FLD backward Euler · 32³ cells
Central cell layer at z=dx/2; ray at y=z=dx/2.
FLD backward Euler with the Levermore-Pomraning limiter; stationary material and physical c = 1 in normalized units. Radiation flux is derived from the radiation-energy gradient; it is a diagnostic, not an evolved momentum variable. Analytic references describe the linear diffusion limit and need not solve nonlinear flux-limited diffusion exactly. M1 versus FLD differences compare distinct radiation models and are not analytic-reference errors.
Recorded setup and run provenance
| Origin | Octo-TIGER application |
|---|---|
| Domain | Cube of side 2.000000e+00 (code length); centered at the origin |
| Resolution | 32³ cells; finest Δx = 6.250000e-02 (code length) |
| Final comparison time | 6.000000e+01 (code time) |
| Radiation model | FLD |
| Radiation integration | FLD backward Euler (first order in time) |
| Flux semantics | Derived FLD flux: F = -D grad E |
| Analytic reference | su-olson-linear-halfspace; linear diffusion-limit reference, not exact for the nonlinear FLD limiter |
| Reference norm scope | Area-weighted projected positive-side slice; no full-volume norm or convergence order inferred |
| Radiation backend | cpu |
| Physical light speed | 1.000000e+00 (code speed) |
| Reduced-speed factor α | 1.000000e+00 |
| Radiation transport speed | 1.000000e+00 (code speed) |
| Periodic boundaries | off |
| Hydrodynamics | off |
| Gravity | off |
| Implicit radiation source | on |
| Uniform grid | on |
| CFL | 0.4 |
| Timestep cap | 0.050000000000000003 (code time) |
| Output interval | 0.5 (code time) |
{
"background": 0.0,
"c": 1.0,
"case": "marshak",
"cells": 32,
"command": [
"/ddnB/work/dmarce1/octotiger-m1-fld-20261014/campaign/control/launch-solver",
"/ddnB/work/dmarce1/octotiger-m1-fld-20261014/build/octotiger",
"--config_file=/ddnB/work/dmarce1/octotiger-m1-fld-20261014/campaign/runs/l2-marshak-fld/marshak/l2/run.ini",
"--hpx:threads=64"
],
"comparison_signature": {
"atomic_mass": "1",
"atomic_number": "1",
"cfl": "0.4",
"code_to_cm": "1",
"code_to_g": "1",
"code_to_s": "1",
"correct_am_hydro": "off",
"disable_analytic": "on",
"disable_diagnostics": "on",
"eos": "IDEAL",
"gravity": "off",
"hard_dt": "0.050000000000000003",
"hydro": "off",
"hydro_device_kernel_type": "OFF",
"hydro_host_kernel_type": "LEGACY",
"monopole_device_kernel_type": "OFF",
"multipole_device_kernel_type": "OFF",
"n_species": "1",
"omega": "0",
"periodic": "off",
"problem": "MARSHAK",
"rad_implicit": "on",
"radiation": "on",
"radiation_algorithm_version": 1,
"radiation_integrator": "backward_euler",
"radiation_limiter": "levermore_pomraning",
"radiation_model": "fld",
"radiation_reduced_c_factor": "1",
"stop_step": "1000000",
"stop_time": "60",
"unigrid": "on",
"xscale": "1"
},
"config": {
"atomic_mass": "1",
"atomic_number": "1",
"cfl": "0.4",
"code_to_cm": "1",
"code_to_g": "1",
"code_to_s": "1",
"correct_am_hydro": "off",
"datadir": "/ddnB/work/dmarce1/octotiger-m1-fld-20261014/campaign/runs/l2-marshak-fld/marshak/l2/",
"disable_analytic": "on",
"disable_diagnostics": "on",
"disable_output": "off",
"eos": "IDEAL",
"gravity": "off",
"hard_dt": "0.050000000000000003",
"hydro": "off",
"hydro_device_kernel_type": "OFF",
"hydro_host_kernel_type": "LEGACY",
"max_level": "2",
"min_level": "2",
"monopole_device_kernel_type": "OFF",
"multipole_device_kernel_type": "OFF",
"n_species": "1",
"odt": "0.5",
"omega": "0",
"periodic": "off",
"problem": "MARSHAK",
"rad_implicit": "on",
"radiation": "on",
"radiation_backend": "cpu",
"radiation_integrator": "backward_euler",
"radiation_limiter": "levermore_pomraning",
"radiation_model": "fld",
"radiation_reduced_c_factor": "1",
"stop_step": "1000000",
"stop_time": "60",
"unigrid": "on",
"xscale": "1"
},
"conservation": [
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"executable_sha256": "ca38f12e338eed0b7074dbb15c70c089a8d31d1c12aa87f5b044c42824721f0b",
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],
"substeps": 1201
},
"inx": 8,
"length": 2.0,
"level": 2,
"marshak_capacity_ratio": 1.0,
"marshak_opacity": 100.0,
"movie_capture": {
"hard_dt": 0.05,
"odt": 0.5,
"requested_snapshots": 121,
"steps_per_output_check": 1
},
"origin": "Octo-TIGER application",
"physical_c": 1.0,
"radiation_algorithm_version": 1,
"radiation_backend": "cpu",
"radiation_equations": "stationary physical-c FLD",
"radiation_flux_semantics": "derived_fld_flux",
"radiation_integrator": "backward_euler",
"radiation_limiter": "levermore_pomraning",
"radiation_model": "fld",
"radiation_reduced_c_factor": 1.0,
"reference_exact_for_solver": false,
"reference_kind": "linear-diffusion-limit",
"reference_model": "su-olson-linear-halfspace",
"reference_sampling": "cell-center point values",
"status": "complete",
"time": 60.0,
"transport_c": 1.0,
"units": {
"c": 1.0,
"energy_density": "normalized energy density",
"flux": "normalized flux",
"length": "normalized length",
"system": "dimensionless",
"time": "normalized time"
},
"validation_scope": "Su-Olson linear nonequilibrium half-space diffusion reference, with equal radiation/material capacities. Nonlinear flux limiting and the finite far boundary can differ from the reference; reported errors are slice differences, not full-volume convergence evidence."
