hasattr(expr, 't1') and setattr(expr, 't1', time)
hasattr(expr, 't2') and setattr(expr, 't2', time+fluid_parameters['dt'])
# Solve fluid problem
uf_, pf_ = solve_fluid(Wf, f=Constant((0, 0)), u_n=uf_n, p_n=pf_n, bdries=fluid_bdries, bcs=bcs_fluid,
parameters=fluid_parameters)
# Update current solution
uf_n.assign(uf_)
pf_n.assign(pf_)
# Solve ALE
# compute the displacement
#ale_u_bottom=Expression((UALE_vessel,'0'), t1 = time, t2=time+dt, degree=2)
eta_f = solve_ale(Va, f=Constant((0, 0)), bdries=fluid_bdries, bcs=bcs_ale,
parameters=ale_parameters)
# Move domains
ALE.move(mesh_f, eta_f)
# Save output
if(timestep % int(Toutput/fluid_parameters['dt']) == 0):
eta_f.rename("eta_f", "tmp")
etaf_out << (eta_f, time)
uf_.rename("uf", "tmp")
pf_.rename("pf", "tmp")
uf_out << (uf_, time)
def PVS_simulation(args):
""" Solve the flow and tracer transport in the PVS :
Outputs :
- a logfile with information about the simulation
- .pvd files with the u, p and c field at specified args.toutput time period
Return : u, p, c 1D array of the u, p, c fields on the middle line """
# output folder name
outputfolder=args.output_folder+'/'+args.job_name+'/'
if not os.path.exists(outputfolder):
os.makedirs(outputfolder)
if not os.path.exists(outputfolder+'/profiles'):
os.makedirs(outputfolder+'/profiles')
if not os.path.exists(outputfolder+'/fields'):
os.makedirs(outputfolder+'/fields')
# Create output files
#txt files
csv_p=open(outputfolder+'profiles'+'/pressure.txt', 'w')
csv_u=open(outputfolder+'profiles'+'/velocity.txt', 'w')
csv_c=open(outputfolder+'profiles'+'/concentration.txt', 'w')
csv_rv=open(outputfolder+'profiles'+'/radius.txt', 'w')
#pvd files
uf_out, pf_out= File(outputfolder+'fields'+'/uf.pvd'), File(outputfolder+'fields'+'/pf.pvd')
c_out= File(outputfolder+'fields'+'/c.pvd')
facets_out=File(outputfolder+'fields'+'/facets.pvd')
# Create logger
logger = logging.getLogger()
logger.setLevel(logging.INFO)
# log to a file
now = datetime.now().strftime("%Y%m%d_%H%M%S")
filename = os.path.join(outputfolder+'/', 'PVS_info.log')
file_handler = logging.FileHandler(filename,mode='w')
file_handler.setLevel(logging.INFO)
#formatter = logging.Formatter("%(asctime)s %(filename)s, %(lineno)d, %(funcName)s: %(message)s")
#file_handler.setFormatter(formatter)
logger.addHandler(file_handler)
# log to the console
console_handler = logging.StreamHandler()
level = logging.INFO
console_handler.setLevel(level)
logger.addHandler(console_handler)
# initialise logging
logging.info(title1("Simulation of the PVS flow and tracer transport using non steady solver and diffusion-advection solvers"))
logging.info("Date and time:"+datetime.now().strftime("%m/%d/%Y, %H:%M:%S"))
logging.info('Job name : '+args.job_name)
logging.debug('logging initialized')
# Set parameters
logging.info(title1("Parameters"))
# Geometry params
logging.info('\n * Geometry')
Rv = args.radius_vessel # centimeters
Rpvs =args.radius_pvs # centimeters
L = args.length # centimeters
logging.info('Vessel radius : %e cm'%Rv)
logging.info('PVS radius : %e cm'%Rpvs)
logging.info('PVS length : %e cm'%L)
#Mesh
logging.info('\n * Mesh')
#number of cells in the radial direction
Nr=args.N_radial
DR=(Rpvs-Rv)/Nr
#number of cells in the axial direction
if args.N_axial :
Nl=args.N_axial
else :
Nl=round(L/DR)
DY=L/Nl
logging.info('N axial : %i'%Nl)
logging.info('N radial : %e'%Nr)
#time parameters
logging.info('\n * Time')
toutput=args.toutput
tfinal=args.tend
dt=args.time_step
logging.info('final time: %e s'%tfinal)
logging.info('output period : %e s'%toutput)
logging.info('time step : %e s'%dt)
