Coupling 1D Advection Diffusion Reaction PDEs with FiPy
I tried to solve 1D coupled PDEs for an advection-diffusion-reaction problem with the Matlab function Pdepe (https://www.mathworks.com/help/matlab/ref/pdepe.html). This function is not working properly in my case of a high advection term as compared to the diffusion term.
Therefore, I searched and found this option of using the Python library FiPy to solve my PDEs system.
My initial conditions are u1=1 for 4*L/10
My coupled equations are of the following form:
du1/dt = d/dx(D1 * du1/dx) + g * x * du1/dx - mu1 * u1 / (K + u1) * u2
du2/dt = d/dx(D2 * du2/dx) + g * x * du2/dx + mu2 * u1 / (K + u1) * u2
I tried to write it by combining the FiPy examples (examples.convection.exponential1DSource.mesh1D, examples.levelSet.advection.mesh1D, examples.cahnHilliard.mesh2DCoupled).
The following lines are not a working example but my first attempt to write the code. This is my first use of FiPy (out of the tests and examples of the documentation), so this might seem to miss the point completely for the regular users.
Could you help me correct this code to get it working on a small number of timesteps?
from fipy import *
g = 0.66
L = 10.
nx = 1000
mu1 = 1.
mu2 = 1.
K = 1.
D1 = 1.
D2 = 1.
mesh = Grid1D(dx=L / 1000, nx=nx)
x = mesh.cellCenters[0]
convCoeff = g*(x-L/2)
u10 = 4*L/10 < x < 6*L/10
u20 = 1.
u1 = CellVariable(name="u1", mesh=mesh, value=u10)
u2 = CellVariable(name="u2", mesh=mesh, value=u20)
## Neumann boundary conditions
u1.faceGrad.constrain(0., where=mesh.facesLeft)
u1.faceGrad.constrain(0., where=mesh.facesRight)
u2.faceGrad.constrain(0., where=mesh.facesLeft)
u2.faceGrad.constrain(0., where=mesh.facesRight)
sourceCoeff1 = -1*mu1*u1/(K+u1)*u2
sourceCoeff2 = 1*mu2*u1/(K+u1)*u2
eq11 = (TransientTerm(var=u1) == DiffusionTerm(coeff=D1, var=u1) + ConvectionTerm(coeff=convCoeff))
eq21 = (TransientTerm(var=u2) == DiffusionTerm(coeff=D2, var=u2) + ConvectionTerm(coeff=convCoeff))
eq12 = ImplicitSourceTerm(coeff=sourceCoeff1, var=u1)
eq22 = ImplicitSourceTerm(coeff=sourceCoeff2, var=u2)
eq1 = eq11 & eq12
eq2 = eq21 & eq22
eqn = eq1 & eq2
vi = Viewer((u1, u2))
for t in range(100):
u1.updateOld()
u2.updateOld()
eqn.solve(dt=1.e-3)
vi.plot()
Thank you for any suggestion or correction.
If you happen to know a good tutorial for this specific kind of problem, I would be happy to read it, since I did not find anything better than the examples in the FiPy documentation.
python
asked 10 mins ago
Antoine
11
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Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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I tried to solve 1D coupled PDEs for an advection-diffusion-reaction problem with the Matlab function Pdepe (https://www.mathworks.com/help/matlab/ref/pdepe.html). This function is not working properly in my case of a high advection term as compared to the diffusion term.
Therefore, I searched and found this option of using the Python library FiPy to solve my PDEs system.
My initial conditions are u1=1 for 4*L/10
My coupled equations are of the following form:
du1/dt = d/dx(D1 * du1/dx) + g * x * du1/dx - mu1 * u1 / (K + u1) * u2
du2/dt = d/dx(D2 * du2/dx) + g * x * du2/dx + mu2 * u1 / (K + u1) * u2
I tried to write it by combining the FiPy examples (examples.convection.exponential1DSource.mesh1D, examples.levelSet.advection.mesh1D, examples.cahnHilliard.mesh2DCoupled).
The following lines are not a working example but my first attempt to write the code. This is my first use of FiPy (out of the tests and examples of the documentation), so this might seem to miss the point completely for the regular users.
