def define_ode(self, current_time):
x, y = self.mesh.faceCenters
# Internal source specificatio - currently no functional
internal_source_value = self.parameter.internal_source_value
internal_source_region = self.parameter.internal_source_region
internal_source_mask = (
(x > internal_source_region.xmin) &
(x < internal_source_region.xmax) &
(y > internal_source_region.ymin) &
(y < internal_source_region.ymax)
)
# Get convection data
convection = self.define_convection_variable(current_time)
eq = TransientTerm() == - ConvectionTerm(coeff=convection) \
+ DiffusionTerm(coeff=self.parameter.Diffusivity)\
- ImplicitSourceTerm(coeff=self.parameter.Decay)\
# + ImplicitSourceTerm(coeff=internal_source_value*internal_source_mask) # Internal source not working
return eq
'''Equations to solve for each varible must be defined:
-TransientTerm = dvar/dt
-ConvectionTerm = dvar/dx
-DiffusionTerm = d^2var/dx^2
-Source terms can be described as they would appear mathematically
Notes: coeff = terms that are multiplied by the Term.. must be rank-1 FaceVariable for ConvectionTerm
"var" must be defined for each Term if they are not all the variable being solved for,
otherwise will see "fipy.terms.ExplicitVariableError: Terms with explicit Variables cannot mix with Terms with implicit Variables." '''
#In English: dPion/dt = -1/q * divergence.Jp(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jp = q * mu_p * E(x,t) * Pion(x,t) - q * Dp * grad.Pion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Pion.equation = TransientTerm(
coeff=1,
var=Pion) == mu_p * (ConvectionTerm(coeff=potential.faceGrad, var=Pion) +
Pion * potential.faceGrad.divergence) + DiffusionTerm(
coeff=Dp, var=Pion) - k_rec * Pion * Nion
#In English: dNion/dt = 1/q * divergence.Jn(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jn = q * mu_n * E(x,t) * Nion(x,t) - q * Dn * grad.Nion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Nion.equation = TransientTerm(
coeff=1, var=Nion
) == -mu_n * (ConvectionTerm(coeff=potential.faceGrad, var=Nion) +
Nion * potential.faceGrad.divergence) + DiffusionTerm(
coeff=Dn, var=Nion) - k_rec * Pion * Nion
#In English: d^2potential/dx^2 = -q/epsilon * Charge_Density and Charge Density = Pion + Nion
# Poisson's Equation
# plt.plot(x, y01(x)) # plt.plot(x, y03(x)) # plt.show() mesh = Grid1D(dx=dx, nx=nx) # Establish mesh in how many dimensions necessary Pion = CellVariable(mesh=mesh, name='Positive ion Charge Density', value=y01(x)) Nion = CellVariable(mesh=mesh, name='Negative ion Charge Density', value=y02(x)) # Hole = CellVariable(mesh=mesh, name='Hole Density',value=y03(x)) # Electron = CellVariable(mesh=mesh, name='Electron Density',value=y04(x)) potential = CellVariable(mesh=mesh, name='Potential') #### Equations set-up #### # In English: dPion/dt = -1/q * divergence.Jp(x,t) - k_rec * Nion(x,t) * Pion(x,t) where # Jp = q * mu_p * E(x,t) * Pion(x,t) - q * Dp * grad.Pion(x,t) and E(x,t) = -grad.potential(x,t) # Continuity Equation Pion_equation = TransientTerm(coeff=1., var=Pion) == mu_p_1 * ConvectionTerm(coeff=potential.faceGrad, var=Pion) + Dp_1 * DiffusionTerm(coeff=1., var=Pion) - k_rec * Pion * Nion # In English: dNion/dt = 1/q * divergence.Jn(x,t) - k_rec * Nion(x,t) * Pion(x,t) where # Jn = q * mu_n * E(x,t) * Nion(x,t) - q * Dn * grad.Nion(x,t) and E(x,t) = -grad.potential(x,t) # Continuity Equation Nion_equation = TransientTerm(coeff=1., var=Nion) == -mu_n_1 * ConvectionTerm(coeff=potential.faceGrad, var=Nion) + Dn_1 * DiffusionTerm(coeff=1., var=Nion) - k_rec * Pion * Nion # Electron_equation = TransientTerm(coeff=1., var=Electron) == -mu_n_2 * ConvectionTerm(coeff=potential.faceGrad, var=Electron) + Dn_2 * DiffusionTerm(coeff=1., var=Electron) - k_rec * Electron * Hole # Hole_equation = TransientTerm(coeff=1., var=Hole) == mu_p_2 * ConvectionTerm(coeff=potential.faceGrad, var=Hole) + Dp_2 * DiffusionTerm(coeff=1., var=Hole) - k_rec * Electron * Hole # In English: d^2potential/dx^2 = -q/epsilon * Charge_Density and Charge Density= Pion-Nion # Poisson's Equation potential_equation = DiffusionTerm(coeff=1., var=potential) == -(q / epsilon) * (Pion - Nion) # potential_equation = DiffusionTerm(coeff=1., var=potential) == -(q / epsilon) * (Pion - Nion + Hole - Electron) ### Boundary conditions ### # Fipy is defaulted to be no-flux, so we only need to constrain potential potential.constrain(0., where=mesh.exteriorFaces)
y02 = np.zeros(nx)
y02[0:500] = 0.5e21
mesh = Grid1D(dx=dx, nx=nx) # Establish mesh in how many dimensions necessary
Pion = CellVariable(mesh=mesh, name='Positive ion Charge Density', value=y01)
Nion = CellVariable(mesh=mesh, name='Negative ion Charge Density', value=y02)
potential = CellVariable(mesh=mesh, name='Potential')
#### Equations set-up ####
# In English: dPion/dt = -1/q * divergence.Jp(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jp = q * mu_p * E(x,t) * Pion(x,t) - q * Dp * grad.Pion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Pion_equation = TransientTerm(coeff=1., var=Pion) == mu_p * ConvectionTerm(
coeff=potential.faceGrad, var=Pion) + Dp * DiffusionTerm(
coeff=1., var=Pion) - k_rec * Pion * Nion
# In English: dNion/dt = 1/q * divergence.Jn(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jn = q * mu_n * E(x,t) * Nion(x,t) - q * Dn * grad.Nion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Nion_equation = TransientTerm(coeff=1., var=Nion) == -mu_n * ConvectionTerm(
coeff=potential.faceGrad, var=Nion) + Dn * DiffusionTerm(
coeff=1., var=Nion) - k_rec * Pion * Nion
# In English: d^2potential/dx^2 = -q/epsilon * Charge_Density and Charge Density= Pion-Nion
# Poisson's Equation
potential_equation = DiffusionTerm(
coeff=1., var=potential) == -(q / epsilon) * (Pion - Nion)
### Boundary conditions ###
mesh = Grid1D(dx=dx, nx=nx) # Establish mesh in how many dimensions necessary
Pion = CellVariable(mesh=mesh,
name='Positive ion Charge Density',
value=y01(x))
Nion = CellVariable(mesh=mesh,
name='Negative ion Charge Density',
value=y02(x))
Hole = CellVariable(mesh=mesh, name='Hole Density', value=y03(x))
Electron = CellVariable(mesh=mesh, name='Electron Density', value=y04(x))
potential = CellVariable(mesh=mesh, name='Potential')
#### Equations set-up ####
# In English: dPion/dt = -1/q * divergence.Jp(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jp = q * mu_p * E(x,t) * Pion(x,t) - q * Dp * grad.Pion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Pion_equation = TransientTerm(coeff=1., var=Pion) == mu_p_1 * ConvectionTerm(
coeff=potential.faceGrad, var=Pion) + Dp_1 * DiffusionTerm(
coeff=1., var=Pion) - k_rec * Pion * Nion
# In English: dNion/dt = 1/q * divergence.Jn(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jn = q * mu_n * E(x,t) * Nion(x,t) - q * Dn * grad.Nion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
Nion_equation = TransientTerm(coeff=1., var=Nion) == -mu_n_1 * ConvectionTerm(