# approximate CFL for fluid solver : need to compute max velocity depending on the wall displacement...
# maybe just add a warning in computation with actual velocity
#Uapprox=500e-4 #upper limit for extected max velocity
#CFL_dt=0.25*DY/Uapprox
#if CFL_dt < dt :
# logging.warning('The specified time step of %.2e s does not fullfil the fluid CFL condition. New fluid time step : %.2e s'%(dt, CFL_dt))
#dt_fluid=min(dt,CFL_dt)
dt_fluid=dt
# approximate CFL for tracer solver
dt_advdiff=dt
# material parameters
logging.info('\n * Fluid properties')
mu=args.viscosity
rho=args.density
logging.info('density: %e g/cm3'%rho)
logging.info('dynamic viscosity : %e dyn s/cm2'%mu)
logging.info('\n* Tracer properties')
D=args.diffusion_coef
sigma_gauss=args.sigma
logging.info('Free diffusion coef: %e cm2/s'%D)
logging.info('STD of initial gaussian profile: %e '%sigma_gauss)
xi_gauss=args.initial_pos
logging.info('Initial position: %e cm2'%xi_gauss)
logging.info('\n * ALE')
kappa=args.ale_parameter
logging.info('ALE parameter: %e '%kappa)
logging.info('\n * Lateral BC')
resistance=args.resistance
logging.info('inner resistance: %e '%resistance)
if resistance == 0 :
lateral_bc='free'
logging.info('right BC will be set to the free assumption')
elif resistance < 0 :
lateral_bc='noflow'
logging.info('right BC will be set to the no flow assumption')
else :
lateral_bc='resistance'
logging.info('right BC will be set to the resistance assumption')
fluid_parameters = {'mu': mu, 'rho': rho, 'dt':dt_fluid}
tracer_parameters={'kappa': D, 'dt':dt_advdiff}
ale_parameters = {'kappa': kappa}
# Mesh
logging.info(title1('Meshing'))
logging.info('cell size : %e cm'%(np.sqrt(DR**2+DY**2)))
logging.info('nb cells: %i'%(Nl*Nr*2))
mesh_f= RectangleMesh(Point(0, Rv), Point(L, Rpvs), Nl, Nr)
fluid_bdries = MeshFunction("size_t", mesh_f, mesh_f.topology().dim()-1,0)
# Label facets
xy = mesh_f.coordinates().copy()
x, y = xy.T
xmin=x.min()
xmax=x.max()
ymin=y.min()
ymax=y.max()
tol=min(DR,DY)/2 #cm
class Boundary_left(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[0],xmin,tol) #left
class Boundary_right(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[0],xmax,tol)# right
class Boundary_bottom(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[1], ymin,tol) #bottom
class Boundary_top(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[1], ymax,tol) #top
btop= Boundary_top()
bbottom = Boundary_bottom()
bleft = Boundary_left()
bright = Boundary_right()
bbottom.mark(fluid_bdries, 2)
btop.mark(fluid_bdries, 4)
bleft.mark(fluid_bdries, 1)
bright.mark(fluid_bdries, 3)
facet_lookup = {'x_min': 1 ,'y_min': 2, 'x_max': 3, 'y_max': 4}
facets_out << fluid_bdries
#FEM space
logging.info(title1("Set FEM spaces"))
logging.info('\n * Fluid')
Vf_elm = VectorElement('Lagrange', triangle, 2)
Qf_elm = FiniteElement('Lagrange', triangle, 1)
Wf_elm = MixedElement([Vf_elm, Qf_elm])
Wf = FunctionSpace(mesh_f, Wf_elm)
logging.info('Velocity : "Lagrange", triangle, 2')
logging.info('Pressure : "Lagrange", triangle, 1')
logging.info('\n * Tracer')
Ct_elm = FiniteElement('Lagrange', triangle, 1)
Ct = FunctionSpace(mesh_f, Ct_elm)
logging.info('Concentration : "Lagrange", triangle, 1')
logging.info('\n * ALE')
Va_elm = VectorElement('Lagrange', triangle, 1)
Va = FunctionSpace(mesh_f, Va_elm)
logging.info('ALE displacement: "Lagrange", triangle, 1')
# Setup of boundary conditions
logging.info(title1("Boundary conditions"))
import sympy
tn = sympy.symbols("tn")
tnp1 = sympy.symbols("tnp1")
sin = sympy.sin
sqrt = sympy.sqrt
logging.info('\n * Cross section area parameters')
ai=args.ai
fi=args.fi
phii=args.phii
logging.info('ai (dimensionless): '+'%e '*len(ai)%tuple(ai))
logging.info('fi (Hz) : '+'%e '*len(fi)%tuple(fi))
logging.info('phii (rad) : '+'%e '*len(phii)%tuple(phii))
functionR = Rpvs-(Rpvs-Rv)*(1+sum([a*sin(2*pi*f*tn+phi) for a,f,phi in zip(ai,fi,phii)])) # displacement
R_vessel = sympy.printing.ccode(functionR)
functionV = sympy.diff(functionR,tn) # velocity
V_vessel = sympy.printing.ccode(functionV)
#Delta U for ALE. I dont really like this
functionUALE=-(Rpvs-Rv)*(1+sum([a*sin(2*pi*f*tnp1+phi) for a,f,phi in zip(ai,fi,phii)]))+(Rpvs-Rv)*(1+sum([a*sin(2*pi*f*tn+phi) for a,f,phi in zip(ai,fi,phii)]))
UALE_vessel = sympy.printing.ccode(functionUALE)
vf_bottom = Expression(('0',V_vessel ), tn = 0, degree=2) # no slip no gap condition at vessel wall
uale_bottom = Expression(('0',UALE_vessel ), tn = 0, tnp1=1, degree=2) # displacement for ALE at vessel wall
logging.info('\n * Lateral assumption')
logging.info(lateral_bc)
logging.info('\n * Fluid')
logging.info('Left : zero pressure')
if lateral_bc=='free' :
logging.info('Right : zero pressure')
elif lateral_bc=='resistance' :
logging.info('Right : resistance')
else :
logging.info('Right : no flow')
logging.info('Top : no slip no gap fixed wall')
logging.info('Bottom : no slip no gap moving wall')
logging.info('\n * Tracer concentration')
logging.info('Left : zero concentration')
if lateral_bc=='free' :
logging.info('Right : zero concentration')
else :
logging.info('Right : no flux')
logging.info('Top : no flux')
logging.info('Bottom : no flux')
logging.info('\n * ALE')
logging.info('Left : no flux')
logging.info('Right : no flux')
logging.info('Top : no displacement')
logging.info('Bottom : vessel displacement')
# Now we wire up
if lateral_bc=='free' :
bcs_fluid = {'velocity': [(facet_lookup['y_min'],vf_bottom),
(facet_lookup['y_max'], Constant((0,0)))],
'traction': [],
'pressure': [(facet_lookup['x_min'], Constant(0)),
(facet_lookup['x_max'], Constant(0))]}
elif lateral_bc=='resistance' :
