Forensic Verification of a Legacy Annular-Sheet Solver Historically Intended for Injector Primary-Breakup Analysis

Abstract

Undocumented scientific solvers can remain executable after their governing derivation, assumptions, and provenance have become uncertain. This article develops a forensic verification workflow for that situation and demonstrates it on a legacy one-dimensional three-fluid flux-corrected-transport (FCT) solver historically intended for injector primary-breakup analysis through annular-sheet calculations. The workflow freezes provenance, reconstructs the implemented state, flux, source, constraints, and inverse map, proves primitive-recovery conditions, cross-checks analytical operators, verifies selected forced code paths, and separates equation, algorithm, and parameterization effects. Applied to the recovered solver, the audit establishes three principal findings. First, the velocity-difference rows are differences of unweighted constant-density Burgers-type balances rather than conventional phase momenta. Second, the analytical Jacobian is non-hyperbolic at the nominal state and real but defective at equal velocity; exact linear eigenvalue splitting is established only along four declared structured paths. Third, manufactured solutions verify selected discrete paths, but a seven-grid limited-FCT sequence does not demonstrate Cauchy convergence. The numerical campaign is necessary because low-order diffusion, componentwise limiting, and global admissibility retraction could mask or reshape the algebraic defect; varying the accepted-correction factor changes and delays resolution-dependent structure, while pure low-order transport suppresses it. Wavenumber-resolved disagreement shows no monotonic migration toward fine-grid Nyquist scales. A scale-controlled reference-repair study gives a 1.77% normalized-margin spread. The contribution is an auditable legacy-code forensics method, not a breakup theory or validation study. The recovered equation set should be regarded as deprecated for physical prediction and should not be calibrated or regularized by coefficient tuning. A rights-safe Supplement S1 accompanies the manuscript; it contains machine-readable equations, numerical records, figures, tables, manifests, checksums, source-to-claim documentation, and author-created analysis scripts, but excludes the legacy Fortran source and compiled binaries because public release rights have not been formally established. Persistent DOI archival and unaffiliated human execution remain external pre-acceptance actions.This preprint presents a forensic reconstruction, numerical verification, and structural diagnosis of a legacy three-fluid flux-corrected transport equation set developed for annular liquid-sheet applications. The work distinguishes verified implementation behaviour from observed numerical behaviour and from physical-model limitations. This version has not yet undergone formal journal peer review.