Data-Free Finite-Volume Convolutional Neural Networks for Steady Compressible Euler Flow around a Circular Cylinder

arXiv:2603.01001v2 Announce Type: replace-cross Abstract: A data-free finite-volume convolutional neural network (FV-CNN) is formulated for steady Euler flow around a cylinder at eight Mach numbers, 2--15. Shared-face fluxes define conservative spatial balances, while automatic differentiation supplies parameter gradients. The derivative mismatch in the earlier automatic-differentiation-based convolutional neural network (AD-CNN) is derived. No computational fluid dynamics (CFD) or experimental field targets enter training; reference-independent selection of coefficients, seeds, and checkpoints is not established. Billig-based upstream fixing conditions shock-location agreement.For eight adopted fields, density and pressure relative $L_2$ discrepancies from finite-resolution CFD are $5.43$--$18.69\%$ and $6.25$--$19.70\%$. Closed-band defects are smaller than AD-CNN in 32/32 self-centered and 22--31/32 CFD-centered comparisons over seven half-widths, 0.06--0.12 cylinder diameters. AD-CNN retains smaller enthalpy root-mean-square (RMS) discrepancies in 7/8 cases, shock-position RMS at Mach 11 and 15, and temperature and transverse-velocity discrepancies at Mach 3.Ten new Mach-15 initializations and adopted seed 42 yield density discrepancies of $12.04$--$43.70\%$ (mean $24.34\%$, sample standard deviation $11.78$ percentage points); the new ten alone give $25.04\%$ and $12.17$ points. Dispersion exceeds the historical adopted-field gap of $3.40$ points; six of eleven outcomes are below AD-CNN. Transition-width ratios of AD-CNN to FV-CNN remain $4.07$--$4.66$, and all 44 self-centered seed--component balances at half-width 0.10 cylinder diameters are smaller for FV-CNN. Local sharpness and this balance metric persist, while initialization-robust accuracy superiority is not established.Component interventions remain one-seed conditional responses; Mach 2 uses a separate budget-limited protocol.