All problem comparisons · Campaign
Marshak: Euler and ADER2
Reference: Su–Olson diffusion reference. The supplied Su–Olson radiation/material reference solves the linear thermal-capacity diffusion problem in normalized units. The saved parameter values define its match to the source model; diffusion and finite-speed M1 transport can differ. Reference values are evaluated at cell centers, without an additional cell-volume average.
Coupled ADER2 accuracy remains under investigation. A completed run or a small difference does not establish uniform second-order accuracy.
Revision 6 validation limits. Streaming-wave temporal-order thresholds failed at limiter transitions even with resolved references. Optically thick radiation temporal probes remain unresolved under the unchanged 1e-12 measurement guard. Strict stiff coupled temporal tests have not been rerun for revision 6 and remain an open limitation.
Level 2
Euler (first order): complete results, parameters and reference discussion
Coupled ADER2: 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)
ADER2 minus Euler: slice discrepancy
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 8.318004e-02 | 3.046462e-01 | 1.447607e+00 |
| Radiation flux x | normalized flux | 2.273613e-03 | 8.824560e-03 | 4.698007e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 8.267613e-02 | 3.033556e-01 | 1.443975e+00 |
Euler (first order) versus Su–Olson diffusion reference
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 5.825905e-02 | 1.963974e-01 | 8.907747e-01 |
| Radiation flux x | normalized flux | 4.134736e-03 | 1.438703e-02 | 7.059959e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 5.796755e-02 | 1.956904e-01 | 8.869638e-01 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 5.825905e-02 | 1.963974e-01 | 8.907747e-01 |
| Radiation flux x | normalized flux | 4.134736e-03 | 1.438703e-02 | 7.059959e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 5.796755e-02 | 1.956904e-01 | 8.869638e-01 |
Source slice CSV · Run metadata
Coupled ADER2 versus Su–Olson diffusion reference
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.939480e-02 | 1.522552e-01 | 8.594192e-01 |
| Radiation flux x | normalized flux | 2.941168e-03 | 1.359233e-02 | 7.580205e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.915356e-02 | 1.515333e-01 | 8.553697e-01 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.939480e-02 | 1.522552e-01 | 8.594192e-01 |
| Radiation flux x | normalized flux | 2.941168e-03 | 1.359233e-02 | 7.580205e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.915356e-02 | 1.515333e-01 | 8.553697e-01 |
Level 3
Euler (first order): complete results, parameters and reference discussion
Coupled ADER2: 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)
ADER2 minus Euler: slice discrepancy
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 4.822940e-02 | 2.034221e-01 | 1.104716e+00 |
| Radiation flux x | normalized flux | 2.263366e-03 | 8.809519e-03 | 4.676294e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 4.801267e-02 | 2.029451e-01 | 1.105102e+00 |
Euler (first order) versus Su–Olson diffusion reference
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.876046e-02 | 1.117458e-01 | 6.246538e-01 |
| Radiation flux x | normalized flux | 2.266185e-03 | 1.044080e-02 | 7.504904e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.864960e-02 | 1.115211e-01 | 6.247201e-01 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.876046e-02 | 1.117458e-01 | 6.246538e-01 |
| Radiation flux x | normalized flux | 2.266185e-03 | 1.044080e-02 | 7.504904e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.864960e-02 | 1.115211e-01 | 6.247201e-01 |
Source slice CSV · Run metadata
Coupled ADER2 versus Su–Olson diffusion reference
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.065564e-02 | 1.108698e-01 | 7.965644e-01 |
| Radiation flux x | normalized flux | 1.788943e-03 | 8.431122e-03 | 5.432214e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.054846e-02 | 1.106992e-01 | 7.967297e-01 |
Solver-reported full-volume reference norms
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | normalized energy density | 2.065564e-02 | 1.108698e-01 | 7.965644e-01 |
| Radiation flux x | normalized flux | 1.788943e-03 | 8.431122e-03 | 5.432214e-02 |
| Radiation flux y | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Radiation flux z | normalized flux | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| Material energy density | normalized energy density | 2.054846e-02 | 1.106992e-01 | 7.967297e-01 |
Level 4
Euler (first order): pending.
Coupled ADER2: pending.
How these comparisons are measured
All field values use the saved units (CGS for the seven original problems; normalized units for Marshak). The 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, with no extrapolation or time interpolation. Different leaf sizes may average different z extents adjacent to the plane. The plotted curves therefore represent the saved finite-volume slices.
Slice L₁ is mean absolute difference, L₂ is root-mean-square difference, and L∞ is maximum absolute difference, with area weighting. These are two-dimensional slice diagnostics. The separately labeled solver norms cover the full volume.
Marshak numerical values are leaf-cell averages, while the Su–Olson reference is evaluated at those cell centers without a cell-volume average. The reported reference errors include this sampling difference as well as transport/model and discretization effects.