Unused Boundary Condition Error while solving coupled PDEs

[DelightE99]

Hi David and Team.
I encountered an issue when trying to solve the coupled PDE equation below

It's a 1D energy equation for a porous gas-solid media and when I implemented the code below, I got the error "unused boundary conditions" and the equation was not solved.

Code

Error

I have searched the documentation to see where the source of error could be or to find a template for the coupled equations, but I haven't found any so far.

I am not sure if I am cascading the PDEs in the right format or if the problem is with the field definition or how I specified the bc's (bc didn't work so I used bc_ops)....

For better context, the boundary conditions at the left/top is Dirichlet for fluid and Neumann for solid and at the right is Neumann for both fluid and solid and I do not know how to implement that.

I would appreciate it if you point me in the right direction on this one. Thanks in advance!

[david-zwicker]

It looks as if you used the wrong syntax for setting the boundary conditions. Generally, the bc_ops argument of the PDE class expects boundary conditions given for each operator. If you want to use the same conditions for all operators in the expression for the evolution rate of a particular field, you can simply use the wildcard symbol * to denote all operators. Consequently, the definition of bc_total in your case should rather read bc_total = {"T_f:*": bc_fluid, "T_s:*": bc_solid}.

By the way, it would help tremendously if you provided the code of an actual example demonstrating the problem instead of screenshots!

[DelightE99]

Thank you so so much @david-zwicker it worked. I actually saw that on the bc_ops documentation, but I did not know how to implement it in my case. Thanks again.

And oops, my bad, here is the code (and some further questions below):

#Specifying Boundary Conditions
# Boundary conditions for fluid
bc_fluid = {
    "x-": {"value": T_hot},     # Dirichlet condition at the top
    "x+": {"derivative": 0}     # Neumann condition at the bottom
    #"x+": {"derivative": 0},   # Neumann condition at the top  
}

# Boundary conditions for solid
bc_solid = {
    "x": {"derivative": 0},   # Neumann condition at the top and bottom     
}

# Combining boundary conditions
#bc_total = {"T_f": bc_fluid, "T_s": bc_solid}
bc_total = {"T_f:*": bc_fluid, "T_s:*": bc_solid}



#Initial Conditions: Converting previous temperatures (inital conditions) to "field values" which is the right format for Pypde solver
# Define the grid
grid = CartesianGrid(bounds=[(0, TES_Height_total)], shape=(len(Temp_fluid_prev)), periodic=False)

# Convert numpy arrays to ScalarField objects
T_f = ScalarField(grid, data=Temp_fluid_prev, label='T_f')
T_s = ScalarField(grid, data=Temp_solid_prev, label='T_s')

#Combine the two fields into a FieldCollection
#FieldCollection is a Pypde object that allows to combine multiple fields (here fluid and solid) into one object
Initial_conditions = FieldCollection([T_f, T_s])
#print("Initial conditions:", Initial_conditions)


#Defining PDE with boundary conditions
eq = PDE({
    "T_f": f" ({Df}  * laplace(T_f))  +  ({-Cf}  * d_dx(T_f)) + ({Alpha_f}  * (T_s - T_f)) + ({Beta_f}  * ({Tamb} - T_f))",
    "T_s": f" ( {Ds}  * laplace(T_s)) + ( {Alpha_s}  * (T_f - T_s))"
}, bc_ops = bc_total)


#print("Grid:", grid)
#print("PDE system:", eq)

# Simulation
# Solve the coupled PDEs with initial conditions
result = eq.solve(Initial_conditions, t_range=time_simulated, dt=dt, solver="explicit")
Temp_fluid_now = result.data[0]
Temp_solid_now = result.data[1] 

Right now, the code works, but it takes a lot of time, thus, I would like to switch to an implicit solver. From the documentation, the way to implement this is via

ImplicitSolver(pde, *, maxiter=100, maxerror=0.0001, backend='auto')

But I do not know how to implement this in my solution line below (more so, especially how to provide good initial guesses to reduce computational time).

result = eq.solve(Initial_conditions, t_range=time_simulated, dt=dt, solver="explicit")

I would really appreciate your inputs on this and apologies if this seems a bit trivial.