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Multicomponent demo sub bcs for EquationBC #4695

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Multicomponent demo sub bcs for EquationBC #4695

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55a3ebc
sub bcs for EquationBC
KarsKnook Oct 31, 2025
295d307
explanation sub_bcs
KarsKnook Nov 12, 2025
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14 changes: 12 additions & 2 deletions demos/multicomponent/multicomponent.py.rst
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Expand Up @@ -428,7 +428,15 @@ only apply to the normal component of H(div) functions.
Elsewhere on the boundary we enforce :math:`J_i \cdot N = 0`. Finally, instead of specifying
the value of the barycentric velocity :math:`v` on the inflows and outflows,
we enforce :math:`v = \rho^{-1}(G_1 + G_2)`. Boundary conditions that couple
unknowns and/or are nonlinear must be implemented with :class:`~.EquationBC` instead of :class:`~.DirichletBC`. ::
unknowns and/or are nonlinear must be implemented with :class:`~.EquationBC` instead of :class:`~.DirichletBC`.
Since the barycentric velocity is in :math:`[\textrm{CG}_k]^2` it has degrees of freedom located at the points
where the inlets/outlet meet the walls. Even though the boundary conditions on the inlets/outlet
and the walls are compatible at these points, :class:`~.EquationBC` enforces the boundary conditions weakly whilst
:class:`~.DirichletBC` enforces them strongly. Hence, to avoid ambiguity, we set Dirichlet boundary
conditions on the boundary of the boundary, i.e. the points where the inlets/outlet meet the walls.
To enforce these Dirichlet boundary conditions, tuples with the numbers of the boundary edges coincidental
to these points need to be constructed first. This is then passed on to a Dirichlet boundary condition
which is passed on to :class:`~.EquationBC`.::

# Reference species velocities, which we choose to symmetrize so that the molar fluxes agree
v_ref_1 = Constant(0.4e-6) # Reference inflow velocity of benzene, m / s
Expand All @@ -449,7 +457,9 @@ unknowns and/or are nonlinear must be implemented with :class:`~.EquationBC` ins
# Boundary conditions on the barycentric velocity are enforced via EquationBC
bc_data = {inlet_1_id: rho_v_inflow_1_bc_func, inlet_2_id: rho_v_inflow_2_bc_func, outlet_id: rho_v_outflow_bc_func}
F_bc = sum(inner(v - rho_inv * flux, u) * ds(*subdomain) for subdomain, flux in bc_data.items())
v_bc = EquationBC(F_bc == 0, solution, (*inlet_1_id, *inlet_2_id, *outlet_id), V=Z_h.sub(2))
ridges = [(i, j) for i in [*inlet_1_id, *inlet_2_id, *outlet_id] for j in walls_ids]
sub_bcs = [DirichletBC(Z_h.sub(2), 0, ridges)] # bc on the boundary of the boundary
v_bc = EquationBC(F_bc == 0, solution, (*inlet_1_id, *inlet_2_id, *outlet_id), V=Z_h.sub(2), bcs=sub_bcs)

# The boundary conditions on the fluxes and barycentric velocity
# Note that BCs on H(div) spaces only apply to the normal component
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