Subcritical Shock: Euler and ADER2

Runtime revision and continuation

Revision 6 with Newton rejection classification and physical initialization for damped Radau recovery. A collectively rejected AP trial is restored and retried at the same timestep using conservative HLL fluxes for all radiation moments; existing timestep halving remains if both trials fail. Physical guards, source equations, tolerances and iteration limits are unchanged. HLL fallback can change diffusion-limit accuracy on affected steps; no universal second-order or AP accuracy is claimed. Same physical model with a qualified realizability recovery change. An AP trial rejection can trigger a conservative whole-step HLL fallback. This may change diffusion-limit accuracy on fallback steps; no universal order or AP claim is made. Earlier completed results retain their original runtime and source hashes. Approved comparisons spanning revisions are explicitly qualified; their differences include runtime-revision effects. Checkpoint continuations retain states from both runtime segments and are excluded from clean timing claims. Conservation diagnostics reset at the checkpoint. Displayed new-ledger budgets cover only the resumed segment, with its own starting totals. The original raw ledger is retained separately; its abandoned post-checkpoint tail is not used.

Per-run runtime identities and qualifications

Reference: no supplied analytic or digitized numerical profile. Ensman (1994), Figure 9, is the existing published numerical comparison target. Its curves are not embedded; the local Cartesian adaptation differs from that original setup.

Ensman (1994). Method-to-method differences below measure disagreement, not error against an exact solution. Per-method pages retain their numerical resolution comparisons.

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): pending.

Coupled ADER2: interrupted.

Quantitative comparison and input hashes (JSON)

Level 3

Euler (first order): pending.

Coupled ADER2: pending.

Quantitative comparison and input hashes (JSON)

Level 4

Euler (first order): pending.

Coupled ADER2: pending.

Quantitative comparison and input hashes (JSON)

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.