Rpressure=Expression('R*Q+p0', R = resistance, Q=0, p0=0, degree=1) #
# Compute pressure to impose according to the flow at previous time step and resistance.
bcs_fluid = {'velocity': [(facet_lookup['y_min'],vf_bottom),
(facet_lookup['y_max'], Constant((0,0)))],
'traction': [],
'pressure': [(facet_lookup['x_min'], Constant(0)),
(facet_lookup['x_max'], Rpressure)]}
else :
bcs_fluid = {'velocity': [(facet_lookup['y_min'],vf_bottom),
(facet_lookup['y_max'], Constant((0,0))),
(facet_lookup['x_max'], Constant((0,0)))], # I would like only normal flow to be zero
'traction': [],
'pressure': [(facet_lookup['x_min'], Constant(0))]}
if lateral_bc=='free' :
bcs_tracer = {'concentration': [(facet_lookup['x_max'], Constant(0)),
(facet_lookup['x_min'], Constant(0))],
'flux': [(facet_lookup['y_max'], Constant(0)),
(facet_lookup['y_min'], Constant(0))]}
else :
bcs_tracer = {'concentration': [(facet_lookup['x_min'], Constant(0))],
'flux': [(facet_lookup['x_max'], Constant(0)),
(facet_lookup['y_max'], Constant(0)),
(facet_lookup['y_min'], Constant(0))]}
bcs_ale = {'dirichlet': [(facet_lookup['y_min'], uale_bottom),
(facet_lookup['y_max'], Constant((0, 0)))],
'neumann': [(facet_lookup['x_min'], Constant((0, 0))),
(facet_lookup['x_max'], Constant((0, 0)))]}
# We collect the time dependent BC for update
driving_expressions = (uale_bottom,vf_bottom)
# Initialisation :
logging.info(title1("Initialisation"))
logging.info("\n * Fluid")
logging.info("Velocity : zero field")
logging.info("Pressure : zero field")
uf_n = project(Constant((0, 0)), Wf.sub(0).collapse())
pf_n = project(Constant(0), Wf.sub(1).collapse())
logging.info("\n * Tracer")
logging.info("Concentration : Gaussian profile")
logging.info(" Centered at mid length")
logging.info(" STD parameter = %e"%sigma_gauss)
c_0 = Expression('exp(-a*pow(x[0]-b, 2)) ', degree=1, a=1/2/sigma_gauss**2, b=xi_gauss)
c_n = project(c_0,Ct)
# Save initial state
uf_n.rename("uf", "tmp")
pf_n.rename("pf", "tmp")
c_n.rename("c", "tmp")
uf_out << (uf_n, 0)
pf_out << (pf_n, 0)
c_out << (c_n, 0)
files=[csv_p,csv_u,csv_c]
fields=[pf_n,uf_n.sub(0),c_n]
slice_line = line([0,(Rpvs+Rv)/2],[L,(Rpvs+Rv)/2], 100)
for csv_file,field in zip(files,fields) :
#print the x scale
values=np.linspace(0,L,100)
row=[0]+list(values)
csv_file.write(('%e'+', %e'*len(values)+'\n')%tuple(row))
#print the initial 1D slice
values = line_sample(slice_line, field)
row=[0]+list(values)
csv_file.write(('%e'+', %e'*len(values)+'\n')%tuple(row))
############# RUN ############3
logging.info(title1("Run"))
# Time loop
time = 0.
