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 = 29979245800 cm/s. Radiation flux is derived from the radiation-energy gradient; it is a diagnostic, not an evolved momentum variable. No independent analytic or digitized FLD reference profile is supplied. 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 6.000000e+10 cm; centered at the origin |
| Resolution | 32³ cells; finest Δx = 1.875000e+09 cm |
| Final comparison time | 2.000000e-01 s |
| Radiation model | FLD |
| Radiation integration | FLD backward Euler (first order in time) |
| Flux semantics | Derived FLD flux: F = -D grad E |
| Analytic reference | No analytic spatial FLD solution supplied; exact periodic energy integral checked separately |
| Reference norm scope | No analytic-profile norms or convergence orders |
| Radiation backend | cpu |
| Physical light speed | 2.997925e+10 cm/s |
| Reduced-speed factor α | 1.000000e+00 |
| Radiation transport speed | 2.997925e+10 cm/s |
| Periodic boundaries | on |
| Hydrodynamics | off |
| Gravity | off |
| Implicit radiation source | on |
| Uniform grid | on |
| CFL | 0.4 |
| Timestep cap | 0.001 s |
| Output interval | 0.0016666666666666668 s |
{
"analytic_mean_energy": 0.50000000005,
"background": 1.0,
"c": 29979245800.0,
"case": "streaming_front",
"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-streaming_front-fld/streaming_front/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",
"disable_analytic": "on",
"disable_diagnostics": "on",
"eos": "IDEAL",
"gravity": "off",
"hard_dt": "0.001",
"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": "on",
"problem": "RADIATION_STREAMING_FRONT",
"rad_implicit": "on",
"rad_test_amplitude": "0.01",
"rad_test_background": "1",
"rad_test_chi": "1.6666666666666668e-15",
"rad_test_luminosity": "2.6981321220000001e+29",
"rad_test_width": "6000000000",
"radiation": "on",
"radiation_algorithm_version": 1,
"radiation_integrator": "backward_euler",
"radiation_limiter": "levermore_pomraning",
"radiation_model": "fld",
"radiation_reduced_c_factor": "1",
"stop_step": "100000",
"stop_time": "0.20000000000000001",
"unigrid": "on",
"xscale": "30000000000"
},
"config": {
"atomic_mass": "1",
"atomic_number": "1",
"cfl": "0.4",
"code_to_cm": "1",
"code_to_g": "1",
"code_to_s": "1",
"datadir": "/ddnB/work/dmarce1/octotiger-m1-fld-20261014/campaign/runs/l2-streaming_front-fld/streaming_front/l2/",
"disable_analytic": "on",
"disable_diagnostics": "on",
"disable_output": "off",
"eos": "IDEAL",
"gravity": "off",
"hard_dt": "0.001",
"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": "0.0016666666666666668",
"omega": "0",
"periodic": "on",
"problem": "RADIATION_STREAMING_FRONT",
"rad_implicit": "on",
"rad_test_amplitude": "0.01",
"rad_test_background": "1",
"rad_test_chi": "1.6666666666666668e-15",
"rad_test_luminosity": "2.6981321220000001e+29",
"rad_test_width": "6000000000",
"radiation": "on",
"radiation_backend": "cpu",
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"radiation_reduced_c_factor": "1",
"stop_step": "100000",
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"unigrid": "on",
"xscale": "30000000000"
},
"conservation": [
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"field": "er",
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"history_end_time": 0.2,
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"initial_fraction": 1.0,
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"executable_sha256": "ca38f12e338eed0b7074dbb15c70c089a8d31d1c12aa87f5b044c42824721f0b",
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"inx": 8,
"length": 60000000000.0,
"level": 2,
"movie_capture": {
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"odt": 0.0016666666666666668,
"requested_snapshots": 121,
"steps_per_output_check": 1
},
"origin": "Octo-TIGER application",
"physical_c": 29979245800.0,
"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": "unavailable",
"reference_model": "none",
"reference_sampling": "none",
"status": "complete",
"streaming_opacity": 1.6666666666666668e-15,
"streaming_optical_depth": 0.0001,
"time": 0.2,
"transport_c": 29979245800.0,
"units": {
"chi": "1/cm",
"energy_density": "erg/cm^3",
"flux": "erg/(cm^2 s)",
"length": "cm",
"luminosity": "erg/s",
"mass": "g",
"source": "erg/(cm^3 s)",
"system": "CGS",
"time": "s"
},
"validation_scope": "Thin positive-opacity FLD closure comparison from the same initial energy as M1. FLD derives flux down the energy gradient and does not obey the M1 unidirectional translation solution. No analytic FLD profile or profile-error norm is claimed; use periodic energy conservation, positivity and the flux bound."
