Building a Verified Foundation for Computational Fluid-Flow Research

A verified foundation before a larger claim

The Phase I work addressed a canonical computational fluid-flow problem: the two-dimensional Taylor–Green vortex. It is a useful benchmark because an analytical solution gives the numerical methods something precise to test against. It is not an aircraft or wing-flow validation, and the programme never treated it as one.

Across milestones M1 to M3, Qonduit established the problem contract, reconciled dimensional and Reynolds-number conventions, constructed an analytical reference and defined the metrics and operational controls needed for a trustworthy run. That foundation mattered. It prevented later results from drifting between different equations, units, profiles or acceptance rules.

From equations to inspectable flow fields

M4 moved from preparation into bounded computation. It produced eight successful N16 smoke trajectories across two numerical methods, two admitted profiles, two Reynolds labels and four output times. After a retained correction, all 24 independent final gates passed, with no material discrepancies.

The accepted velocity and pressure fields also support an interactive vortex-field viewer. The viewer makes the structure of the computed flow easier to inspect while remaining tied to authenticated, admitted fields.

Numerical credibility means keeping an inconclusive result

M5 tested the numerical foundation more deeply across profiles, methods, Reynolds labels, grids and output times. All 40 process starts completed without retries, and the evidence was independently reproduced.

The spectral method produced strong finest-grid velocity results, approximately 8.58 × 10⁻¹⁵ to 1.23 × 10⁻¹⁴, meeting the programme’s internal target. The accepted finite-volume implementation did not meet the locked accuracy and second-order convergence targets: finest-grid velocity errors ranged from 0.01158 to 0.04766, with observed spatial orders from 0.8796 to 0.9579.

Those finite-volume findings remained inconclusive instead of being reframed after the fact. That is part of the result. A credible research system must be able to preserve a failed gate, explain what it means and stop before the evidence supports a larger claim.

M6 clarified the boundary

M6 produced useful scientific-integration and control learning. It showed where content integrity, issuer authority, admission checks and enforced resource limits must align before a later result can be accepted as scientific evidence.

For the Phase I submission, Qonduit therefore relies on the accepted M1–M5 evidence. M6’s unresolved scientific work remains preserved for future research. This boundary does not erase the value of M6; it makes clear which lessons improve the next programme and which results belong in the current claim set.

A disciplined pathway toward quantum methods

Qonduit’s technology screened three possible targets: a pressure-Poisson or sparse-linear solve, a declared linearized viscous substep, and a tensor-network representation within a finite-volume method.

Each target was tested against a demanding question: could it become a precise, end-to-end component whose loading, execution, measurement, reconstruction and classical comparison costs were all defensible? The current evidence did not justify admitting any of the three for end-to-end quantum execution.

No quantum execution occurred, and no quantum advantage is claimed. The useful capability is the qualification process itself: Qonduit can define candidate kernels, identify the evidence needed to support them, reject premature claims and admit a quantum target when the complete case becomes defensible.

What the programme demonstrates

This work demonstrates more than the production of a numerical answer. Qonduit can investigate a difficult problem, translate it into explicit computational contracts, build and run bounded systems, independently verify the evidence, preserve inconvenient results and communicate what the work does—and does not—support.

That combination is useful wherever a technical programme has real uncertainty, several possible solution paths and a high cost for overstating the result.

Evidence basis

This journal entry is based on Qonduit’s accepted Airbus Phase I M1–M5 records, independently reproduced M4 and M5 evidence, the bounded M4 visualization record, the M6 scientific-integration disposition, and the Airbus hybrid-target preflight assessment. Numerical values are reported only within those recorded boundaries.