Bc for multiple pde's

[s133314]

I have a basic convection-diffusion-reaction system and got most of everything implemented based on the Brusselator example. However, I want to supply different boundary conditions for the two equations. (Equation is d_tc_i=-ud_xc_i+Dd_xxc_i - kc_i)
I tried a couple of things which were not succesfull. One of my approaches was:

eq = pde.PDE({'c0': f"-{u[0]}*get_x(gradient(c0)) + {d[0]}*laplace(c0) - {k[0]}*c0",
              'c1': f"-{u[1]}*get_x(gradient(c1)) + {d[1]}*laplace(c1) - 2*{k[1]}*c1"},
             user_funcs={"get_x": lambda arr: arr[0]}, 
             bc=[{"value": bc_c0, "value": bc_c1}, #Two dirchlet bc at the left with different value 
                 {"derivative": 0.0}]) #Neuman bc for both c0 and c1 at the right

This approaches doesn't give any errors but all equations have the same left bc...
I also tried

eq = pde.PDE({'c0': f"-{u[0]}*get_x(gradient(c0)) + {d[0]}*laplace(c0) - {k[0]}*c0",
              'c1': f"-{u[1]}*get_x(gradient(c1)) + {d[1]}*laplace(c1) - 2*{k[1]}*c1"},
             user_funcs={"get_x": lambda arr: arr[0]}, 
             bc=[{"value": numpy.array([bc_c0, bc_c1])}, #Two dirchlet bc at the left with different value 
                 {"derivative": 0.0}]) #Neuman bc for both c0 and c1 at the right

But this gave an error that name 'laplace'is not defined

[s133314]

Aah I found the solution while reading another post and a bit more in the documentation. I shouldn't use bc but bc_ops.
The PDE would be defined as such than:

eq = pde.PDE({'c0': f"-{u[0]}*get_x(gradient(c0)) + {d[0]}*laplace(c0) - {k[0]}*c0",
              'c1': f"-{u[1]}*get_x(gradient(c1)) + {d[1]}*laplace(c1) - 2*{k[1]}*c1"},
             user_funcs={"get_x": lambda arr: arr[0]}, 
             bc_ops={"c0:*": [{"value": bc_c0},  {"derivative": 0.0}],
                     "c1:*": [{"value": bc_c1},  {"derivative": 0.0}]})

[sashahexe]

Aah I found the solution while reading another post and a bit more in the documentation. I shouldn't use bc but bc_ops. The PDE would be defined as such than:

eq = pde.PDE({'c0': f"-{u[0]}*get_x(gradient(c0)) + {d[0]}*laplace(c0) - {k[0]}*c0",
              'c1': f"-{u[1]}*get_x(gradient(c1)) + {d[1]}*laplace(c1) - 2*{k[1]}*c1"},
             user_funcs={"get_x": lambda arr: arr[0]}, 
             bc_ops={"c0:*": [{"value": bc_c0},  {"derivative": 0.0}],
                     "c1:*": [{"value": bc_c1},  {"derivative": 0.0}]})

Hi! I am working on a similar problem. Could I ask you to share your code if you'd be so kind? I'm getting errors when trying to use this solution for different bcs. Thank you!

[s133314]

    eq = pde.PDE({'c0': f"-{simulation_parameters['u'][0]}*get_x(gradient(c0)) + {simulation_parameters['D'][0]}*laplace(c0)",
                  'c1': f"-{simulation_parameters['u'][0]}*get_x(gradient(c1)) + {simulation_parameters['D'][1]}*laplace(c1) - {simulation_parameters['k']}*c1**1",
                  'c2': f"-{simulation_parameters['u'][0]}*get_x(gradient(c2)) + {simulation_parameters['D'][2]}*laplace(c2) + {simulation_parameters['k']}*c1**1"},
             user_funcs={"get_x": lambda arr: arr[0]}, 
             bc_ops={"c0:*": [{"value": simulation_parameters["bc"][0]}, {"derivative": 0.0}],
                     "c1:*": [{"value": simulation_parameters["bc"][1]}, {"derivative": 0.0}],  #Dirichlet one side, Neumann other side, not sure how it would work for 2D or 3D
                     "c2:*": [{"value": simulation_parameters["bc"][2]}, {"derivative": 0.0}]})

    # initialize state
    grid = pde.CartesianGrid([[0, 1]], nx, periodic=False)
    state = pde.FieldCollection([pde.ScalarField(grid, simulation_parameters["ini"][0]),
                                 pde.ScalarField(grid, simulation_parameters["ini"][1]),
                                 pde.ScalarField(grid, simulation_parameters["ini"][2])])

    # simulate the pde
    # solve the equation and store the trajectory
    storage = pde.MemoryStorage()
    sol = eq.solve(state, t_range=0.002, dt=1e-5,tracker=storage.tracker(interval=1e-3))
    c_ref = storage.data[2]

simulation_parameters is a dictionary. I'm filling that one based on reading another file so it doesn't make sense to share that part. But simulation_parameters['u'][i] is the velocity in direction i. simulation_parameters['D'][i] is the diffusion coefficient of component i. simulation_parameters['k'] is the reaction rate constant. simulation_parameters["bc"][i] is the dirichlet boundary condition of component i at zero (the boundary condition at 1 is a Neumann boundary condition. simulation_parameters["ini"][i] is the initial concentration of i