Could you help me correct this code to get it working on a small number of timesteps?
from fipy import *
g = 0.66
L = 10.
nx = 1000
mu1 = 1.
mu2 = 1.
K = 1.
D1 = 1.
D2 = 1.
mesh = Grid1D(dx=L / 1000, nx=nx)
x = mesh.cellCenters[0]
convCoeff = g*(x-L/2)
u10 = 4*L/10 < x < 6*L/10
u20 = 1.
u1 = CellVariable(name="u1", mesh=mesh, value=u10)
u2 = CellVariable(name="u2", mesh=mesh, value=u20)
## Neumann boundary conditions
u1.faceGrad.constrain(0., where=mesh.facesLeft)
u1.faceGrad.constrain(0., where=mesh.facesRight)
u2.faceGrad.constrain(0., where=mesh.facesLeft)
u2.faceGrad.constrain(0., where=mesh.facesRight)
sourceCoeff1 = -1*mu1*u1/(K+u1)*u2
sourceCoeff2 = 1*mu2*u1/(K+u1)*u2
eq11 = (TransientTerm(var=u1) == DiffusionTerm(coeff=D1, var=u1) + ConvectionTerm(coeff=convCoeff))
eq21 = (TransientTerm(var=u2) == DiffusionTerm(coeff=D2, var=u2) + ConvectionTerm(coeff=convCoeff))
eq12 = ImplicitSourceTerm(coeff=sourceCoeff1, var=u1)
eq22 = ImplicitSourceTerm(coeff=sourceCoeff2, var=u2)
eq1 = eq11 & eq12
eq2 = eq21 & eq22
eqn = eq1 & eq2
vi = Viewer((u1, u2))
for t in range(100):
u1.updateOld()
u2.updateOld()
eqn.solve(dt=1.e-3)
vi.plot()
Thank you for any suggestion or correction.
If you happen to know a good tutorial for this specific kind of problem, I would be happy to read it, since I did not find anything better than the examples in the FiPy documentation.
python
asked 10 mins ago
Antoine
11
New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I tried to solve 1D coupled PDEs for an advection-diffusion-reaction problem with the Matlab function Pdepe (https://www.mathworks.com/help/matlab/ref/pdepe.html). This function is not working properly in my case of a high advection term as compared to the diffusion term.
Therefore, I searched and found this option of using the Python library FiPy to solve my PDEs system.
My initial conditions are u1=1 for 4*L/10
My coupled equations are of the following form:
du1/dt = d/dx(D1 * du1/dx) + g * x * du1/dx - mu1 * u1 / (K + u1) * u2
du2/dt = d/dx(D2 * du2/dx) + g * x * du2/dx + mu2 * u1 / (K + u1) * u2
I tried to write it by combining the FiPy examples (examples.convection.exponential1DSource.mesh1D, examples.levelSet.advection.mesh1D, examples.cahnHilliard.mesh2DCoupled).
The following lines are not a working example but my first attempt to write the code. This is my first use of FiPy (out of the tests and examples of the documentation), so this might seem to miss the point completely for the regular users.
Could you help me correct this code to get it working on a small number of timesteps?
from fipy import *
g = 0.66
L = 10.
nx = 1000
mu1 = 1.
mu2 = 1.
K = 1.
D1 = 1.
D2 = 1.
mesh = Grid1D(dx=L / 1000, nx=nx)
x = mesh.cellCenters[0]
convCoeff = g*(x-L/2)
u10 = 4*L/10 < x < 6*L/10
u20 = 1.