timestep=0
# Here I dont know if there will be several dt for advdiff and fluid solver
while time < tfinal:
# Update boundary conditions
for expr in driving_expressions:
hasattr(expr, 'tn') and setattr(expr, 'tn', time)
hasattr(expr, 'tnp1') and setattr(expr, 'tnp1', time+dt)
if lateral_bc=='resistance' :
z, r = SpatialCoordinate(mesh_f)
ds = Measure('ds', domain=mesh_f, subdomain_data=fluid_bdries)
n = FacetNormal(mesh_f)
Flow=assemble(2*pi*r*dot(uf_n, n)*ds(facet_lookup['x_max']))
print('Right outflow : %e \n'%Flow)
setattr(Rpressure, 'Q', Flow)
#Solve ALE and move mesh
eta_f = solve_ale(Va, f=Constant((0, 0)), bdries=fluid_bdries, bcs=bcs_ale,
parameters=ale_parameters)
ALE.move(mesh_f, eta_f)
mesh_f.bounding_box_tree().build(mesh_f)
# Solve fluid problem
uf_, pf_ = solve_fluid(Wf, u_0=uf_n, f=Constant((0, 0)), bdries=fluid_bdries, bcs=bcs_fluid,
parameters=fluid_parameters)
tracer_parameters["T0"]=time
tracer_parameters["nsteps"]=1
tracer_parameters["dt"]=dt
# Solve tracer problem
c_, T0= solve_adv_diff(Ct, velocity=uf_-eta_f/Constant(dt), phi=Constant(1), f=Constant(0), c_0=c_n, phi_0=Constant(1),
bdries=fluid_bdries, bcs=bcs_tracer, parameters=tracer_parameters)
# Update current solution
uf_n.assign(uf_)
pf_n.assign(pf_)
c_n.assign(c_)
#Update time
time += dt
timestep+=1
# Save output
if(timestep % int(toutput/dt) == 0):
logging.info("\n*** save output time %e s"%time)
logging.info("number of time steps %i"%timestep)
# may report Courant number or other important values that indicate how is doing the run
uf_.rename("uf", "tmp")
pf_.rename("pf", "tmp")
c_.rename("c", "tmp")
uf_out << (uf_, time)
pf_out << (pf_, time)
c_out << (c_, time)
# Get the 1 D profiles at umax (to be changed in cyl coordinate)
mesh_points=mesh_f.coordinates()
x=mesh_points[:,0]
y=mesh_points[:,1]
xmin=min(x)
xmax=max(x)
ymin=min(y)
ymax=max(y)
#slice_line = line([xmin,(ymin+ymax)/2],[xmax,(ymin+ymax)/2], 100)
logging.info('Rpvs : %e'%ymax)
logging.info('Rvn : %e'%ymin)
files=[csv_p,csv_u,csv_c]
fields=[pf_n,uf_n.sub(0),c_n]
field_names=['pressure (dyn/cm2)','axial velocity (cm/s)','concentration']
for csv_file,field,name in zip(files,fields,field_names) :
#values = line_sample(slice_line, field)
values =profile(field,xmin,xmax,ymin,ymax)
logging.info('Max '+name+' : %.2e'%max(abs(values)))
#logging.info('Norm '+name+' : %.2e'%field.vector().norm('linf'))
row=[time]+list(values)
csv_file.write(('%e'+', %e'*len(values)+'\n')%tuple(row))
csv_rv.write('%e, %e\n'%(time,ymin))
def PVS_simulation(args):
""" Solve the flow and tracer transport in the PVS, assumption flat plates :
Outputs :
- a logfile with information about the simulation
- .pvd files with the u, p and c field at specified args.toutput time period
Return : u, p, c 1D array of the u, p, c fields on the middle line """
# output folder name
outputfolder = args.output_folder + '/' + args.job_name + '/'
if not os.path.exists(outputfolder):
os.makedirs(outputfolder)
if not os.path.exists(outputfolder + '/profiles'):
os.makedirs(outputfolder + '/profiles')
if not os.path.exists(outputfolder + '/fields'):
os.makedirs(outputfolder + '/fields')
# Create output files
#txt files
csv_p = open(outputfolder + 'profiles' + '/pressure.txt', 'w')
csv_u = open(outputfolder + 'profiles' + '/velocity.txt', 'w')
csv_c = open(outputfolder + 'profiles' + '/concentration.txt', 'w')
csv_rv = open(outputfolder + 'profiles' + '/radius.txt', 'w')
#pvd files
uf_out, pf_out = File(outputfolder + 'fields' +
'/uf.pvd'), File(outputfolder + 'fields' + '/pf.pvd')
c_out = File(outputfolder + 'fields' + '/c.pvd')
facets_out = File(outputfolder + 'fields' + '/facets.pvd')
# Create logger
logger = logging.getLogger()
logger.setLevel(logging.INFO)
# log to a file
now = datetime.now().strftime("%Y%m%d_%H%M%S")
filename = os.path.join(outputfolder + '/', 'PVS_info.log')
file_handler = logging.FileHandler(filename, mode='w')
file_handler.setLevel(logging.INFO)
#formatter = logging.Formatter("%(asctime)s %(filename)s, %(lineno)d, %(funcName)s: %(message)s")
#file_handler.setFormatter(formatter)
logger.addHandler(file_handler)
# log to the console
console_handler = logging.StreamHandler()
level = logging.INFO
console_handler.setLevel(level)
logger.addHandler(console_handler)
# initialise logging
logging.info(
' ______ ______ _ _ _ _ \n'
)
logging.info(
'| _ \ \ / / ___| ___(_)_ __ ___ _ _| | __ _| |_(_) ___ _ __ \n'
)
logging.info(
"| |_) \ \ / /\___ \ / __| | '_ ` _ \| | | | |/ _` | __| |/ _ \| '_ \ \n"
)
logging.info(
'| __/ \ V / ___) | \__ \ | | | | | | |_| | | (_| | |_| | (_) | | | |\n'
)
logging.info(
'|_| \_/ |____/ |___/_|_| |_| |_|\__,_|_|\__,_|\__|_|\___/|_| |_|\n\n'
)
logging.info(
title1(
