Vibrated-Interface

Multiphase interfacial dynamics in vibrated domains

Linear Floquet stability analysis

Start with linear_floquet/examples/run_linear_floquet.m. It accepts SI fluid properties, two layer depths, 2D/3D Cartesian or 3D cylindrical geometry, vibration amplitude/frequency/acceleration phase, and one or more initial modal disturbances. It returns growth rates, multipliers, periodic Floquet coefficients, and time-dependent interface displacement, with plots and optional CSV/MAT output. The driver defaults to 2D Cartesian geometry, scans k_eff*h from 0.2 to 20 (81 samples), and reconstructs dynamics only for the sample with the largest growth rate. All sampled rates are saved in growth_rates.csv.

run('linear_floquet/examples/run_linear_floquet.m')
% Or:
addpath('linear_floquet')
cfg = vi_linear_defaults('cartesian3d');
result = vi_linear_floquet(cfg);

See linear_floquet/README.md for input units, spatial mode selection, the retained boundary conditions, numerical convergence checks, output dimensions, and tests. The initial disturbance amplitude and selected modes are required in addition to the material and forcing inputs. Forcing phase and disturbance phase are separate inputs. This is a linear Floquet-mode evolution, not an arbitrary initial-velocity solver or a nonlinear saturation model.

The root-level reduced solvers remain available for compatibility with older scripts. Shared coefficients now also accept unequal layer depths; omitted depths retain the original equal-depth model. The new workflow is organized in linear_floquet/; generated run folders are ignored by Git.

Weakly nonlinear analysis

The weakly_nonlinear folder contains the MATLAB coefficient engine for Floquet modes, including adjoints, quadratic-resonance tests, forced second-order fields, self/cross Landau coefficients, and the full-state cylinder_wnl_operators.m ALE discretization. Start with weakly_nonlinear/README.md and run weakly_nonlinear/tests/run_wnl_tests.m.

WNL MAT caches and reports are organized under weakly_nonlinear/data. Loaders support historical saved paths, and default WNL runs save new MAT records there.

The existing reduced interface solver supplies an independent threshold and mode-validation target. Converge the full-state linear recovery before using the physical nonlinear coefficients quantitatively.

The supported editable driver is weakly_nonlinear/examples/vi_wnl_user_run_full_cylinder.m. It accepts one or two Floquet modes, a user-defined magnitude and phase for each initial complex amplitude, and any requested vibration acceleration. With input.weaklyNonlinear.reference='analysisAmplitude', both modes and all nonlinear coefficients are evaluated at that physical operating point; the modes do not need a common critical acceleration. The full implementation uses Bessel-enriched radial differentiation, matched multi-domain vertical Chebyshev grids, full primitive-variable eigenpair refinement, and separate linear, coefficient, and forced-field residual gates.

The editable driver defaults to input.execution.profile='balanced'. Use development only for a quick feasibility/recovery pass and final for a resolution study and reportable coefficients. Full-eigenpair corrections anchor their phase and scale to the interface displacement and preserve the physical Bslow*phi descriptor branch, so an algebraic pressure/gauge null vector cannot masquerade as a converged interface mode. A descriptor-aware residual normalization excludes zero-mass pressure/gauge variables from the state norm while retaining every primitive equation in the residual numerator. The LSQR correction fallback also works in physical coordinates through a regularized objective assembled before column scaling, preventing that scaling from favoring a pressure-inflated candidate. Poorly solved bordered corrections are rejected before line search. A promising GMRES update whose descriptor direction is correct but whose norm is dominated by zero-mass pressure/gauge variables receives a descriptor-DAE algebraic completion. The velocity/interface variables are held fixed while only algebraic variables are recomputed in a regularized minimum-norm solve; the completed state must then pass the original physical residual and branch gates. The same pressure-safe DAE completion now treats the nonzero right-hand sides of quadratic mean/combination/second-harmonic fields. Forced corrections are physically regularized, while acceptance still uses the original forcing-relative full-operator residual. Two-mode cross branches fail fast after an invalid required field, avoiding downstream solves that cannot restore that coefficient. The cylinder forced-field solver now exploits that vibration couples adjacent Floquet harmonics only through interface-displacement columns. It factors the primitive spatial blocks, solves a small temporal interface Schur system, and reconstructs the full state before checking the original equation residual. The column-equilibrated adaptive-rank minimum-norm calculation remains the fallback; the older temporal-block GMRES path remains optional. The cylinder nonlinear action also removes the exact flat-interface linear remainder before directional differentiation and checks a factor-of-two step sequence with Richardson extrapolation. This prevents linear cancellation error from appearing as a spurious incompatible quadratic forcing. A near-converged full eigenpair uses temporal-block preconditioned corrections whose GMRES candidate is physically tested before any LSQR fallback. It can continue algebraically without repeating its expensive interface lift; coefficient evaluation still requires both strict residual convergence and agreement between the reduced and full operating-point exponents. Coefficient runs can also reuse coefficient-ready direct/adjoint modes from a saved recovery MAT-file. Reuse requires an exact operating-point/grid/branch signature match and rechecks every current full-operator residual and reduced/full exponent gate. By default, a coefficient run stops immediately on a cache miss instead of silently repeating an hours-long mode recovery. For two modes, numerical coefficient validity and slow-envelope validity are reported separately. An arbitrary-acceleration operating-point reduction may be computed for diagnostics, but the driver withholds a quantitative WNL transient when either retained exponent is not slow relative to the forcing. The conjugate cylinder adjoint also applies the required swap of the two axis-regularity equation rows under m -> -m; direct states and algebraic adjoints therefore use their mathematically distinct conjugation maps.