# 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 colored
simulProp.set_outputFolder(
"./Data/height_contained") # set the directory to save the simulation
simulProp.tmStpPrefactor = 1.0 # decreasing the size of time step
simulProp.plotVar = ['footprint'] # plotting footprint
simulProp.set_mesh_extension_direction(
['horizontal']) # allow the mesh to extend horizontally
simulProp.set_mesh_extension_factor(1.35) # setting the mesh extension factor
simulProp.useBlockToeplizCompression = True # use the Toepliz elasticity to save memory
# 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
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
# run the simulation
controller.run()
####################
# plotting results #
####################
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
f = interpolate.interp1d(gamma * L * xw[:, 0],
L * eps * xw[:, 1],
bounds_error=False,
fill_value='extrapolate')
w = f(Mesh.distCenter)
w[w < 0] = 0.
# initialization parameters
Fr_geometry = Geometry('radial', radius=gamma * L)
from elasticity import load_isotropic_elasticity_matrix
C = load_isotropic_elasticity_matrix(Mesh, Eprime)
init_param = InitializationParameters(Fr_geometry,
regime='static',
width=w,
elasticity_matrix=C,
tip_velocity=Vel)
# creating fracture object
Fr = Fracture(Mesh,
init_param,
Solid,
Fluid,
Injection,
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1e2 # the time at which the simulation stops
simulProp.set_tipAsymptote(
'K'
) # the tip asymptote is evaluated with the toughness dominated assumption
simulProp.set_volumeControl(
True
) # use the inviscid fluid solver(toughness dominated), imposing volume balance
simulProp.set_outputFolder(
"./Data/K_radial_symmetric") # the disk address where the files are saved
simulProp.symmetric = True # assume fracture geometry to be symmetric (only available for volume control)
simulProp.plotTSJump = 10 # plotting every 10 time steps
# initializing fracture
Fr_geometry = Geometry('radial', radius=0.15)
init_param = InitializationParameters(Fr_geometry, regime='K')
# 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()
####################
# plotting results #
####################
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
viscosity = 0.001 / 12 # mu' =0.001
Fluid = FluidProperties(viscosity=viscosity)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1e7 # the time at which the simulation stops
simulProp.saveTSJump, simulProp.plotTSJump = 5, 5 # save and plot after every 5 time steps
simulProp.set_outputFolder(
"./Data/MtoK_leakoff") # the disk address where the files are saved
simulProp.frontAdvancing = 'explicit' # setting up explicit front advancing
# initializing fracture
Fr_geometry = Geometry('radial')
init_param = InitializationParameters(Fr_geometry, regime='M', time=0.5)
# 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()
####################
# plotting results #
####################
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)
Fr = Fracture(Mesh,
init_param,
Solid,
Fluid,
Injection,
simulProp)
# create a controller
controller = Controller(Fr,
Solid,
Fluid = FluidProperties(viscosity=1.1e-3) # toughness dominated solution
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 4000 # the time at which the simulation stops
simulProp.set_volumeControl(True) # to set up the solver in volume control mode (inviscid fluid)
simulProp.tolFractFront = 4e-3 # increase tolerance for the anisotropic case
simulProp.set_outputFolder("./Data/toughness_jump") # the disk address where the files are saved
simulProp.set_simulation_name('anisotropic_toughness_jump')
simulProp.symmetric = True # set the fracture to symmetric
simulProp.projMethod = 'ILSA_orig'
simulProp.set_tipAsymptote('U')
# initializing fracture
gamma = (K1c_func(np.pi/2) / K1c_func(0))**2 # gamma = (Kc1/Kc3)**2
Fr_geometry = Geometry('elliptical', minor_axis=15., gamma=gamma)
init_param = InitializationParameters(Fr_geometry, regime='E_K')
# creating fracture object
Fr = Fracture(Mesh,
init_param,
Solid,
Fluid,
Injection,
simulProp)
# create a Controller
controller = Controller(Fr,
Solid,
Fluid,
Injection,