"Simulation of the PVS flow and tracer transport using steady stokes solver and diffusion-advection solver. Flat plates geometry"
))
logging.info("Date and time:" +
datetime.now().strftime("%m/%d/%Y, %H:%M:%S"))
logging.info('Job name : ' + args.job_name)
logging.debug('logging initialized')
# Set parameters
logging.info(title1("Parameters"))
# Geometry params
logging.info('\n * Geometry')
Rv = args.radius_vessel # centimeters
Rpvs = args.radius_pvs # centimeters
L = args.length # centimeters
Rsas = args.radius_sas + Rv
Lsas = args.length_sas
logging.info('Vessel radius : %e cm' % Rv)
logging.info('PVS radius : %e cm' % Rpvs)
logging.info('PVS length : %e cm' % L)
logging.info('SAS length : %e cm' % Lsas)
logging.info('SAS radius : %e cm' % Rsas)
logging.info('\n * Cross section area deformation parameters')
ai = args.ai
fi = args.fi
phii = args.phii
logging.info('ai (dimensionless): ' + '%e ' * len(ai) % tuple(ai))
logging.info('fi (Hz) : ' + '%e ' * len(fi) % tuple(fi))
logging.info('phii (rad) : ' + '%e ' * len(phii) % tuple(phii))
#Mesh
logging.info('\n * Mesh')
#number of cells in the radial direction
Nr = args.N_radial
DR = (Rpvs - Rv) / Nr
logging.info('N radial : %e' % Nr)
#time parameters
logging.info('\n * Time')
toutput = args.toutput
tfinal = args.tend
dt = args.time_step
logging.info('final time: %e s' % tfinal)
logging.info('output period : %e s' % toutput)
logging.info('time step : %e s' % dt)
# approximate CFL for fluid solver : need to compute max velocity depending on the wall displacement...
# maybe just add a warning in computation with actual velocity
#Uapprox=500e-4 #upper limit for extected max velocity
#CFL_dt=0.25*DY/Uapprox
#if CFL_dt < dt :
# logging.warning('The specified time step of %.2e s does not fullfil the fluid CFL condition. New fluid time step : %.2e s'%(dt, CFL_dt))
#dt_fluid=min(dt,CFL_dt)
dt_fluid = dt
# approximate CFL for tracer solver
dt_advdiff = dt
# material parameters
logging.info('\n * Fluid properties')
mu = args.viscosity
rho = args.density
logging.info('density: %e g/cm3' % rho)
logging.info('dynamic viscosity : %e dyn s/cm2' % mu)
logging.info('\n* Tracer properties')
D = args.diffusion_coef
sigma_gauss = args.sigma
logging.info('Free diffusion coef: %e cm2/s' % D)
logging.info('STD of initial gaussian profile: %e ' % sigma_gauss)
xi_gauss = args.initial_pos
logging.info('Initial position: %e cm2' % xi_gauss)
logging.info('\n * ALE')
kappa = args.ale_parameter
logging.info('ALE parameter: %e ' % kappa)
logging.info('\n * Lateral BC')
resistance = args.resistance
logging.info('inner resistance: %e ' % resistance)
if resistance == 0:
lateral_bc = 'free'
logging.info('right BC will be set to the free assumption')
elif resistance < 0:
lateral_bc = 'noflow'
logging.info('right BC will be set to the no flow assumption')
else:
lateral_bc = 'resistance'
logging.info('right BC will be set to the resistance assumption')
fluid_parameters = {'mu': mu, 'rho': rho, 'dt': dt_fluid}
tracer_parameters = {'kappa': D, 'dt': dt_advdiff}
ale_parameters = {'kappa': kappa}
# Mesh
logging.info(title1('Meshing'))
logging.info('cell size : %e cm' % (DR))
from sleep.mesh import mesh_model2d, load_mesh2d, set_mesh_size
import sys
gmsh.initialize(['', '-format', 'msh2'])
model = gmsh.model
import math
Apvs0 = math.pi * Rpvs**2
Av0 = math.pi * Rv**2
A0 = Apvs0 - Av0
# progressive mesh
factory = model.occ
a = factory.addPoint(-Lsas, Rv, 0)
b = factory.addPoint(L, Rv, 0)
c = factory.addPoint(L, Rpvs, 0)
d = factory.addPoint(0, Rpvs, 0)
e = factory.addPoint(0, Rsas, 0)
f = factory.addPoint(-Lsas, Rsas, 0)
fluid_lines = [
factory.addLine(*p)
for p in ((a, b), (b, c), (c, d), (d, e), (e, f), (f, a))
]
named_lines = dict(
zip(('bottom', 'pvs_right', 'pvs_top', 'brain_surf', 'sas_top',
'sas_left'), fluid_lines))
fluid_loop = factory.addCurveLoop(fluid_lines)
fluid = factory.addPlaneSurface([fluid_loop])
factory.synchronize()
model.addPhysicalGroup(2, [fluid], 1)
for name in named_lines:
tag = named_lines[name]
model.addPhysicalGroup(1, [tag], tag)
# boxes for mesh refinement
cell_size = DR * (Rpvs - Rv) / (Rpvs - Rv)
boxes = []
# add box on the PVS for mesh
field = model.mesh.field
fid = 1
field.add('Box', fid)
field.setNumber(fid, 'XMin', 0)
field.setNumber(fid, 'XMax', L)
field.setNumber(fid, 'YMin', Rv)
field.setNumber(fid, 'YMax', Rpvs)
field.setNumber(fid, 'VIn', cell_size)
field.setNumber(fid, 'VOut', DR * 50)
field.setNumber(fid, 'Thickness', Rsas)
boxes.append(fid)
# Combine
field.add('Min', 2)
field.setNumbers(2, 'FieldsList', boxes)
field.setAsBackgroundMesh(2)
model.occ.synchronize()
h5_filename = outputfolder + '/mesh.h5'
tags = {'cell': {'F': 1}, 'facet': {}}
mesh_model2d(model, tags, h5_filename)
mesh_f, markers, lookup = load_mesh2d(h5_filename)
gmsh.finalize()
