All problem comparisons · Campaign
Subcritical Shock: M1 RK1 and FLD backward Euler
Saved-state movies
Movies use stored numerical states, held without solution interpolation.
M1 reference: no supplied analytic or digitized numerical profile. Ensman (1994), Figure 9, is the existing published numerical comparison target. Its curves are not embedded; the local Cartesian adaptation differs from that original setup.
FLD reference: no supplied independent reference profile. Moving gas and radiation evolve together with mixed-frame FLD. The published benchmark curves are not embedded; comparisons with M1 measure closure and discretization differences, not exact-solution error.
M1 and FLD solve different transport closures. Both updates are first order in time. A small model discrepancy does not establish accuracy against an exact solution. M1 evolves radiation flux; FLD reconstructs diagnostic flux from its energy gradient. Flux differences are not errors in a shared radiation-momentum conservation law. FLD uses physical light speed on the CPU. Moving cases include gas transport and radiation force/work; their derived lab-frame flux includes radiation enthalpy advection.
Level 2
M1 RK1 ran on one QueenBee node, qbd065, job 1094257. Its executable, source, libraries, configuration, and imported outputs are bound to the verified completion receipt.
M1 RK1: complete results, parameters and reference discussion
FLD backward Euler ran on one QueenBee node, qbd224, job 1101716. Its executable, source, libraries, configuration, and imported outputs are bound to the verified completion receipt.
FLD backward Euler: complete results, parameters and reference discussion
matched. No other refinement level or physical time is substituted for a missing partner.
Matched profile coordinates and values (CSV)
FLD minus M1: model discrepancy on the saved slice
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Gas density | g/cm^3 | 1.408353e-10 | 2.835235e-10 | 8.444841e-10 |
| Gas velocity x | cm/s | 3.478777e+04 | 8.231057e+04 | 2.834571e+05 |
| Gas velocity y | cm/s | 6.148076e-11 | 8.734386e-11 | 5.447843e-10 |
| Gas velocity z | cm/s | 4.431633e-11 | 6.287020e-11 | 3.301442e-10 |
| Gas temperature | K | 4.854880e+01 | 1.099013e+02 | 3.960508e+02 |
| Radiation temperature | K | 3.618136e+01 | 5.339379e+01 | 1.755168e+02 |
| Radiation energy density | erg/cm^3 | 2.267162e-04 | 7.115766e-04 | 3.310370e-03 |
| Radiation flux x | erg/(cm^2 s) | 1.045275e+06 | 2.407438e+06 | 7.587828e+06 |
| Radiation flux y | erg/(cm^2 s) | 2.600482e-08 | 6.688990e-08 | 6.819737e-07 |
| Radiation flux z | erg/(cm^2 s) | 2.873077e-08 | 7.423091e-08 | 5.043468e-07 |
M1 RK1: model-specific reference diagnostics
Numerical-only output: no applicable embedded reference curve or analytic error norm.
Source slice CSV · Run metadata
FLD backward Euler: model-specific reference diagnostics
Numerical-only output: no applicable embedded reference curve or analytic error norm.
Source slice CSV · Run metadata
Total gas and radiation momentum
Momentum components, magnitude, and available boundary balances
Level 3
M1 RK1: pending.
FLD backward Euler: pending.
Level 4
M1 RK1: pending.
FLD backward Euler: pending.
How these comparisons are measured
All field values retain their saved units. Central profiles share x coordinates and the positive row adjacent to y = z = 0. Adaptive leaf-cell averages are prolonged as constants onto the finest common Cartesian x-y partition, without extrapolation or time interpolation. Different leaf sizes may average different z extents adjacent to the plane. These are saved finite-volume slices.
Slice L₁ is mean absolute discrepancy, L₂ is root-mean-square discrepancy, and L∞ is maximum absolute discrepancy, with area weighting. These are two-dimensional diagnostics; separately labeled solver reference norms cover the full volume. Each model is measured against its own saved reference. A diffusion-limit error includes departures of the nonlinear closure from that limit.