All problem comparisons · Campaign
Equilibrium Sphere: M1 RK1 and FLD backward Euler
Saved-state movies
Movies use stored numerical states, held without solution interpolation.
M1 reference: diffusion-limit analytic reference. Steady diffusion solution for a Gaussian emitter. Finite-flux nonlinear M1 and quadrature errors can produce a reference-error floor.
FLD reference: steady Gaussian-emitter diffusion-limit analytic reference. The steady Gaussian-emitter solution assumes constant linear diffusion. Saved reference values are cell averages evaluated with four Gauss points per axis. Nonlinear flux limiting, finite-domain boundary treatment, quadrature, and discretization can contribute to departures from this reference; it is not an exact stationary solution of nonlinear FLD.
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, qbd005, job 1094184. 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, qbd065, job 1094213. 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 | 5.572663e-05 | 1.740922e-04 | 1.225671e-03 |
| Radiation flux x | erg/(cm^2 s) | 7.477824e+05 | 1.970367e+06 | 1.512247e+07 |
| Radiation flux y | erg/(cm^2 s) | 7.477824e+05 | 1.970367e+06 | 1.512247e+07 |
| Radiation flux z | erg/(cm^2 s) | 1.089809e+06 | 2.360990e+06 | 1.512247e+07 |
M1 RK1: model-specific reference diagnostics
diffusion-limit analytic reference. Steady diffusion solution for a Gaussian emitter. Finite-flux nonlinear M1 and quadrature errors can produce a reference-error floor.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 4.447228e-05 | 1.327480e-04 | 7.992172e-04 |
| Radiation flux x | erg/(cm^2 s) | 8.246912e+05 | 2.499738e+06 | 1.723608e+07 |
| Radiation flux y | erg/(cm^2 s) | 8.246912e+05 | 2.499738e+06 | 1.723608e+07 |
| Radiation flux z | erg/(cm^2 s) | 1.222346e+06 | 2.726075e+06 | 1.723608e+07 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 1.431205e-05 | 5.752160e-05 | 7.992172e-04 |
| Radiation flux x | erg/(cm^2 s) | 2.047977e+05 | 9.004692e+05 | 1.723608e+07 |
| Radiation flux y | erg/(cm^2 s) | 2.047977e+05 | 9.004692e+05 | 1.723608e+07 |
| Radiation flux z | erg/(cm^2 s) | 2.047977e+05 | 9.004692e+05 | 1.723608e+07 |
Source slice CSV · Run metadata
FLD backward Euler: model-specific reference diagnostics
steady Gaussian-emitter diffusion-limit analytic reference. The steady Gaussian-emitter solution assumes constant linear diffusion. Saved reference values are cell averages evaluated with four Gauss points per axis. Nonlinear flux limiting, finite-domain boundary treatment, quadrature, and discretization can contribute to departures from this reference; it is not an exact stationary solution of nonlinear FLD.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 1.541166e-05 | 5.045256e-05 | 4.264541e-04 |
| Radiation flux x | erg/(cm^2 s) | 4.691296e+05 | 9.879944e+05 | 5.123159e+06 |
| Radiation flux y | erg/(cm^2 s) | 4.691296e+05 | 9.879944e+05 | 5.123159e+06 |
| Radiation flux z | erg/(cm^2 s) | 1.325364e+05 | 3.701645e+05 | 2.113611e+06 |
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: 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.
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.