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Rigid-Body FSI

PenguinStokes.jl provides rigid-body coupling wrappers around MovingStokesModelMono.

1. Core Types and Helpers

Main exported FSI-related symbols:

  • StokesFSIProblem, StokesFSIProblem2D
  • RigidBodyState, RigidBodyState2D, RigidBodyState3D
  • RigidBodyParams, RigidBodyParams2D, RigidBodyParams3D
  • shapes: Circle, Sphere, Ellipse, Ellipsoid
  • motion helpers: rigid_boundary_velocity, rigid_cut_bc_tuple, rigid_body_levelset

2. Governing ODEs

Translation:

\[m \frac{dV}{dt} = F_{hyd} + F_{ext}, \qquad \frac{dX}{dt} = V.\]

Rotation:

\[I \frac{d\omega}{dt} = T_{hyd} + T_{ext}\]

(with scalar I, omega in 2D and scalar/tensor inertia with vector angular velocity in 3D).

Rigid boundary velocity:

  • 2D: u_b(x) = V + omega * k × (x - X)
  • 3D: u_b(x) = V + Omega × (x - X)

3. Split Coupling (step_fsi!)

step_fsi! performs one partitioned loose-coupling update:

  1. predict rigid state over slab,
  2. solve moving-boundary fluid step,
  3. evaluate hydrodynamic force/torque from end-time static model,
  4. advance rigid ODE state (:symplectic_euler or :forward_euler).

simulate_fsi! repeats this loop and stores compact diagnostics.

4. Rotation Aliases

  • step_fsi_rotation!
  • simulate_fsi_rotation!

These are 2D aliases specialized for RigidBodyState2D workflows.

5. Strong Coupling (step_fsi_strong!)

Strong partitioned coupling is implemented via fixed-point iterations:

  • iterate between fluid solve and rigid update at t_{n+1},
  • optional relaxation: :none, :constant, :aitken,
  • convergence monitored by state-update residual,
  • optional non-converged return path (allow_nonconverged=true).

6. Force/Torque Evaluation Path

Hydrodynamic loads are computed from:

  1. solve_unsteady_moving! output,
  2. endtime_static_model(model) reconstruction,
  3. integrated_embedded_force(...) with selected pressure reconstruction.

This path is used by both split and strong coupling variants.

7. Scope and Limitations

Implemented:

  • single rigid body,
  • 2D and 3D rigid states,
  • rotational state evolution (2D and 3D),
  • split and strong coupling variants.

Current limits:

  • no contact/collision model,
  • no multi-body coupling,
  • no deformable-body model.

8. Minimal Usage Sketch

model = MovingStokesModelMono(grid, body, mu, rho; bc_u=(bc, bc), bc_cut_u=(Dirichlet(0.0), Dirichlet(0.0)))
state = RigidBodyState2D((0.5, 0.5), (0.0, 0.0); theta=0.0, omega=0.0)
params = RigidBodyParams2D(1.0, 1.0, Circle(0.1), SVector(0.0, -9.81))
fsi = StokesFSIProblem(model, state, params)
out = step_fsi!(fsi; t=0.0, dt=0.01, fluid_scheme=:CN, ode_scheme=:symplectic_euler)