# todo : how to know nb of cells ?
#logging.info('nb cells: %i'%(Nl*Nr*2))
fluid_bdries = MeshFunction("size_t", mesh_f,
mesh_f.topology().dim() - 1, 0)
# Label facets
xy = mesh_f.coordinates().copy()
x, y = xy.T
xmin = x.min()
xmax = x.max()
ymin = y.min()
ymax = y.max()
tol = cell_size / 2 #cm
class Boundary_sas_left(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[0], -Lsas, tol)
# downstream
class Boundary_pvs_right(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[0], L, tol)
class Boundary_sas_top(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[1], Rsas, tol) and (x[0] < tol)
class Boundary_pvs_top(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[1], Rpvs, tol) and (x[0] > -tol)
# brain
class Boundary_brainsurf(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[0], 0, tol) and (x[1] > Rpvs - tol)
class Boundary_bottom(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and near(x[1], ymin, tol)
btop_sas = Boundary_sas_top()
btop_pvs = Boundary_pvs_top()
bbottom = Boundary_bottom()
bvert_left = Boundary_sas_left()
bvert_brain = Boundary_brainsurf()
bvert_right = Boundary_pvs_right()
btop_sas.mark(fluid_bdries, 1)
btop_pvs.mark(fluid_bdries, 2)
bbottom.mark(fluid_bdries, 3)
bvert_left.mark(fluid_bdries, 4)
bvert_brain.mark(fluid_bdries, 5)
bvert_right.mark(fluid_bdries, 6)
facet_lookup = {
'sas_top': 1,
'pvs_top': 2,
'vessel': 3,
'sas_left': 4,
'brain_surf': 5,
'pvs_right': 6
}
facets_out << fluid_bdries
#FEM space
logging.info(title1("Set FEM spaces"))
logging.info('\n * Fluid')
Vf_elm = VectorElement('Lagrange', triangle, 2)
Qf_elm = FiniteElement('Lagrange', triangle, 1)
Wf_elm = MixedElement([Vf_elm, Qf_elm])
Wf = FunctionSpace(mesh_f, Wf_elm)
logging.info('Velocity : "Lagrange", triangle, 2')
logging.info('Pressure : "Lagrange", triangle, 1')
logging.info('\n * Tracer')
Ct_elm = FiniteElement('Lagrange', triangle, 1)
Ct = FunctionSpace(mesh_f, Ct_elm)
logging.info('Concentration : "Lagrange", triangle, 1')
logging.info('\n * ALE')
Va_elm = VectorElement('Lagrange', triangle, 1)
Va = FunctionSpace(mesh_f, Va_elm)
logging.info('ALE displacement: "Lagrange", triangle, 1')
# Setup of boundary conditions
logging.info(title1("Boundary conditions"))
import sympy
tn = sympy.symbols("tn")
tnp1 = sympy.symbols("tnp1")
sin = sympy.sin
sqrt = sympy.sqrt
functionR = Rpvs - (Rpvs - Rv) * (1 + sum(
[a * sin(2 * pi * f * tn + phi)
for a, f, phi in zip(ai, fi, phii)])) # displacement bottom plate
R_vessel = sympy.printing.ccode(functionR)
functionV = sympy.diff(functionR, tn) # velocity
V_vessel = sympy.printing.ccode(functionV)
#Delta U for ALE. I dont really like this
functionUALE = -(Rpvs - Rv) * (1 + sum([
a * sin(2 * pi * f * tnp1 + phi) for a, f, phi in zip(ai, fi, phii)
])) + (Rpvs - Rv) * (1 + sum(
[a * sin(2 * pi * f * tn + phi) for a, f, phi in zip(ai, fi, phii)]))
UALE_vessel = sympy.printing.ccode(functionUALE)
vf_bottom = Expression(('0', V_vessel), tn=0,
degree=2) # no slip no gap condition at vessel wall
uale_bottom = Expression(('0', UALE_vessel), tn=0, tnp1=1,
degree=2) # displacement for ALE at vessel wall
logging.info('\n * Lateral assumption')
logging.info(lateral_bc)
logging.info('\n * Fluid')
logging.info('Left : zero pressure')
if lateral_bc == 'free':
logging.info('Right : zero pressure')
elif lateral_bc == 'resistance':
logging.info('Right : resistance')
else:
logging.info('Right : no flow')
logging.info('Top : no slip no gap fixed wall')
logging.info('Bottom : no slip no gap moving wall')
logging.info('\n * Tracer concentration')
logging.info('Left : zero concentration')
if lateral_bc == 'free':
logging.info('Right : zero concentration')