coeff=potential.faceGrad, var=Nion) + Dn_1 * DiffusionTerm(
coeff=1., var=Nion) - k_rec * Pion * Nion
Electron_equation = TransientTerm(
coeff=1., var=Electron) == -mu_n_2 * ConvectionTerm(
coeff=potential.faceGrad, var=Electron) + Dn_2 * DiffusionTerm(
coeff=1., var=Electron) - k_rec * Electron * Hole
Hole_equation = TransientTerm(coeff=1., var=Hole) == mu_p_2 * ConvectionTerm(
coeff=potential.faceGrad, var=Hole) + Dp_2 * DiffusionTerm(
coeff=1., var=Hole) - k_rec * Electron * Hole
# In English: d^2potential/dx^2 = -q/epsilon * Charge_Density and Charge Density= Pion-Nion
#m = odeint(model, m0, t)
#vol = volt(m,t)
xx = mesh.faceCenters[0]
yy = mesh.faceCenters[1]
zz = mesh.faceCenters[2]
ll = len(xx)
print("size of ll = " + str(ll))
lista = []
for i in range(0, 5):
for j in range(0, ll):
point = np.array([xx[j], yy[j], zz[j]])
gradient = model(point, i * 1e-9)
print(Diffusion)
eq = (TransientTerm() == DiffusionTerm(coeff=Diffusion) -
ConvectionTerm(coeff=gradient))
eq.solve(Phi, dt=1e-9, solver=DefaultSolver(precon=None))
print("size of Phi = " + str(len(Phi)))
lista.append(Phi[j])
Phi = lista.copy()
lista.clear()
if __name__ == "__main__": #Parameters to be changed are in the seciton below.
viewer.plot(
filename="trial.vtk"
) #It will only save the final vtk file. You can change the name
if not i % 10 or i == 0:
dest_name = '/home/zhaoshi/Zhao_test/img_' + str(
i
) + '.vtk' #Path and name of the intermediate file. The Green Part should be changed to your path & name
copyfile('/home/zhaoshi/trial.vtk',
dest_name) #Specify the path of your trial.vtk file
# EQUATION SETUP BASIC DESCRIPTION
'''Equations to solve for each variable must be defined:
-TransientTerm = dvar/dt
-ConvectionTerm = dvar/dx
-DiffusionTerm = d^2var/dx^2
-Source terms can be described as they would appear mathematically
Notes: coeff = terms that are multiplied by the Term.. must be rank-1 FaceVariable for ConvectionTerm
"var" must be defined for each Term if they are not all the variable being solved for,
otherwise will see "fipy.terms.ExplicitVariableError: Terms with explicit Variables cannot mix with Terms with implicit Variables." '''
# In English: dPion/dt = -1/q * divergence.Jp(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jp = q * mu_p * E(x,t) * Pion(x,t) - q * Dp * grad.Pion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
# Pion.equation = TransientTerm(coeff=1, var=Pion) == mu_p * (ConvectionTerm(coeff=potential.faceGrad,var=Pion) + Pion * potential.faceGrad.divergence) + DiffusionTerm(coeff=Dp,var=Pion) - k_rec*Pion*Nion
Pion.equation = TransientTerm(coeff=1, var=Pion) == mu_p * (ConvectionTerm(coeff=potential.faceGrad, var=Pion) + Pion * potential.faceGrad.divergence)
# In English: dNion/dt = 1/q * divergence.Jn(x,t) - k_rec * Nion(x,t) * Pion(x,t) where
# Jn = q * mu_n * E(x,t) * Nion(x,t) - q * Dn * grad.Nion(x,t) and E(x,t) = -grad.potential(x,t)
# Continuity Equation
# Nion.equation = TransientTerm(coeff=1, var=Nion) == -mu_n * (ConvectionTerm(coeff=potential.faceGrad,var=Nion) + Nion * potential.faceGrad.divergence) + DiffusionTerm(coeff=Dn,var=Nion) - k_rec*Pion*Nion
# In English: d^2potential/dx^2 = -q/epsilon * Charge_Density and Charge Density = Pion + Nion
# Poisson's Equation
# potential.equation = DiffusionTerm(coeff=1, var=potential) == (-q/epsilon)*(Pion + Nion)
potential.equation = DiffusionTerm(coeff=1, var=potential) == (-q/epsilon)*Pion