}
Derived FLD flux maps
Accepted implicit solves
Accepted steps: 1201; substeps: 1201; timestep retries: 0; maximum nonlinear residual: 9.526069e-11; maximum absolute coupled energy error per accepted step: 2.907708e-11.
Projected-slice differences from the analytic reference
Area-weighted L1, L2, and maximum differences on the exported positive-side slice; these are not full-volume norms or a pure discretization error. No convergence order is inferred. Energy-density and flux units are those recorded in the slice-units download.
| Field | L1 difference | L2 difference | Maximum difference |
|---|---|---|---|
| er | 1.757820e-03 | 2.736475e-03 | 6.050785e-03 |
| fx | 1.458552e-05 | 2.697280e-05 | 1.318034e-04 |
| fy | 3.478360e-18 | 8.894457e-18 | 5.920429e-17 |
| fz | 1.429447e-18 | 5.051465e-18 | 3.552451e-17 |
| material_egas | 1.757975e-03 | 2.736841e-03 | 6.051874e-03 |
Radiation energy conservation
All values below are dimensionless fractions of the fixed normalization scale at t_ref = 0.
| Field | Scale | Q(t_ref)/scale | Q(t)/scale | Boundary B/scale | Source S/scale | Residual R/scale | Maximum |R|/scale |
|---|---|---|---|---|---|---|---|
| er | Ebath V | 0.000000e+00 | 1.746101e-01 | -3.492052e-01 | -1.745952e-01 | 2.364398e-11 | 2.364778e-11 |
Saved-state movie
Marshak · L2 · FLD backward Euler
121 stored states; 121 shown. Physical time: 0–60 normalized time. Playback: 60 s.
Zero-order hold; no solution interpolation. Playback holds each saved numerical state over its time interval and includes endpoint holds.
All 121 snapshot times
Snapshot times: 0, 0.55, 1, 1.5, 2, 2.55, 3.05, 3.55, 4.05, 4.55, 5.05, 5.55, 6.05, 6.55, 7.05, 7.55, 8.05, 8.55, 9.05, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19, 19.5, 20, 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, 25.5, 26, 26.5, 27, 27.5, 28, 28.5, 29, 29.5, 30, 30.5, 31, 31.5, 32, 32.5, 33, 33.5, 34, 34.5, 35, 35.5, 36, 36.5, 37, 37.5, 38.05, 38.55, 39.05, 39.55, 40.05, 40.55, 41.05, 41.55, 42.05, 42.55, 43.05, 43.55, 44.05, 44.55, 45.05, 45.55, 46.05, 46.55, 47.05, 47.55, 48.05, 48.55, 49.05, 49.55, 50.05, 50.55, 51.05, 51.55, 52.05, 52.55, 53.05, 53.55, 54.05, 54.55, 55.05, 55.55, 56.05, 56.55, 57.05, 57.55, 58.05, 58.55, 59.05, 59.55, 60 normalized time.
Arrows show derived FLD diagnostic flux -D grad(E); radiation momentum is not evolved. Arrows have equal length and show direction only.
Final-time profiles compare FLD with a linear diffusion-limit analytic reference, not an exact solution of nonlinear flux-limited diffusion. The movie shows numerical states only.
Central z=0+ radiation energy slice with faint cell mesh and equal-length flux direction arrows. Arrows show derived FLD diagnostic flux -D grad(E); radiation momentum is not evolved. Fixed color limits; actual stored Silo times held without solution interpolation. Final-time profiles compare FLD with a linear diffusion-limit analytic reference, not an exact solution of nonlinear flux-limited diffusion. The movie shows numerical states only. The maps show the full simulation domain without cropping.
Download MP4 · Rendering and timing metadata · Full run report
Data and reproducibility
Effective configurationRun metadataSolver logNumerical/reference/difference slice CSVSlice unitsFLD diagnosticsAccepted solve history CSVSlice reference-difference norms CSVRadiation energy history CSVEnergy budget summary CSVFinal numerical Silo (local file; excluded from staged site)