else:
logging.info('Right : no flux')
logging.info('Top : no flux')
logging.info('Bottom : no flux')
logging.info('\n * ALE')
logging.info('Left : no flux')
logging.info('Right : no flux')
logging.info('Top : no displacement')
logging.info('Bottom : vessel displacement')
# Now we wire up
if lateral_bc == 'free':
bcs_fluid = {
'velocity': [(facet_lookup['vessel'], vf_bottom),
(facet_lookup['sas_left'], Constant((0, 0))),
(facet_lookup['brain_surf'], Constant((0, 0))),
(facet_lookup['pvs_top'], Constant((0, 0)))],
'traction': [],
'pressure': [(facet_lookup['sas_top'], Constant(0)),
(facet_lookup['pvs_right'], Constant(0))]
}
elif lateral_bc == 'resistance':
Rpressure = Expression('R*Q+p0', R=resistance, Q=0, p0=0, degree=1) #
# Compute pressure to impose according to the flow at previous time step and resistance.
bcs_fluid = {
'velocity': [(facet_lookup['vessel'], vf_bottom),
(facet_lookup['sas_left'], Constant((0, 0))),
(facet_lookup['brain_surf'], Constant((0, 0))),
(facet_lookup['pvs_top'], Constant((0, 0)))],
'traction': [],
'pressure': [(facet_lookup['sas_top'], Constant(0)),
(facet_lookup['pvs_right'], Rpressure)]
}
else:
bcs_fluid = {
'velocity':
[(facet_lookup['vessel'], vf_bottom),
(facet_lookup['sas_left'], Constant((0, 0))),
(facet_lookup['brain_surf'], Constant((0, 0))),
(facet_lookup['pvs_top'], Constant((0, 0))),
(facet_lookup['pvs_right'], Constant(
(0, 0)))], # would be more correct to impose only on u x
'traction': [],
'pressure': [(facet_lookup['sas_top'], Constant(0))]
}
if lateral_bc == 'free':
bcs_tracer = {
'concentration': [(facet_lookup['sas_top'], Constant(0)),
(facet_lookup['pvs_right'], Constant(0))],
'flux': [(facet_lookup['vessel'], Constant(0)),
(facet_lookup['sas_left'], Constant(0)),
(facet_lookup['brain_surf'], Constant(0)),
(facet_lookup['pvs_top'], Constant(0))]
}
else:
bcs_tracer = {
'concentration': [(facet_lookup['sas_top'], Constant(0))],
'flux': [(facet_lookup['vessel'], Constant(0)),
(facet_lookup['sas_left'], Constant(0)),
(facet_lookup['brain_surf'], Constant(0)),
(facet_lookup['pvs_top'], Constant(0)),
(facet_lookup['pvs_right'], Constant(0))]
}
bcs_ale = {
'dirichlet': [(facet_lookup['vessel'], uale_bottom),
(facet_lookup['sas_top'], Constant((0, 0))),
(facet_lookup['pvs_top'], Constant((0, 0))),
(facet_lookup['brain_surf'], Constant((0, 0)))],
'neumann': [(facet_lookup['sas_left'], Constant((0, 0))),
(facet_lookup['pvs_right'], Constant((0, 0)))]
}
# We collect the time dependent BC for update
driving_expressions = (uale_bottom, vf_bottom)
# Initialisation :
logging.info(title1("Initialisation"))
# We start at a time shift
tshift = -1 / 4 / fi[0] ##todo : modify to be compatible with phii
# Update boundary conditions
for expr in driving_expressions:
hasattr(expr, 'tn') and setattr(expr, 'tn', 0)
hasattr(expr, 'tnp1') and setattr(expr, 'tnp1', tshift)
#Solve ALE and move mesh
eta_f = solve_ale(Va,
f=Constant((0, 0)),
bdries=fluid_bdries,
bcs=bcs_ale,
parameters=ale_parameters)
ALE.move(mesh_f, eta_f)
mesh_f.bounding_box_tree().build(mesh_f)
logging.info("\n * Fluid")
logging.info("Velocity : zero field")
logging.info("Pressure : zero field")
uf_n = project(Constant((0, 0)), Wf.sub(0).collapse())
pf_n = project(Constant(0), Wf.sub(1).collapse())
logging.info("\n * Tracer")
logging.info("Concentration : Gaussian profile")
logging.info(" Centered at mid length")
logging.info(" STD parameter = %e" % sigma_gauss)
c_0 = Expression('exp(-a*pow(x[0]-b, 2)) ',
degree=1,
a=1 / 2 / sigma_gauss**2,
b=xi_gauss)
c_n = project(c_0, Ct)
# Save initial state
uf_n.rename("uf", "tmp")
pf_n.rename("pf", "tmp")
