I'm working on drift-diffusion simulation and am having difficulties setting up boundary conditions to describe my system. I have the bare bones of the system attached in a .txt file.
I have the potential on the left constrained to 9 and on the right to 0 to reflect applying a 9V bias to the system. Now, what I want to include is essentially an insulating layer to the left and right side.. let's say 10 mesh cells on both sides. So, I don't want any positive or negative charges to start in those cells, or be able to flow into those cells. Is that possible? I've tried extracting the mesh face values and constraining Pion and Nion to be zero in those cells, but that didn't seem to run properly. Any advice? Justin Pothoof The University of Washington - Department of Chemistry Pre-Candidacy PhD Student Ginger Group
nx = 500 # Number of cells in system y01 = np.zeros(nx) y01[0:nx+1] = 2.5e21 # Positive ion density y02 = np.zeros(nx) y02[0:nx+1] = 2.5e21 # Negative ion density 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') 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 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 potential_equation = DiffusionTerm(coeff=1., var=potential) == -(q / epsilon) * (Pion - Nion) potential.constrain(9., where=mesh.facesLeft) potential.constrain(0., where=mesh.facesRight) eq = Pion_equation & Nion_equation & potential_equation
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