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Jigyasa Watwani / growth-pattern-control

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Commit fa0f1d88 by Jigyasa Watwani
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2D, 3D analytical solution for all growth models with specified initial condition

parents 82b94e80 2c482e06
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Showing with 42 additions and 65 deletions
growing_domain/diffusion_on_growing_domain.py
import dolfin as df import dolfin as df
import mshr as ms
import numpy as np import numpy as np
import progressbar import progressbar
import os import os
import meshzoo
df.set_log_level(df.LogLevel.ERROR) df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True df.parameters['form_compiler']['optimize'] = True
...@@ -12,40 +12,27 @@ class GrowthDiffusion(object): ...@@ -12,40 +12,27 @@ class GrowthDiffusion(object):
# read in parameters # read in parameters
for key in parameters: for key in parameters:
setattr(self, key, parameters[key]) setattr(self, key, parameters[key])
sigma = {'none': '0.0',
'linear': 'b/(L0+b*t)',
'exponential': 'b'}
# define the growth velocity field
growth_direction = tuple(['x['+str(i)+']' for i in range(self.dimension)])
#growth_direction = ('x[0]', )
self.growth_direction = df.Expression(growth_direction, degree=1)
self.sigma = df.Expression(sigma[self.growth],
L0=self.system_size,
b=self.growth_parameter,
t=0, degree=1)
# set up mesh # set up mesh
# and define the growth velocity field
if self.dimension==1: if self.dimension==1:
if self.growth=='none':
self.velocity = df.Expression(('s*x[0]',), s=df.Constant(0), t=0, degree=0)
if self.growth == 'linear':
self.velocity = df.Expression(('b*x[0]/(L0 + b*t)',), b = self.growth_parameter, L0=self.system_size, t=0, degree=0)
if self.growth=='exponential':
self.velocity = df.Expression(('s*x[0]'), s=df.Constant(self.growth_parameter), t=0, degree=0)
self.mesh = df.IntervalMesh(self.resolution, 0, self.system_size) self.mesh = df.IntervalMesh(self.resolution, 0, self.system_size)
elif self.dimension==2:
elif self.dimension==2: geometry = ms.Circle(df.Point(0, 0), self.system_size)
if self.growth=='none': self.mesh = ms.generate_mesh(geometry, self.resolution)
self.velocity = df.Expression(('s*x[0]','s*x[1]'), s=df.Constant(0), t=0, degree=0) elif self.dimension==3:
if self.growth == 'linear': geometry = ms.Sphere(df.Point(0, 0, 0), self.system_size)
self.velocity = df.Expression(('b*x[0]/(L0 + b*t)','b*x[1]/(L0 + b*t)'), b = self.growth_parameter, L0=self.system_size, t=0, degree=0) self.mesh = ms.generate_mesh(geometry, self.resolution)
if self.growth=='exponential':
self.velocity = df.Expression(('s*x[0]', 's*x[1]'), s=df.Constant(self.growth_parameter), t=0, degree=0)
points, cells = meshzoo.disk(self.resolution, 2*self.resolution)
points *= self.system_size
self.mesh = df.Mesh()
e = df.MeshEditor()
e.open(self.mesh, type='triangle', tdim=2, gdim=2)
e.init_vertices(len(points))
e.init_cells(len(cells))
for n in range(len(points)):
e.add_vertex(n, [points[n, 0], points[n, 1]])
for n in range(len(cells)):
e.add_cell(n, cells[n])
e.close()
# create mesh, function space, define function, test function # create mesh, function space, define function, test function
self.SFS = df.FunctionSpace(self.mesh, 'P', 1) self.SFS = df.FunctionSpace(self.mesh, 'P', 1)
...@@ -54,69 +41,59 @@ class GrowthDiffusion(object): ...@@ -54,69 +41,59 @@ class GrowthDiffusion(object):
self.c0 = df.Function(self.SFS) self.c0 = df.Function(self.SFS)
tc = df.TestFunction(self.SFS) tc = df.TestFunction(self.SFS)
# self.velocity.t = 0 self.velocity = df.project(self.sigma * self.growth_direction, self.VFS)
self.vel = df.project(self.velocity, self.VFS)
self.form = ( df.inner((self.c-self.c0)/self.timestep, tc) self.form = ( df.inner((self.c-self.c0)/self.timestep, tc)
