PenguinStokes.jl

PenguinStokes.jl assembles and solves cut-cell Stokes systems on MAC-style staggered Cartesian grids, with support for:

• monophasic steady and unsteady Stokes,
• prescribed moving embedded boundaries,
• fixed-interface two-phase Stokes,
• rigid-body FSI wrappers (split and strong coupling).

Within PenguinxCutCell, it sits on:

• CartesianGeometry.jl for geometric moments,
• CartesianOperators.jl for cut-cell operators,
• PenguinBCs.jl for BC types,
• PenguinSolverCore.jl for linear solves.

Implemented Model Families

• StokesModelMono: steady/unsteady monophasic Stokes.
• MovingStokesModelMono: unsteady monophasic moving-boundary Stokes (body(x..., t) + bc_cut_u).
• StokesModelTwoPhase: fixed-interface two-phase Stokes with shared interface velocity trace and traction/interface-force rows.
• StokesFSIProblem: rigid-body coupling layer on top of moving-boundary monophasic Stokes (2D/3D states, split and strong coupling paths).

Compact Feature Summary

See Feature Matrix for a detailed implemented/partial/missing breakdown.

Quick Start (Steady Monophasic)

using CartesianGrids, PenguinBCs, PenguinStokes

grid = CartesianGrid((0.0, 0.0), (1.0, 1.0), (33, 33))
body(x...) = -1.0

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),
    force=(0.0, 0.0),
)

sys = solve_steady!(model)

Navigation

• Models and Equations
• Algorithms
• Boundary Conditions and Gauges
• FSI
• Postprocessing
• API
• Examples and Verification
• Feature Matrix
• Developer Notes

Validation Surface

Package tests and the examples/ scripts are the primary validation surface. The examples page maps each family (MMS, Couette/Poiseuille, moving-boundary, traction/outlet/symmetry, FSI, 3D runs) to what it verifies.