+ if slice_obj is not None and len(slice_obj) > self.data_handling.dim:
+ assert len(slice_obj) - 1 == self.data_handling.dim
+ last_index = slice_obj[-1]
+ slice_obj = slice_obj[:-1]
+ else:
+ last_index = None
+
phi = self.phi_slice(slice_obj)
- return phi if self.order_parameters_to_concentrations is None else self.order_parameters_to_concentrations(phi)
+ if self.order_parameters_to_concentrations is None:
+ return phi
+ else:
+ result = self.order_parameters_to_concentrations(phi)
+ if last_index is not None:
+ result = result[..., last_index]
+ return result
def mu_slice(self, slice_obj=None):
return self._get_slice(self.mu_field_name, slice_obj)
diff --git a/phasefield/scenarios.py b/phasefield/scenarios.py
index 851446d1..807970ea 100644
--- a/phasefield/scenarios.py
+++ b/phasefield/scenarios.py
@@ -36,6 +36,7 @@ def create_three_phase_model(alpha=1, kappa=(0.015, 0.015, 0.015), include_rho=T
return PhaseFieldStep(free_energy, order_parameters, density_order_parameter=None,
transformation_matrix=transformation_matrix,
order_parameters_to_concentrations=order_parameters_to_concentrations,
+ cahn_hilliard_gammas=[1, 1, 1 / 3],
**kwargs)
--
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