K_Ic,
confining_stress_func=sigmaO_func)
# injection parameters
Q0 = 0.001 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(viscosity=1.1e-3)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 145. # the time at which the simulation stops
simulProp.bckColor = 'sigma0' # setting the parameter according to which the mesh is color coded
simulProp.set_outputFolder("./Data/height_contained")
simulProp.tmStpPrefactor = 1.0 # decreasing the size of time step
simulProp.plotVar = ['footprint'] # plotting footprint
# initializing fracture
Fr_geometry = Geometry(shape='radial', radius=1.)
init_param = InitializationParameters(Fr_geometry, regime='M')
# creating fracture object
Fr = Fracture(Mesh,
init_param,
Solid,
Fluid,
Injection,
simulProp)
# create a Controller
# fluid properties
Fluid = FluidProperties(viscosity=30, density=2400)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 560000 # the time at which the simulation stops
simulProp.set_outputFolder(
"./Data/neutral_buoyancy") # the disk address where the files are saved
simulProp.gravity = True # set up the gravity flag
simulProp.tolFractFront = 3e-3 # increase the tolerance for fracture
# front iteration
simulProp.plotTSJump = 4 # plot every fourth time step
simulProp.saveTSJump = 2 # save every second time step
simulProp.maxSolverItrs = 200 # increase the Anderson iteration limit for the
# elastohydrodynamic solver
simulProp.tmStpPrefactor = np.asarray([[0, 80000], [0.5, 0.1]
]) # set up the time step prefactor
simulProp.timeStepLimit = 5000 # time step limit
simulProp.plotVar = ['w',
'v'] # plot fracture width and fracture front velocity
simulProp.set_mesh_extension_direction(
['top', 'horizontal']) # allow the fracture to extend in positive y and x
simulProp.set_mesh_extension_factor(1.2) # set the extension factor to 1.4
simulProp.useBlockToeplizCompression = True # use the Toepliz elasticity matrix to save memory
# initializing a static fracture
C = load_isotropic_elasticity_matrix_toepliz(Mesh, Solid.Eprime)
Fr_geometry = Geometry('radial', radius=300)
init_param = InitializationParameters(Fr_geometry,
regime='static',
net_pressure=0.5e6,
elasticity_matrix=C)
minimum_width=1e-8)
# injection parameters
Q0 = 0.001 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(viscosity=1.1e-3)
# simulation properties
simulProp = SimulationProperties()
simulProp.bckColor = 'sigma0'
simulProp.finalTime = 0.28 # the time at which the simulation stops
simulProp.outputTimePeriod = 1e-4 # to save after every time step
simulProp.tmStpPrefactor = 0.5 # decrease the pre-factor due to explicit front tracking
simulProp.set_outputFolder("./Data/stress_heterogeneities") # the disk address where the files are saved
simulProp.saveFluidFluxAsVector = True
simulProp.plotVar = ['ffvf']
simulProp.projMethod = 'LS_continousfront' # <--- mandatory use
simulProp.saveToDisk = True
simulProp.set_mesh_extension_factor(1.1)
simulProp.set_mesh_extension_direction(['all'])
simulProp.useBlockToeplizCompression = True
# initialization parameters
Fr_geometry = Geometry('radial', radius=0.12)
init_param = InitializationParameters(Fr_geometry, regime='M')
# creating fracture object
Q0 = np.asarray([[0, 6000], [0.001, 0]])
Injection = InjectionProperties(Q0, Mesh, source_coordinates=[0, -20])
# fluid properties
Fluid = FluidProperties(viscosity=1e-3)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1.6e4 # the time at which the simulation stops
simulProp.set_outputFolder(
"./Data/fracture_closure") # the disk address where the files are saved
simulProp.bckColor = 'confining stress' # setting the parameter for the mesh color coding
simulProp.plotTSJump = 4 # set to plot every four time steps
simulProp.plotVar = ['w', 'lk', 'footprint'
] # setting the parameters that will be plotted
simulProp.tmStpPrefactor = np.asarray(
[[0, 6000], [0.8, 0.4]]) # decreasing the time step pre-factor after 6000s
simulProp.maxSolverItrs = 120 # increase maximum iterations for the elastohydrodynamic solver
# initialization parameters
Fr_geometry = Geometry('radial', radius=20)
init_param = InitializationParameters(Fr_geometry, regime='M')
# creating fracture object
Fr = Fracture(Mesh, init_param, Solid, Fluid, Injection, simulProp)
# create a Controller
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
# run the simulation
controller.run()
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 38000 # the time at which the simulation stops
simulProp.set_outputFolder("./Data/HB") # the disk address where the files are saved
simulProp.set_simulation_name('HB_Gauss_Chebyshev_comparison') # setting simulation name
simulProp.saveG = True # enable saving the coefficient G
simulProp.plotVar = ['w', 'G'] # plot width of fracture
simulProp.saveEffVisc = True # enable saving of the effective viscosity
simulProp.relaxation_factor = 0.3 # relax Anderson iteration
simulProp.maxSolverItrs = 200 # set maximum number of Anderson iterations to 200
simulProp.collectPerfData = True # enable collect performance data
simulProp.tolFractFront = 3e-3 # increasing fracture front iteration tolerance
simulProp.plotTSJump = 5 # plotting after every five time steps
simulProp.tmStpPrefactor = 0.6 # reducing time steps for better convergence
simulProp.Anderson_parameter = 10 # saving last 10 solutions for better performance
# initializing the fracture width with the solution provided by Madyarova & Detournay 2004 for power-law fluids.
w = np.zeros(Mesh.NumberOfElts)
xw = np.genfromtxt('width_n_05.csv', delimiter=',') # loading dimensionless width profile for n = 0.5
t = 2e-2
n = Fluid.n
gamma = 0.699
Mprime = 2**(n + 1) * (2 * n + 1)**n / n**n * Fluid.k
Vel = 2 * (n + 1) / (n + 2) / 3 * gamma * (Eprime * Q0 ** (n + 2) / Mprime
) ** (1 / (3 * n + 6)) / t ** ((n + 4) / (3 * n + 6))
eps = (Mprime / Eprime / t**n) ** (1 / (n + 2))
L = (Eprime * Q0**(n + 2) * t**(2 * n + 2) / Mprime) ** (1 / (3 * n + 6))
# interpolating width on cell centers