u1 = CellVariable(name="u1", mesh=mesh, value=u10)
u2 = CellVariable(name="u2", mesh=mesh, value=u20)
## Neumann boundary conditions
u1.faceGrad.constrain(0., where=mesh.facesLeft)
u1.faceGrad.constrain(0., where=mesh.facesRight)
u2.faceGrad.constrain(0., where=mesh.facesLeft)
u2.faceGrad.constrain(0., where=mesh.facesRight)
sourceCoeff1 = -1*mu1*u1/(K+u1)*u2
sourceCoeff2 = 1*mu2*u1/(K+u1)*u2
eq11 = (TransientTerm(var=u1) == DiffusionTerm(coeff=D1, var=u1) + ConvectionTerm(coeff=convCoeff))
eq21 = (TransientTerm(var=u2) == DiffusionTerm(coeff=D2, var=u2) + ConvectionTerm(coeff=convCoeff))
eq12 = ImplicitSourceTerm(coeff=sourceCoeff1, var=u1)
eq22 = ImplicitSourceTerm(coeff=sourceCoeff2, var=u2)
eq1 = eq11 & eq12
eq2 = eq21 & eq22
eqn = eq1 & eq2
vi = Viewer((u1, u2))
for t in range(100):
u1.updateOld()
u2.updateOld()
eqn.solve(dt=1.e-3)
vi.plot()
Thank you for any suggestion or correction.
If you happen to know a good tutorial for this specific kind of problem, I would be happy to read it, since I did not find anything better than the examples in the FiPy documentation.
python
asked 10 mins ago
Antoine
11
New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I tried to solve 1D coupled PDEs for an advection-diffusion-reaction problem with the Matlab function Pdepe (https://www.mathworks.com/help/matlab/ref/pdepe.html). This function is not working properly in my case of a high advection term as compared to the diffusion term.
Therefore, I searched and found this option of using the Python library FiPy to solve my PDEs system.
My initial conditions are u1=1 for 4*L/10
My coupled equations are of the following form:
du1/dt = d/dx(D1 * du1/dx) + g * x * du1/dx - mu1 * u1 / (K + u1) * u2
du2/dt = d/dx(D2 * du2/dx) + g * x * du2/dx + mu2 * u1 / (K + u1) * u2
I tried to write it by combining the FiPy examples (examples.convection.exponential1DSource.mesh1D, examples.levelSet.advection.mesh1D, examples.cahnHilliard.mesh2DCoupled).
The following lines are not a working example but my first attempt to write the code. This is my first use of FiPy (out of the tests and examples of the documentation), so this might seem to miss the point completely for the regular users.
Could you help me correct this code to get it working on a small number of timesteps?
from fipy import *
g = 0.66
L = 10.
nx = 1000
mu1 = 1.
mu2 = 1.
K = 1.
D1 = 1.
D2 = 1.
mesh = Grid1D(dx=L / 1000, nx=nx)
x = mesh.cellCenters[0]
convCoeff = g*(x-L/2)
u10 = 4*L/10 < x < 6*L/10
u20 = 1.
u1 = CellVariable(name="u1", mesh=mesh, value=u10)
u2 = CellVariable(name="u2", mesh=mesh, value=u20)
## Neumann boundary conditions
u1.faceGrad.constrain(0., where=mesh.facesLeft)
u1.faceGrad.constrain(0., where=mesh.facesRight)
u2.faceGrad.constrain(0., where=mesh.facesLeft)
u2.faceGrad.constrain(0., where=mesh.facesRight)
sourceCoeff1 = -1*mu1*u1/(K+u1)*u2
sourceCoeff2 = 1*mu2*u1/(K+u1)*u2
eq11 = (TransientTerm(var=u1) == DiffusionTerm(coeff=D1, var=u1) + ConvectionTerm(coeff=convCoeff))
eq21 = (TransientTerm(var=u2) == DiffusionTerm(coeff=D2, var=u2) + ConvectionTerm(coeff=convCoeff))
eq12 = ImplicitSourceTerm(coeff=sourceCoeff1, var=u1)
eq22 = ImplicitSourceTerm(coeff=sourceCoeff2, var=u2)
eq1 = eq11 & eq12
eq2 = eq21 & eq22
eqn = eq1 & eq2
vi = Viewer((u1, u2))
for t in range(100):
u1.updateOld()
u2.updateOld()
eqn.solve(dt=1.e-3)
vi.plot()
Thank you for any suggestion or correction.
If you happen to know a good tutorial for this specific kind of problem, I would be happy to read it, since I did not find anything better than the examples in the FiPy documentation.
python
python
asked 10 mins ago
Antoine
11
New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
Antoine
11
New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
Antoine
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New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
Antoine
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asked 10 mins ago
Antoine
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New contributor
Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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Antoine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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