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Boundary Conditions and Gauges

This page documents boundary-condition semantics and consistency rules in the current implementation.

1. Outer Velocity BCs (bc_u)

bc_u is provided component-wise as NTuple{N,BorderConditions}.

Dirichlet

  • Physical meaning: prescribed velocity component.
  • Row effect: momentum-row elimination or distance-based weak closure depending on staggered wall collocation and strong_wall_bc.

Neumann

  • Physical meaning: prescribed normal derivative/flux of velocity component.
  • Row effect: RHS flux contribution on boundary-adjacent momentum rows.

Periodic

  • Physical meaning: periodic domain in that axis.
  • Row effect: periodic operator construction; no explicit wall overwrite row.

Traction / PressureOutlet / DoNothing

  • Physical meaning: side-level Stokes traction law.
  • Row effect: side-based overwrite of boundary momentum rows including pressure coupling and symmetric-gradient cross terms.
  • Must be declared on all velocity components on that side.

Symmetry

  • Physical meaning: axis-aligned free-slip/symmetry wall.
  • Row effect: normal velocity constrained to zero, tangential traction rows set to homogeneous condition.
  • Must be declared on all velocity components on that side.

2. Pressure Handling (bc_p + Gauge)

  • bc_p is optional (nothing by default).
  • When present, pressure wall rows can enforce Dirichlet/Neumann/Periodic wall constraints.
  • Gauge is still required (PinPressureGauge or MeanPressureGauge).

Compatibility restrictions (enforced):

  • if a side uses traction-family velocity BC (Traction, PressureOutlet, DoNothing) or Symmetry, bc_p on that side is not allowed,
  • side-level vector BCs are incompatible with periodicity in that axis.

3. Cut/Interface Velocity BCs

Monophasic cut BC (bc_cut)

  • Current support: Dirichlet only.
  • Neumann and Periodic are explicitly rejected (ArgumentError).

Moving model cut BC (bc_cut_u)

  • Per-component tuple of cut Dirichlet BCs applied at end-time in assemble_unsteady_moving!.
  • Used directly by rigid-body FSI wrappers via rigid_cut_bc_tuple.

Two-phase interface

  • StokesModelTwoPhase does not use a separate bc_cut argument.
  • Interface behavior is encoded through shared ugamma and traction/interface force rows.

4. Consistency Rules Summary

Implemented checks enforce:

  • traction-type BC must be set on all components of a side,
  • symmetry must be set on all components of a side,
  • no mixing symmetry with traction-type BC on same side,
  • pressure BC on a traction/symmetry side is disallowed,
  • gauge remains required.

5. Compact Examples

No-slip mono with pin gauge

bc = BorderConditions(; left=Dirichlet(0.0), right=Dirichlet(0.0), bottom=Dirichlet(0.0), top=Dirichlet(0.0))
model = StokesModelMono(grid, body, 1.0, 1.0; bc_u=(bc, bc), bc_cut=Dirichlet(0.0), gauge=PinPressureGauge())

Pressure outlet side law

bcx = BorderConditions(; left=Dirichlet(1.0), right=PressureOutlet(0.0), bottom=Dirichlet(0.0), top=Dirichlet(0.0))
bcy = BorderConditions(; left=Dirichlet(0.0), right=PressureOutlet(0.0), bottom=Dirichlet(0.0), top=Dirichlet(0.0))
model = StokesModelMono(grid, body, mu, rho; bc_u=(bcx, bcy), bc_cut=Dirichlet(0.0))

Unsupported cut Neumann (expected to throw)

model = StokesModelMono(grid, body, 1.0, 1.0; bc_u=(bc, bc), bc_cut=Neumann(0.0))
solve_steady!(model)  # throws ArgumentError