All problem comparisons · Campaign
Gaussian Pulse: M1 RK1 and FLD backward Euler
Saved-state movies
Movies use stored numerical states, held without solution interpolation.
M1 reference: linearized analytic reference. Fourier telegraph-equation reference for isotropic, linearized radiation moments. Nonlinear M1 can retain a closure-model error at finite amplitude.
FLD reference: periodic constant-diffusion analytic reference. Each retained Fourier mode decays as exp[-D |k|² t], with D = c/(3χ) and reference flux -D grad(E). It uses the same filtered initial energy as the M1 run, while M1 has its separate telegraph reference. This is an analytic diffusion-limit reference, not an exact solution of nonlinear flux-limited diffusion.
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 1094139. 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, qbd009, job 1094158. 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 | 1.592255e-05 | 2.129693e-05 | 7.095782e-05 |
| Radiation flux x | erg/(cm^2 s) | 9.892215e+04 | 1.229774e+05 | 2.890000e+05 |
| Radiation flux y | erg/(cm^2 s) | 9.892215e+04 | 1.229774e+05 | 2.890000e+05 |
| Radiation flux z | erg/(cm^2 s) | 9.374452e+03 | 1.363121e+04 | 3.950953e+04 |
M1 RK1: model-specific reference diagnostics
linearized analytic reference. Fourier telegraph-equation reference for isotropic, linearized radiation moments. Nonlinear M1 can retain a closure-model error at finite amplitude.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 2.130774e-06 | 2.599343e-06 | 6.179307e-06 |
| Radiation flux x | erg/(cm^2 s) | 1.873297e+04 | 2.769644e+04 | 1.155563e+05 |
| Radiation flux y | erg/(cm^2 s) | 1.873297e+04 | 2.769644e+04 | 1.155563e+05 |
| Radiation flux z | erg/(cm^2 s) | 4.945954e+03 | 5.587073e+03 | 1.039545e+04 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 1.627470e-06 | 2.164338e-06 | 6.541292e-06 |
| Radiation flux x | erg/(cm^2 s) | 1.171820e+04 | 1.809334e+04 | 1.155563e+05 |
| Radiation flux y | erg/(cm^2 s) | 1.171820e+04 | 1.809334e+04 | 1.155563e+05 |
| Radiation flux z | erg/(cm^2 s) | 1.171820e+04 | 1.809334e+04 | 1.155563e+05 |
Source slice CSV · Run metadata
FLD backward Euler: model-specific reference diagnostics
periodic constant-diffusion analytic reference. Each retained Fourier mode decays as exp[-D |k|² t], with D = c/(3χ) and reference flux -D grad(E). It uses the same filtered initial energy as the M1 run, while M1 has its separate telegraph reference. This is an analytic diffusion-limit reference, not an exact solution of nonlinear flux-limited diffusion.
Area-weighted reference errors on this model’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 5.085350e-07 | 9.136406e-07 | 3.453973e-06 |
| Radiation flux x | erg/(cm^2 s) | 1.954445e+03 | 2.985430e+03 | 9.510618e+03 |
| Radiation flux y | erg/(cm^2 s) | 1.954445e+03 | 2.985430e+03 | 9.510618e+03 |
| Radiation flux z | erg/(cm^2 s) | 2.478718e+02 | 4.367391e+02 | 1.539978e+03 |
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.