Independent evidence across the solver

Purpose. Verify that a closed, uniform field remains unchanged when every boundary flux is zero. Mesh. 500 cells. Evidence and finding. The exact solution is the initial state; the reported density remains uniform at 1.0 throughout the domain.

Purpose. Test axisymmetric transient wave propagation through an expansion wave, contact discontinuity and shock. Mesh. 500 cells. Evidence and finding. Density, velocity, pressure and internal-energy profiles are compared with the reference Riemann solution; the principal wave locations and plateau states are reproduced.

Purpose. Test two-dimensional radial expansion of an inviscid pressure discontinuity. Mesh. 10,320 cells. Evidence and finding. Density, radial velocity, pressure and internal energy are compared with the published reference; NeuralFlow follows the expanding cylindrical-wave structure and its main discontinuities.

Purpose. Examine whether a vortex can be advected without excessive numerical diffusion or distortion. Mesh. The mesh count is not specified in the case summary. Evidence and finding. The vorticity profile and initial/final contours show that the transported vortex core remains clearly identifiable with limited distortion.

Purpose. Validate steady, inviscid subsonic acceleration over a channel bump. Mesh. 3,893 cells. Evidence and finding. Upper- and lower-surface Mach distributions are checked against the published bump-flow reference; NeuralFlow follows the expected acceleration and recovery.

Purpose. Test transonic acceleration and shock formation over a channel bump. Mesh. 13,608 cells. Evidence and finding. Surface Mach distributions and the shock region are compared with the published reference; the report shows the characteristic acceleration, shock and downstream recovery.

Purpose. Test steady inviscid supersonic compression and expansion over the bump. Mesh. 30,000 cells. Evidence and finding. Reference Mach profiles and the expected shock/expansion pattern are reproduced with the main discontinuities in the reported locations.

Purpose. Validate a steady oblique shock generated by a 15-degree ramp. Mesh. 165,000 cells. Evidence and finding. Against reference values of 382 K, density 2.277 and Mach 1.874, NeuralFlow reports 377.76 K, 2.231 and 1.898. The respective differences are approximately -1.11%, -2.02% and +1.30%.

Purpose. Test acceleration through a supersonic nozzle followed by a normal shock. Mesh. 8,000 cells. Evidence and finding. The axial Mach profile is compared with the analytical nozzle solution; NeuralFlow reproduces the acceleration, shock position and downstream subsonic branch.

Purpose. Validate a centered inviscid expansion around a corner. Mesh. 8,154 cells. Evidence and finding. The reference downstream Mach number is 3.237 and NeuralFlow reports 3.1896, a difference of approximately -1.46%; the contour shows the expected expansion fan and increasing Mach number.

Purpose. Examine the pressure and Mach response through a two-throat nozzle geometry. Mesh. 37,697 cells. Evidence and finding. Wall pressure, symmetry-line pressure and centreline Mach profiles are compared with the report reference, showing the expected acceleration and pressure variation through both restrictions.

Purpose. Test strong-shock capture in a supersonic channel with a forward-facing step. Mesh. 16,128 cells. Evidence and finding. The reported Mach field is assessed against the established benchmark structure and contains the principal incident, reflected and interacting shock systems.

Purpose. Test a supersonic nozzle flow disturbed by an exit obstacle or tab. Mesh. 267,200 cells. Evidence and finding. Measured wall-pressure data are compared with the NeuralFlow solution, while the Mach field shows the interaction between the supersonic flow and exit obstacle.

Purpose. Validate internal supersonic nozzle acceleration and wall-pressure development. Mesh. 70,800 cells. Evidence and finding. NeuralFlow wall pressure is compared with the Back-Massier-Gier measurements and follows the measured pressure evolution through the converging-diverging nozzle.

Purpose. Validate steady solid heat conduction with prescribed temperatures. Mesh. 500 cells. Evidence and finding. The computed temperature profile follows the analytical one-dimensional distribution and its linear gradient.

Purpose. Validate axisymmetric steady conduction with a specified heat flux and an axis boundary condition. Mesh. 500 cells. Evidence and finding. NeuralFlow reproduces the analytical constant-heat-flux temperature gradient.

Purpose. Validate Mach-3 axisymmetric external aerodynamics on the HB-2 correlation body. Mesh. 13,761 cells. Evidence and finding. The retained drag comparison uses the published supersonic wind-tunnel correlation; the NeuralFlow Mach-3 point lies close to the measured drag trend.

Purpose. Validate turbulent transonic external flow and shock formation over the RAE2822 airfoil. Mesh. 20,061 cells. Evidence and finding. Surface pressure coefficient is compared with the AGARD wind-tunnel measurements; NeuralFlow reproduces the measured surface trend and transonic shock region.

Purpose. Validate a steady turbulent compressible mixing layer between streams of different velocity. Mesh. 10,800 cells. Evidence and finding. The transverse velocity profile is checked against the Goebel-Dutton experiment; NeuralFlow captures the measured transition and shear-layer location.

Purpose. Validate multispecies supersonic mixing using the inert-gas Burrows-Kurkov configuration. Mesh. 17,180 cells. Evidence and finding. Measured species mass fractions and reported total-temperature data are used; the NeuralFlow profiles reproduce the principal mixing development.

Purpose. Test turbulent shock capture in a SCRAMJET-exhaust representation for mixture and multispecies formulations. Mesh. 29,000 and 49,960 cells. Evidence and finding. Measured afterbody pressure is used for the mixture and multispecies formulations. Both formulations reproduce the principal pressure rise associated with the reflected shock.

