SOLVER VERIFICATION / VALIDATION
Review a classified 63-case solver gate, exact and manufactured production-network oracles, named NAFEMS and NASA comparisons, a broader radiation corpus, one narrow hardware-TVAC case, and explicit external-evidence blockers.
63 / 63 FORMAL GATE CASES / GATE A READY / GATE B PARTIAL / GATE C BLOCKED
The three proof lines below are the fastest way to assess the current evidence. The full ledger remains available for technical review.
T3 hardware TVAC — executed
Eight production steady-state solves predict measured radiator-panel outlet temperatures with 1.000 K RMS and 1.449 K maximum residual. The model uses measured inlet temperature, branch flow, absorbed environment, geometry, and optics; no output target was fitted.
63 / 63 classified cases — passing
The machine-readable gate separates analytical verification, numerical verification, public-reference parity, hardware validation, research support, and internal regressions. A passing regression is not automatically counted as validation evidence.
Gate A ready · Gate B partial · Gate C blocked
Gate A is ready only for the declared lumped-network scope. Independent cross-tool executions are not yet attached, and no second source-complete hardware case or claim-eligible T4 flight case is complete.
T3 hardware TVAC — executed
Eight production steady-state solves predict measured radiator-panel outlet temperatures with 1.000 K RMS and 1.449 K maximum residual. The model uses measured inlet temperature, branch flow, absorbed environment, geometry, and optics; no output target was fitted.
63 / 63 classified cases — passing
The machine-readable gate separates analytical verification, numerical verification, public-reference parity, hardware validation, research support, and internal regressions. A passing regression is not automatically counted as validation evidence.
Gate A ready · Gate B partial · Gate C blocked
Gate A is ready only for the declared lumped-network scope. Independent cross-tool executions are not yet attached, and no second source-complete hardware case or claim-eligible T4 flight case is complete.
T1 — implemented
Independent linear-system solutions and prescribed nonlinear trajectories exercise the production steady-state, RK4, and implicit-Euler seams, including convergence and energy-closure checks.
T2 — implemented narrowly
Abaqus NAFEMS T2, T3, and T4 plus the NASA/NASTRAN washer problem reproduce named public targets. These cases support their encoded equations and boundary conditions, not broad equivalence to either commercial tool.
T1 — 37 / 37 checks
Howell, NASA CHAR, and Abaqus references exercise configuration factors, closure, reciprocity, surface ordering, direction, emissivity limits, radiosity, and open-environment accounting within the supported diffuse-gray scope.
T2 support — external runs pending
Tool-neutral cases, exact checkpoints, an immutable execution-evidence schema, and SATMO published inputs are frozen. SciPy, SUNDIALS, GUNNS, TNSolver, CalculiX, SATMO, and Thermal Desktop parity remain unclaimed until real external executions are attached.
T3/T4 readiness — not evidence
Source records and a fail-closed staged TVAC protocol are implemented. They define how future evidence must be acquired; they do not substitute for a second physical test or an untouched flight holdout.
Exploratory — not claim-eligible
The source-informed three-node midpoint comparison does not reproduce the published geometry, orbit, full network, or raw flight telemetry. It is retained as research history, not presented as solver validation or flight correlation.
T1 and source-derived inputs
Deep-space, heliocentric, central-body, Horizons, WebGeocalc, and local SPICE-export workflows drive forcing from explicit profile rows. The trajectory data remain externally sourced.
External forcing check — executed
All 65,952 rows in the MD5-matched public Figshare file were compared with Verixos 1/r² solar forcing: -2.164 W/m² mean bias, 2.190 W/m² RMS residual, 3.126 W/m² maximum absolute residual, and 0.438% maximum absolute percent residual. This tests solar forcing only, not spacecraft temperature prediction.
Telemetry audit — not correlation
The 42,210-row ESA PSA/PDS MIRO housekeeping table was parsed; 41,510 post-ephemeris rows were paired with JPL Horizons Sun-relative geometry. No Rosetta physical thermal model, node map, operating context, or temperature tolerance is attached, so this is not flight-temperature validation.