}
Derived FLD flux maps
Accepted implicit solves
Accepted steps: 200; substeps: 787; timestep retries: 160; maximum nonlinear residual: 9.999201e-11; maximum absolute coupled energy error per accepted step: 4.929578e+16.
Analytic integral and physical bounds
For this source-free periodic problem the exact mean radiation energy is 5.000000e-01. The maximum relative deviation of the recorded full-volume radiation energy from that exact integral is 1.501200e-15. This checks an integral invariant, not the spatial solution.
On the exported projected slice, minimum E = 1.134382e-03; maximum |F|/(cE) = 9.999984e-01. The expected bounds are E ≥ 0 and |F|/(cE) ≤ 1. These are slice checks, not full-volume extrema.
Radiation energy conservation
All values below are dimensionless fractions of the fixed normalization scale at t_ref = 0 s.
| Field | Scale | Q(t_ref)/scale | Q(t)/scale | Boundary B/scale | Source S/scale | Residual R/scale | Maximum |R|/scale |
|---|---|---|---|---|---|---|---|
| er | |Q(t_ref)| | 1.000000e+00 | 1.000000e+00 | 0.000000e+00 | 0.000000e+00 | -5.004000e-16 | 1.668000e-15 |
Saved-state movie
Streaming Front · L2 · FLD backward Euler
121 stored states; 121 shown. Physical time: 0–0.2 s. 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, 0.002, 0.004, 0.005, 0.007, 0.009, 0.01, 0.012, 0.014, 0.015, 0.017, 0.019, 0.02, 0.022, 0.024, 0.025, 0.027, 0.029, 0.03, 0.032, 0.034, 0.035, 0.037, 0.039, 0.04, 0.042, 0.044, 0.045, 0.047, 0.049, 0.05, 0.052, 0.054, 0.055, 0.057, 0.059, 0.06, 0.062, 0.064, 0.065, 0.067, 0.069, 0.07, 0.072, 0.074, 0.075, 0.077, 0.079, 0.08, 0.082, 0.084, 0.085, 0.087, 0.089, 0.09, 0.092, 0.094, 0.095, 0.097, 0.099, 0.1, 0.102, 0.104, 0.105, 0.107, 0.109, 0.11, 0.112, 0.114, 0.115, 0.117, 0.119, 0.12, 0.122, 0.124, 0.125, 0.127, 0.129, 0.13, 0.132, 0.134, 0.135, 0.137, 0.139, 0.14, 0.142, 0.144, 0.145, 0.147, 0.149, 0.15, 0.152, 0.154, 0.155, 0.157, 0.159, 0.16, 0.162, 0.164, 0.165, 0.167, 0.169, 0.17, 0.172, 0.174, 0.175, 0.177, 0.179, 0.18, 0.182, 0.184, 0.185, 0.187, 0.189, 0.19, 0.192, 0.194, 0.195, 0.197, 0.199, 0.2 s.
Arrows show derived FLD diagnostic flux -D grad(E); radiation momentum is not evolved. Arrows have equal length and show direction only.
Movies show saved numerical states. No nonlinear FLD spatial analytic reference is supplied for this benchmark; the M1 streaming profile is not an FLD reference. The final-time report includes exact invariant checks.
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. Movies show saved numerical states. No nonlinear FLD spatial analytic reference is supplied for this benchmark; the M1 streaming profile is not an FLD reference. The final-time report includes exact invariant checks. 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 slice CSVSlice unitsFLD diagnosticsAccepted solve history CSVAnalytic integral invariant checksRadiation energy history CSVEnergy budget summary CSVFinal numerical Silo (local file; excluded from staged site)