+ df.inner(df.div(self.vel*self.c0), tc) + df.inner(df.div(self.velocity*self.c0), tc)
+ self.Dc * df.inner(df.nabla_grad(self.c), df.nabla_grad(tc)) + self.Dc * df.inner(df.nabla_grad(self.c), df.nabla_grad(tc))
- df.inner(self.reaction_rate * self.c, tc) ) * df.dx - df.inner(self.reaction_rate * self.c, tc) ) * df.dx
def solve(self): def solve(self):
times = np.arange(0, self.maxtime+self.timestep, self.timestep) times = np.arange(0, self.maxtime+self.timestep, self.timestep)
if self.growth =='linear': fname = params['timestamp'] + '_concentration'
cFile = df.XDMFFile('concentration_linear.xdmf') cFile = df.XDMFFile(fname+ '.xdmf')
elif self.growth == 'exponential':
cFile = df.XDMFFile('concentration_exponential.xdmf')
elif self.growth == 'none':
cFile = df.XDMFFile('concentration_no_growth.xdmf')
# initial condition # initial condition
if self.dimension==1: r2 = "+".join(['x['+str(i)+']*x['+str(i)+']' for i in range(self.dimension)])
c0 = df.Expression('1 + 0.1*cos(pi*m*x[0]/L)', c0 = '1 + 0.1*cos(pi*m*(%s)/L)' % r2
pi=np.pi, m=1, L=self.system_size, degree=1) c0 = df.Expression(c0, pi=np.pi, m=1, L=self.system_size, degree=1)
elif self.dimension==2:
c0 = df.Expression('1 + 0.1*cos(pi*m*sqrt(x[0]*x[0]+x[1]*x[1])/L)',
pi=np.pi, m=2, L=self.system_size, degree=1)
self.c0.assign(df.project(c0, self.SFS)) self.c0.assign(df.project(c0, self.SFS))
# save data # save data
if self.growth=='linear': cFile.write_checkpoint(self.c0, fname, times[0])
cFile.write_checkpoint(self.c0, 'concentration_linear', 0.0)
elif self.growth=='exponential':
cFile.write_checkpoint(self.c0, 'concentration_exponential', 0.0)
elif self.growth == 'none':
cFile.write_checkpoint(self.c0, 'concentration_no_growth', 0.0)
# time stepping # time stepping
for i in progressbar.progressbar(range(1, len(times))): for i in progressbar.progressbar(range(1, len(times))):
# get velocity # get velocity
self.velocity.t = times[i-1] self.sigma.t = times[i-1]
self.vel.assign(df.project(self.velocity, self.VFS)) self.velocity.assign(df.project(self.sigma*self.growth_direction, self.VFS))
# solve # solve
df.solve(self.form == 0, self.c) df.solve(self.form == 0, self.c)
# update # update
self.c0.assign(self.c) self.c0.assign(self.c)
# save data # save data
if self.growth=='linear': cFile.write_checkpoint(self.c0, fname, times[i], append=True)
cFile.write_checkpoint(self.c0, 'concentration_linear', times[i], append=True)
elif self.growth =='exponential':
cFile.write_checkpoint(self.c0, 'concentration_exponential', times[i], append=True)
elif self.growth == 'none':
cFile.write_checkpoint(self.c0, 'concentration_no_growth', times[i], append=True)
# move mesh # move mesh
displacement = df.project(self.vel*self.timestep, self.VFS) displacement = df.project(self.velocity*self.timestep, self.VFS)
df.ALE.move(self.mesh, displacement) df.ALE.move(self.mesh, displacement)
cFile.close() cFile.close()
if __name__ == '__main__': if __name__ == '__main__':
import json import json, datetime
assert os.path.isfile('parameters.json'), 'parameters.json file not found' assert os.path.isfile('parameters.json'), 'parameters.json file not found'
with open('parameters.json') as jsonFile: with open('parameters.json') as jsonFile:
params = json.load(jsonFile) params = json.load(jsonFile)
# parse parameters # parse parameters
assert params['growth'] in ('none', 'linear', 'exponential'), 'Unknown growth model' assert params['dimension'] in (1,2,3)
assert params['growth'] in ('none','linear','exponential'), 'Unknown growth model'
timestamp = datetime.datetime.now().strftime("%d%m%y-%H%M%S")
params['timestamp'] = timestamp
gd = GrowthDiffusion(params) gd = GrowthDiffusion(params)
gd.solve() gd.solve()
\ No newline at end of file
with open(params['timestamp'] + '_parmeters.json', "w") as fp:
json.dump(params, fp, indent=4)
\ No newline at end of file
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