API Reference

AbstractPressureGauge

Abstract supertype for pressure nullspace constraints in Stokes systems. Concrete options are PinPressureGauge and MeanPressureGauge.

PinPressureGauge(; index=nothing)

Pressure gauge that replaces one pressure equation by a pointwise pinning constraint p[index] = 0 (or the first active pressure DOF when index=nothing).

MeanPressureGauge()

Pressure gauge that replaces one pressure equation by a zero-mean pressure constraint over active pressure cells.

StokesLayout{N}

Unknown ordering for monophasic Stokes: [uomega_1; ugamma_1; ...; uomega_N; ugamma_N; pomega].

StokesLayoutTwoPhase{N}

Unknown ordering for fixed-interface two-phase Stokes: [uomega1_1; ...; uomega1_N; uomega2_1; ...; uomega2_N; ugamma1_1; ...; ugamma1_N; ugamma2_1; ...; ugamma2_N; pomega1; pomega2].

StokesModelMono{N,T}

Monophasic cut-cell Stokes model on a staggered MAC grid.

Use constructors StokesModelMono(gridp, body, mu, rho; ...) or StokesModelMono(cap_p, op_p, cap_u, op_u, mu, rho; ...).

MovingStokesModelMono{N,T}

Unsteady monophasic moving-boundary Stokes model with prescribed embedded boundary velocity through bc_cut_u.

StokesModelTwoPhase{N,T}

Fixed-interface two-phase Stokes model with phase-wise interface velocity traces ugamma1, ugamma2 and one pressure block per phase.

Use constructors StokesModelTwoPhase(gridp, body, mu1, mu2; ...) or StokesModelTwoPhase(cap_p1, op_p1, ..., cap_p2, op_p2, ...; ...).

staggered_velocity_grids(gridp)

Build component-wise staggered velocity grids from a pressure grid gridp by half-cell shifting each component grid along its own axis.

assemble_steady!(sys, model, t=0)

Assemble steady Stokes linear system into sys for StokesModelMono or StokesModelTwoPhase at time t.

Mutates sys.A and sys.b in place.

assemble_unsteady!(sys, model, x_prev, t, dt; scheme=:BE)

Assemble one unsteady theta-step system for StokesModelMono or StokesModelTwoPhase.

scheme supports :BE, :CN, or numeric theta ∈ [0,1].

assemble_unsteady_moving!(sys, model, x_prev, t, dt; scheme=:CN)

Assemble one unsteady moving-boundary theta-step system for MovingStokesModelMono, using slab geometry over [t, t+dt] and end-time box BC/gauge application.

assemble_unsteady_moving!(sys, model::MovingStokesModelTwoPhase, x_prev, t, dt; scheme=:CN)

Assemble one unsteady moving-interface theta-step system for MovingStokesModelTwoPhase, using slab geometry over [t, t+dt] and end-time box BC/gauge application.

solve_steady!(model; t=0, method=:direct, kwargs...)

Assemble and solve a steady Stokes system for StokesModelMono or StokesModelTwoPhase. Returns a LinearSystem with solution in sys.x.

solve_unsteady!(model, x_prev; t=0, dt, scheme=:BE, method=:direct, kwargs...)

Assemble and solve one unsteady theta-step for StokesModelMono or StokesModelTwoPhase.

solve_unsteady_moving!(model, x_prev; t=0, dt, scheme=:CN, method=:direct, kwargs...)

Assemble and solve one unsteady moving-boundary theta-step for MovingStokesModelMono.

solve_unsteady_moving!(model::MovingStokesModelTwoPhase, x_prev; t=0, dt, scheme=:CN, method=:direct, kwargs...)

Assemble and solve one unsteady moving-interface theta-step for MovingStokesModelTwoPhase.

embedded_boundary_quantities(model, x; mu=model.mu, pressure_reconstruction=:linear, x0=nothing)

Compute cut-boundary stress/traction diagnostics on the staggered velocity grids.

Returns a named tuple with:

• stress: stress tensors on pressure-grid cut cells
• traction: traction vectors on pressure-grid cut cells
• force_density: integrated force vectors (traction * Γ) on pressure-grid cut cells
• interface_indices: active cut-cell indices on the pressure grid
• force: total integrated force vector
• force_pressure, force_viscous: pressure/viscous splits of force
• torque: scalar in 2D or vector in 3D about x0

embedded_boundary_traction(model, x; kwargs...)