Published-formulation verification — not correlation
The source-locked telemetry repository, thesis, derived fixture hashes, and Eq. 34 one-node formulation are encoded. The case verifies the transcribed heat-balance formulation under stated closure assumptions; missing attitude, internal heat, as-built coupling, and source-complete thermal state prevent a flight-correlation claim.
Published source-model verification — not hardware validation
The dissertation equations and SEPP stack table are encoded as a reduced-order source-model check. Effective emissivity and specific heat come from the source vacuum run, so this verifies the published formulation rather than independent hardware or flight behavior.
T1 — implemented
Analytical cases cover full Sun, partial penumbra, full umbra, multiple occulting bodies, and row-level body overrides. This verifies illumination geometry and profile handling.
Telemetry audit — not spacecraft validation
The public housekeeping audit extracted 3,796 rows across five Celsius temperature channels. These are instrument-housekeeping data, not a validated spacecraft-bus thermal model.
T1 — implemented
Analytical cases check 1/r² solar forcing at Jupiter distance, 20 AU, and 32 AU. RTG/RHU heat, radiation dose, degradation, and mission thermal response are separate inputs and evidence needs.
Hardware validation, analytical verification, public-reference parity, and exploratory proxies are different evidence classes. They are separated here so a proxy cannot be mistaken for a validation result.
Verixos ran eight sequential steady-state production-solver cases for the NASA Shuttle Modular Radiator System TP1A test. The model predicts radiator-panel outlet temperatures from the measured inlet temperature, measured branch flow, source-reported absorbed environments, radiator geometry, and optical properties. No parameter was fitted to the eight outlet-temperature targets.
A narrow claim for steady-state radiator radiation and energy balance, including sequential coolant-temperature prediction under prescribed measured flow. The 3.333 K screen comes from the approximately 6 °F resolution reported for the plotted AJ temperature channels in Volume IV, Book 1, Table 7, and was fixed before the production solve.
Flight validation, orbital-environment validation, pump or flow-distribution prediction, or a general spacecraft-accuracy claim. The reduced-order model uses mean coolant temperature as the lumped tube temperature, and the source outputs were public before implementation.
Primary sources: Volume II, Volume III, Volume IV, Book 1, and Volume IV, Book 2.
1.1
Single-node lumped capacitance cooling
0.026% RK4 error
Bergman et al.1.2
Coupled conduction to boundary
0.030 K absolute error
Çengel & Ghajar1.3
Solar flux / deep-space balance (3 cases)
< 1 K all cases
NASA SP-81051.4
T⁴ nonlinearity — pure radiative transient
0.0014% RK4 error
Çengel & Ghajar1.5
Grey-body radiation conductor
0.0000% exact match
Bergman et al.1.6
View factor sum rule Σ Fᵢⱼ = 1
0.002% row-sum error
Howell et al.1.7
Three-surface diffuse-gray shield equilibrium
< 0.05 K shield temp error
Bergman et al.B9
Piecewise-effective conductance at cold, nominal, and hot points
0.0039% worst ΔT error
Internal regression
B10
Parallel disks, perpendicular rectangles, and concentric spheres
0.31% worst current error @ 1e5 rays
Howell et al.2B
Material-driven α_solar / ε_IR equilibrium with coating assumptions
< 1 K equilibrium error
NASA SP-8105V8
Laminar air-flow heat rejection to a fixed-temperature sink
< 0.1 K surface temp error
Bergman et al.V18
Refined transient-conduction reproduction against the public NAFEMS T3 target
< 0.1 K refined RK4 error
Abaqus NAFEMS T3V35
Steady conduction-radiation endpoint through the production network seam
< 0.5 K vs 927 K target
Abaqus NAFEMS T2V36
Structured lumped finite-volume refinement toward the point-E target
< 1.0 °C vs 18.3 °C target
Abaqus NAFEMS T4V37
Howell, NASA CHAR, and Abaqus factors through production radiation paths
37 / 37 checks passed
Howell catalogV38
Independent linear-network solutions and prescribed nonlinear transients
22 / 22 checks passed
Independent reference oracles
The repository contains a source-informed three-node comparison with midpoint temperatures reported in the SatTherm paper. It does not reproduce the published spacecraft geometry, orbit and attitude, complete thermal network, material inputs, operating timeline, or raw time-aligned flight telemetry. The proxy is therefore not a source-complete PharmaSat reproduction, not solver validation, and not flight correlation. It will remain outside public validation claims unless those inputs are obtained and the case is rebuilt with pre-registered acceptance criteria.
