All problem comparisons · Campaign
Streaming Front: Euler and ADER2
Reference: exact analytic solution. Exact translated discontinuous-front cell averages. A discontinuity need not converge at second order.
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 | erg/cm^3 | 6.614854e-02 | 8.830900e-02 | 2.255559e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.983083e+09 | 2.647437e+09 | 6.761996e+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 |
Euler (first order) versus exact analytic solution
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 7.860673e-02 | 1.450336e-01 | 4.117855e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.356571e+09 | 4.347999e+09 | 1.234502e+10 |
| 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 | 7.860673e-02 | 1.450336e-01 | 4.117855e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.356571e+09 | 4.347999e+09 | 1.234502e+10 |
| 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
Coupled ADER2 versus exact analytic solution
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 1.409463e-01 | 1.925704e-01 | 3.813136e-01 |
| Radiation flux x | erg/(cm^2 s) | 4.225463e+09 | 5.773115e+09 | 1.143149e+10 |
| 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 | 1.409463e-01 | 1.925704e-01 | 3.813136e-01 |
| Radiation flux x | erg/(cm^2 s) | 4.225463e+09 | 5.773115e+09 | 1.143149e+10 |
| 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 |
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 | erg/cm^3 | 1.914511e-02 | 2.719212e-02 | 6.971668e-02 |
| Radiation flux x | erg/(cm^2 s) | 5.739560e+08 | 8.151992e+08 | 2.090053e+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 |
Euler (first order) versus exact analytic solution
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 7.342051e-02 | 1.396349e-01 | 3.979217e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.201091e+09 | 4.186150e+09 | 1.192939e+10 |
| 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 | 7.342051e-02 | 1.396349e-01 | 3.979217e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.201091e+09 | 4.186150e+09 | 1.192939e+10 |
| 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
Coupled ADER2 versus exact analytic solution
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 9.256562e-02 | 1.601837e-01 | 4.262564e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.775047e+09 | 4.802188e+09 | 1.277884e+10 |
| 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 | 9.256562e-02 | 1.601837e-01 | 4.262564e-01 |
| Radiation flux x | erg/(cm^2 s) | 2.775047e+09 | 4.802188e+09 | 1.277884e+10 |
| 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 |
Level 4
Euler (first order): pending.
Coupled ADER2: complete results, parameters and reference discussion
awaiting matching method. No other refinement level or physical time is substituted for a missing partner.
Matched profile coordinates and values (CSV)
Coupled ADER2 versus exact analytic solution
Area-weighted errors on this method’s original leaf slice.
| Field | Units | L₁ | L₂ | L∞ |
|---|---|---|---|---|
| Radiation energy density | erg/cm^3 | 5.704203e-02 | 1.274014e-01 | 4.547425e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.710077e+09 | 3.819398e+09 | 1.363284e+10 |
| 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 | 5.704203e-02 | 1.274014e-01 | 4.547425e-01 |
| Radiation flux x | erg/(cm^2 s) | 1.710077e+09 | 3.819398e+09 | 1.363284e+10 |
| 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 |
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.
Each method uses its own saved cell-average reference where supplied; finer meshes can change the sampled reference.