Purpose. Validate turbulent dispersed-particle transport through a separated backward-facing-step flow. Mesh. 30,000 cells. Evidence and finding. Particle-velocity profiles at four downstream stations are compared with the experiment; NeuralFlow captures the main acceleration and recovery trends.

Purpose. Test a steady laminar gas-particle nozzle flow across subsonic and supersonic regions. Mesh. 10,000 cells. Evidence and finding. Pressure, Mach number, particle density and particle velocity are compared with the published reference; the carrier and dispersed phases reproduce the principal acceleration and particle-response trends.

Purpose. Validate unsteady vortex shedding and pressure/velocity oscillations in the ONERA C1 planar and C1x axisymmetric solid-propellant rocket motor configurations. Configuration. The C1 case uses x-velocity probes, while the C1x case uses chamber and downstream pressure probes. Mesh. Not specified in the supplied material. Evidence and finding. NeuralFlow vorticity contours and FFT spectra of x-velocity and pressure are compared with the Kourta (1999) benchmark. The supplied comparison evaluates the dominant frequency bands and associated vortex-shedding structure.

Purpose. Evaluate transient high-supersonic aerothermal response and conjugate heat transfer in a UHTC-copper test article. Operating condition. Mach 4.57, 272 Pa free-stream pressure and 740 K free-stream temperature, evaluated to 60 s. Materials. The UHTC region uses thermal conductivity 66 W/mK, density 6,000 kg/m³ and specific heat 628 J/(kg·K); the copper region uses 401 W/mK, 8,920 kg/m³ and 384.91 J/(kg·K). Mesh. Not specified in the supplied material. Evidence and finding. NeuralFlow is compared directly with the supplied experimental temperature histories at probes P1 and P2. The solver captures the heating trend at both locations; the reported final temperature remains below the measured value, with a smaller difference at P2.

Purpose. Assess how condensed aluminum-oxide particle size and dynamic breakup/coalescence affect thrust in a representative two-dimensional solid rocket motor operating at approximately 6 MPa chamber pressure. Configuration. Al₂O₃ particles represent about 35% of the combustion-product mass; the study includes pure-gas, fixed 5, 10 and 20 µm particle cases, and dynamic one-group IATE tracking initialized at 20 µm. Mesh. Not specified in the paper. Evidence and finding. The fixed 20 µm model falls to about 95% of the reference thrust, while dynamic IATE gives the closest numerical agreement with measured motor thrust by reducing particle size in the high-shear, strongly accelerating nozzle region and limiting thermal and momentum lag.

Purpose. Test steady dispersed-phase flow through a shock. Mesh. 2,000 cells. Evidence and finding. Carrier pressure and velocity plus particle density and velocity are compared with the published reference. The comparison documents the carrier-flow and particle response through the shock and shows differences within part of the transition region.

Purpose. Assess the coupled compressible-flow / one-dimensional charring response against the published particle-free EPDM Test-B experiment. Published state. Gas temperature 3016 °C (3289.15 K), chamber pressure 6 MPa, gas speed 42 m/s, exposure time 9 s and no particle phase. The reported external ablation rate is 0.121 mm/s.

Reconstruction. NeuralFlow uses a two-dimensional flat-plate reconstruction with a one-dimensional charring wall and a local 0–50 mm comparison interval. Exact coupon dimensions and upstream boundary-layer development are not fully reported in the source paper, so this is not presented as an exact reproduction of the experimental geometry.

Reconstructed Test-B comparison setup: the published hot-gas state drives the 2-D flat plate, with the primary comparison taken over the local 0–50 mm charring-wall interval.

Evidence and finding. On the fine boundary-layer mesh, the mean equivalent decomposition rate over the comparison interval is 0.121875 mm/s, with mean turbulent-wall y+ = 0.094. On the coarse boundary-layer mesh, the corresponding mean rate is 0.098593 mm/s and mean y+ = 106.36. The fine result is numerically very close to the published 0.121 mm/s measurement, while the coarse case shows stronger streamwise variation and reduced agreement.

Fine-wall result over the reconstructed 0–50 mm interval. The line is the NeuralFlow equivalent decomposition rate; the published Test-B scalar is shown as the experimental reference.

Interpretation. The published experiment measures external material loss/recession, while the current NeuralFlow quantity is equivalent virgin-to-char decomposition with retained char on a fixed CFD wall. These are related but not identical observables, so the numerical closeness should not be interpreted as a strict ablation prediction error.

Reference. Y. Liu, S. Yang, G. He and J. Li, “An overall ablation model of ethylene-propylene-diene monomer based on porous characteristics in char layer,” Advances in Mechanical Engineering, 8(2), 2016, doi:10.1177/1687814016632415.

Additional SRM validation. The charring model has also been validated against real solid-rocket-motor cases. Those datasets are not shown here because the underlying information is proprietary/classified and publication permission was not available at the time of release.

Purpose. Validate low-speed viscous flow with a moving wall at Reynolds number 100. Mesh. 5,944 cells. Evidence and finding. Centreline velocity profiles are compared with the Ghia reference and reproduce the primary recirculation and reference velocity distribution.

Purpose. Validate the moving-wall cavity at Reynolds number 1,000. Mesh. 5,944 cells. Evidence and finding. Centreline velocity profiles agree with the Ghia reference trends, including the stronger primary vortex and secondary corner structures.