Return pressure-grid traction vectors on embedded boundary cells.

embedded_boundary_stress(model, x; kwargs...)

Return pressure-grid stress tensors on embedded boundary cells.

integrated_embedded_force(model, x; kwargs...)

Return integrated embedded-boundary force components and torque.

Circle(R)

2D rigid circular shape with radius R.

Sphere(R)

3D rigid spherical shape with radius R.

Ellipse(a, b)

2D rigid ellipse with semi-axes a and b.

Ellipsoid(a, b, c)

3D rigid ellipsoid with semi-axes a, b, and c.

Orientation2D(theta)

Planar orientation represented by a scalar angle theta (radians).

Orientation3D(Q)

3D orientation represented by a rotation matrix Q (body -> lab frame).

volume(shape)

Geometric volume (2D area for planar shapes, 3D volume for 3D shapes).

sdf(shape, xi)

Level-set convention used in moving-boundary examples (>0 inside).

body_inertia(shape, rho_body)

Return inertia for rigid-body dynamics.

• 2D shapes: scalar out-of-plane moment of inertia (per unit thickness)
• 3D sphere: scalar moment of inertia
• 3D ellipsoid: inertia tensor about center in body frame

RigidBodyState{N,T}

Translation-only rigid-body state with center position X and velocity V.

RigidBodyState2D{T}

2D rigid-body state with translation (X, V) and scalar rotation (theta, omega).

RigidBodyState3D{T}

3D rigid-body state with translation (X, V) and rotational state (Q, Omega). Q maps body-frame coordinates to lab-frame coordinates.

RigidBodyParams{N,T}

Translation-only rigid-body parameters.

RigidBodyParams2D{T,S}

2D rigid-body parameters with scalar inertia I.

RigidBodyParams3D{T,S}

3D rigid-body parameters with isotropic (I::T) or tensor (I::SMatrix) inertia.

external_force(params)

Return gravitational (and optional buoyancy-corrected) external force applied to the rigid body.

external_torque(params, state, t)

Return external torque applied to the rigid body at time t. Defaults to zero for built-in parameter/state types.

rigid_boundary_velocity(x, X, V, omega_or_Omega)
rigid_boundary_velocity(x, state)

Rigid-body boundary velocity.

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

rigid_velocity_2d(x, X, V, omega)
rigid_velocity(x, state2d)

2D convenience wrappers for rigid_boundary_velocity.

rigid_velocity(x, state2d)

2D convenience wrapper for rigid_boundary_velocity(x, state2d).

rigid_body_levelset(shape, statefun)

Build a moving level-set callback body(x..., t) from a rigid shape and a state callback statefun(t).

rigid_cut_bc_tuple(statefun, Val(N))

Build per-component cut-boundary Dirichlet BC tuple for rigid-body motion, compatible with MovingStokesModelMono(...; bc_cut_u=...).

rigid_cut_bc_tuple_2d(statefun)

2D convenience wrapper for rigid_cut_bc_tuple(statefun, Val(2)).

StokesFSIProblem

Dimension-generic rigid-body FSI wrapper around MovingStokesModelMono.

endtime_static_model(model)

Build a static StokesModelMono using the end-time capacities/operators cached by MovingStokesModelMono after assemble_unsteady_moving!/solve_unsteady_moving!.

step_fsi!(fsi; t, dt, fluid_scheme=:CN, ode_scheme=:symplectic_euler)

Advance one rigid-body FSI step with one-pass split coupling.

step_fsi_rotation!(fsi; kwargs...)

2D rotation-focused alias of step_fsi! for RigidBodyState2D.

step_fsi_strong!(fsi; ...)

Strong partitioned coupling using fixed-point iterations with optional Aitken relaxation.

simulate_fsi!(fsi; t0=0, dt, nsteps, fluid_scheme=:CN, ode_scheme=:symplectic_euler, callback=nothing)

Run repeated step_fsi! updates and return a lightweight history vector.

simulate_fsi_rotation!(fsi; kwargs...)

2D rotation-focused alias of simulate_fsi! for RigidBodyState2D.