All problem comparisons · Campaign
Streaming Front: M1 RK1 and FLD backward Euler
Saved-state movies
Movies use stored numerical states, held without solution interpolation.
M1 reference: free-streaming analytic profile. Translated-front cell averages are exact at zero opacity and are a limit reference at positive opacity. A discontinuity need not converge at second order.
FLD reference: no supplied FLD spatial analytic reference. The exact M1 translated-front profile does not solve nonlinear FLD. The periodic radiation-energy integral is an exact invariant, but it does not specify the evolving spatial profile. Cross-model differences measure closure and discretization differences, not FLD error against that M1 solution.
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, qbd006, job 1094030. 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, qbd006, job 1094046. 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∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 2.595264e-01 | 3.343040e-01 | 7.341574e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.499607e+10 | 1.892654e+10 | 3.564843e+10 |
| Radiation flux y | erg/(cm^2 s) | 8.401938e-06 | 1.716893e-05 | 1.270077e-04 |
| Radiation flux z | erg/(cm^2 s) | 8.751775e-06 | 1.968885e-05 | 1.270077e-04 |
M1 RK1: model-specific reference diagnostics
free-streaming analytic profile. Translated-front cell averages are exact at zero opacity and are a limit reference at positive opacity. A discontinuity need not converge at second order.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 3.773699e-02 | 8.106375e-02 | 2.387706e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.131461e+09 | 2.430267e+09 | 7.158391e+09 |
| Radiation flux y | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 3.773699e-02 | 8.106375e-02 | 2.387706e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.131461e+09 | 2.430267e+09 | 7.158391e+09 |
| Radiation flux y | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Source slice CSV · Run metadata
FLD backward Euler: model-specific reference diagnostics
Numerical-only output: no applicable embedded reference curve or analytic error norm.
Exact integral invariant
Saved full-volume energy-history diagnostics. These check the radiation-energy integral, not an analytic spatial profile.
{
"expected_mean_radiation_energy": 0.50000000005,
"maximum_relative_integrated_energy_error": 1.5011998756400455e-15,
"reference_description": "Exact source-free periodic energy integral; no analytic spatial FLD profile is supplied",
"scope": "full-volume-energy-history"
}Source slice CSV · Run metadata
Momentum plots are omitted for this fixed-material problem. The prescribed medium acts as an external momentum reservoir; radiation can exchange momentum with it without evolving a compensating gas momentum.
Level 3
M1 RK1 ran on one QueenBee node, qbd127, job 1102694. 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: pending.
awaiting matching method. No other refinement level or physical time is substituted for a missing partner.
Matched profile coordinates and values (CSV)
M1 RK1: model-specific reference diagnostics
free-streaming analytic profile. Translated-front cell averages are exact at zero opacity and are a limit reference at positive opacity. A discontinuity need not converge at second order.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 2.033188e-02 | 5.546417e-02 | 2.233963e-01 |
| Radiation flux x | erg/(cm^2 s) | 6.096745e+08 | 1.662806e+09 | 6.697487e+09 |
| Radiation flux y | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 2.033188e-02 | 5.546417e-02 | 2.233963e-01 |
| Radiation flux x | erg/(cm^2 s) | 6.096745e+08 | 1.662806e+09 | 6.697487e+09 |
| Radiation flux y | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | erg/(cm^2 s) | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Source slice CSV · Run metadata
Momentum plots are omitted for this fixed-material problem. The prescribed medium acts as an external momentum reservoir; radiation can exchange momentum with it without evolving a compensating gas momentum.
Level 4
M1 RK1: pending.
FLD backward Euler: pending.
Momentum plots are omitted for this fixed-material problem. The prescribed medium acts as an external momentum reservoir; radiation can exchange momentum with it without evolving a compensating gas momentum.
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.