c_n.rename("c", "tmp")
uf_out << (uf_n, 0)
pf_out << (pf_n, 0)
c_out << (c_n, 0)
# Get the 1 D profiles at umax (to be changed in cyl coordinate)
mesh_points = mesh_f.coordinates()
x = mesh_points[:, 0]
y = mesh_points[:, 1]
xmin = 0
xmax = L
ymin = min(y)
ymax = Rpvs
files = [csv_p, csv_u, csv_c]
fields = [pf_n, uf_n.sub(0), c_n]
field_names = [
'pressure (dyn/cm2)', 'axial velocity (cm/s)', 'concentration'
]
for csv_file, field, name in zip(files, fields, field_names):
#values = line_sample(slice_line, field)
values = profile(field, xmin, xmax, ymin, ymax)
logging.info('Max ' + name + ' : %.2e' % max(abs(values)))
#logging.info('Norm '+name+' : %.2e'%field.vector().norm('linf'))
row = [0] + list(values)
csv_file.write(('%e' + ', %e' * len(values) + '\n') % tuple(row))
csv_rv.write('%e, %e' % (0, ymin))
############# RUN ############3
logging.info(title1("Run"))
# Time loop
### We start at the quarter of the period so that velocity=0
print('tini = ', tshift)
time = tshift
timestep = 0
# Here I dont know if there will be several dt for advdiff and fluid solver
while time < tfinal + tshift:
# Update boundary conditions
for expr in driving_expressions:
hasattr(expr, 'tn') and setattr(expr, 'tn', time)
hasattr(expr, 'tnp1') and setattr(expr, 'tnp1', time + dt)
if lateral_bc == 'resistance':
z, r = SpatialCoordinate(mesh_f)
ds = Measure('ds', domain=mesh_f, subdomain_data=fluid_bdries)
n = FacetNormal(mesh_f)
Flow = assemble(2 * pi * r * dot(uf_n, n) *
ds(facet_lookup['x_max']))
print('Right outflow : %e \n' % Flow)
setattr(Rpressure, 'Q', Flow)
#Solve ALE and move mesh
eta_f = solve_ale(Va,
f=Constant((0, 0)),
bdries=fluid_bdries,
bcs=bcs_ale,
parameters=ale_parameters)
ALE.move(mesh_f, eta_f)
mesh_f.bounding_box_tree().build(mesh_f)
# Solve fluid problem
uf_, pf_ = solve_fluid(Wf,
u_0=uf_n,
f=Constant((0, 0)),
bdries=fluid_bdries,
bcs=bcs_fluid,
parameters=fluid_parameters)
tracer_parameters["T0"] = time
tracer_parameters["nsteps"] = 1
tracer_parameters["dt"] = dt
# Solve tracer problem
c_, T0 = solve_adv_diff(Ct,
velocity=uf_ - eta_f / Constant(dt),
phi=Constant(1),
f=Constant(0),
c_0=c_n,
phi_0=Constant(1),
bdries=fluid_bdries,
bcs=bcs_tracer,
parameters=tracer_parameters)
# Update current solution
uf_n.assign(uf_)
pf_n.assign(pf_)
c_n.assign(c_)
#Update time
time += dt
timestep += 1
# Save output
if (timestep % int(toutput / dt) == 0):
logging.info("\n*** save output time %e s" % (time - tshift))
logging.info("number of time steps %i" % timestep)
# may report Courant number or other important values that indicate how is doing the run
uf_.rename("uf", "tmp")
pf_.rename("pf", "tmp")
c_.rename("c", "tmp")
uf_out << (uf_, time - tshift)
pf_out << (pf_, time - tshift)
c_out << (c_, time - tshift)
# Get the 1 D profiles at umax (to be changed in cyl coordinate)
mesh_points = mesh_f.coordinates()
x = mesh_points[:, 0]
y = mesh_points[:, 1]
xmin = 0
xmax = L
ymin = min(y)
ymax = Rpvs
#slice_line = line([xmin,(ymin+ymax)/2],[xmax,(ymin+ymax)/2], 100)
logging.info('Rpvs : %e' % ymax)
logging.info('Rvn : %e' % ymin)
files = [csv_p, csv_u, csv_c]
fields = [pf_n, uf_n.sub(0), c_n]
field_names = [
'pressure (dyn/cm2)', 'axial velocity (cm/s)', 'concentration'
]
for csv_file, field, name in zip(files, fields, field_names):
#values = line_sample(slice_line, field)
values = profile(field, xmin, xmax, ymin, ymax)
logging.info('Max ' + name + ' : %.2e' % max(abs(values)))
#logging.info('Norm '+name+' : %.2e'%field.vector().norm('linf'))
row = [time - tshift] + list(values)
csv_file.write(
('%e' + ', %e' * len(values) + '\n') % tuple(row))
csv_rv.write('%e, %e' % (time - tshift, ymin))