Use the evidence by scope: named benchmark results show solver behavior; mission decisions pair those results with project inputs, review criteria, and customer evidence.
DEMONSTRATED IN CURRENT EVIDENCE
EVIDENCE SCOPE
Mission-dependent
Use MLI abstractions for trade studies, then set project acceptance criteria with blanket-specific test or correlation evidence.
Reduced-order only
Prescribed coolant transport can be represented in a lumped network. Pump, pressure-drop, two-phase, and flow-distribution prediction are outside the validated scope.
Model-dependent
Conductance curves and operating-envelope inputs support network studies; startup, orientation, and transport limits require mission-specific characterization.
Input-sensitive
Contact conductance is an engineering input best bracketed by test data, hardware correlation, or a documented sensitivity range.
Model-dependent
Two-band and temperature-aware optics are supported; use external higher-fidelity evidence when full spectral temperature dependence drives the decision.
External comparison
Abaqus and NASTRAN handoff artifacts carry temperatures and provenance; displacement and stress acceptance occurs in the external structural workflow.
Named cases only
Public parity is scoped to the exact Abaqus NAFEMS T2, T3, and T4 plus NASA/NASTRAN cases listed on this page. No broad Abaqus, Thermal Desktop, ESATAN, or arbitrary FEA parity is claimed.
Diffuse-gray scope
The verified multisurface formulation is bounded to diffuse-gray exchange. Specular and mixed-reflection authoring states are not supported in production solver paths.
Not yet claim-eligible
A completed T4 case requires a named mission, as-flown model inputs, time-aligned telemetry, mapped channels, operating context, and pre-registered acceptance criteria.
The roadmap prioritizes broader published comparison, instrumented hardware correlation, and public flight or heritage evidence with enough context for technical review.
Runtime blocked
Run the frozen tool-neutral cases in SciPy or SUNDIALS and NASA GUNNS, TNSolver, or CalculiX; record tool version, timestamp, immutable output hash, and residuals.
Blocked on source files
Obtain the published study’s paired Thermal Desktop histories or native models before making any SATMO-to-Thermal-Desktop parity claim.
Planned
Attach frozen GMAT or near-Earth SPICE geometry and CERES flux outputs with immutable provenance and declared tolerances.
Planned
Execute the staged protocol on a source-complete test article with uncertainty, fixed calibration rules, and a preregistered held-out interval.
Planned
Requires as-flown spacecraft inputs, time-aligned temperature telemetry, orbit and attitude context, an auditable channel-to-node map, and acceptance criteria fixed before the held-out solve.
Research candidate
The public telemetry audit and geometry pairing are complete. A physical MIRO model, attitude and operations context, channel mapping, and reviewed residual tolerances are still required.
Research candidate
The source repository, thesis, and formulation are locked. A claim-eligible case still needs attitude and operations context, time-resolved internal heat, an as-built thermal network, mapped channels, and pre-registered residual criteria.
Research candidate
The published SEPP source model is encoded. Independent validation requires measured inputs and outputs not already used to fit the reduced-order source parameters.
Blocked on source data
Requires the published mission geometry, orbit and attitude, full thermal network and material inputs, operating timeline, and raw time-aligned flight telemetry.
Tell us the benchmark, deployment, or procurement scope. We’ll share the current source-backed materials relevant to that review.