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. 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 6.000000e+10 cm; centered at the origin |
| Resolution | 32³ cells; finest Δx = 1.875000e+09 cm |
| Final comparison time | 1.500000e+00 s |
| Radiation model | FLD |
| Radiation integration | FLD backward Euler (first order in time) |
| Flux semantics | Derived FLD flux: F = -D grad E |
| Analytic reference | periodic-constant-diffusion; 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 | 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 | 0.0062500000000000003 s |
| Output interval | 0.012500000000000001 s |
| Background energy density | 1 erg/cm³ |
| Scattering coefficient χ | 1.6666666666666666e-10 cm⁻¹ |
| Gaussian width w | 6000000000 cm |
| Pulse amplitude A | 0.01 erg/cm³ |
{
"background": 1.0,
"c": 29979245800.0,
"case": "gaussian_pulse",
"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-gaussian_pulse-fld/gaussian_pulse/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": "0.0062500000000000003",
"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_GAUSSIAN_PULSE",
"rad_implicit": "on",
"rad_test_amplitude": "0.01",
"rad_test_background": "1",
"rad_test_chi": "1.6666666666666666e-10",
"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": "1.5",
"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-gaussian_pulse-fld/gaussian_pulse/l2/",
"disable_analytic": "on",
"disable_diagnostics": "on",
"disable_output": "off",
"eos": "IDEAL",
"gravity": "off",
"hard_dt": "0.0062500000000000003",
"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": "0.012500000000000001",
"omega": "0",
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"problem": "RADIATION_GAUSSIAN_PULSE",
"rad_implicit": "on",
"rad_reference": "/ddnB/work/dmarce1/octotiger-m1-fld-20261014/campaign/runs/l2-gaussian_pulse-fld/gaussian_pulse/l2/reference.bin",
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"rad_test_luminosity": "2.6981321220000001e+29",
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"radiation": "on",
"radiation_backend": "cpu",
"radiation_integrator": "backward_euler",
"radiation_limiter": "levermore_pomraning",
"radiation_model": "fld",
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"stop_step": "100000",
"stop_time": "1.5",
"unigrid": "on",
"xscale": "30000000000"
},
"conservation": [
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"dx": 1875000000.0,
"executable_sha256": "ca38f12e338eed0b7074dbb15c70c089a8d31d1c12aa87f5b044c42824721f0b",
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"L2": 9.136405637690625e-07,
"Linf": 3.4539733104743675e-06
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],
"substeps": 240
},
"inx": 8,
"length": 60000000000.0,
"level": 2,
"movie_capture": {
"hard_dt": 0.00625,
"odt": 0.0125,
"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_diffusion_coefficient": 5.99584916e+19,
"reference_exact_for_solver": false,
"reference_generator_sha256": "f4678af91ad9f7d5740a06e9d64b0b8f5b53b1874ce0fe04a3de466c4ab0f9d4",
"reference_kind": "linear-diffusion-limit",
"reference_model": "periodic-constant-diffusion",
"reference_sampling": "cell averages",
"reference_sha256": "5c92306da6245acbf1b03e0ed829d527711782f9feabae3fb98a666f630d14f5",
"status": "complete",
"time": 1.5,
"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": "Periodic constant-D heat-equation reference for the represented initial energy, D=c/(3 chi), with derived F=-D grad(E). This is a diffusion-limit reference for nonlinear Levermore-Pomraning FLD; finite-gradient limiter differences remain even with vanishing numerical error. Reported errors are slice differences."
}
Derived FLD flux maps
Accepted implicit solves
Accepted steps: 240; substeps: 240; timestep retries: 0; maximum nonlinear residual: 8.849202e-11; maximum absolute coupled energy error per accepted step: 2.719504e+15.
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 | 5.085350e-07 | 9.136406e-07 | 3.453973e-06 |
| fx | 1.954445e+03 | 2.985430e+03 | 9.510618e+03 |
| fy | 1.954445e+03 | 2.985430e+03 | 9.510618e+03 |
| fz | 2.478718e+02 | 4.367391e+02 | 1.539978e+03 |
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 | -1.667907e-16 | 1.667907e-16 |
Saved-state movie
Gaussian Pulse · L2 · FLD backward Euler
121 stored states; 121 shown. Physical time: 0–1.5 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, 0.0125, 0.025, 0.0375, 0.05625, 0.06875, 0.075, 0.0875, 0.1, 0.1125, 0.125, 0.1375, 0.15, 0.1625, 0.175, 0.1875, 0.2, 0.2125, 0.225, 0.2375, 0.25, 0.2625, 0.275, 0.2875, 0.30625, 0.31875, 0.33125, 0.34375, 0.35625, 0.36875, 0.38125, 0.39375, 0.40625, 0.41875, 0.43125, 0.44375, 0.45625, 0.46875, 0.48125, 0.49375, 0.50625, 0.51875, 0.53125, 0.54375, 0.55625, 0.56875, 0.58125, 0.59375, 0.60625, 0.61875, 0.63125, 0.64375, 0.65625, 0.66875, 0.68125, 0.69375, 0.70625, 0.71875, 0.73125, 0.74375, 0.75625, 0.76875, 0.78125, 0.79375, 0.80625, 0.81875, 0.83125, 0.84375, 0.85625, 0.86875, 0.88125, 0.89375, 0.90625, 0.91875, 0.93125, 0.94375, 0.95625, 0.96875, 0.98125, 0.99375, 1.00625, 1.01875, 1.03125, 1.04375, 1.05625, 1.06875, 1.08125, 1.09375, 1.10625, 1.11875, 1.13125, 1.14375, 1.15625, 1.16875, 1.18125, 1.1875, 1.2, 1.2125, 1.225, 1.2375, 1.25, 1.2625, 1.275, 1.2875, 1.3, 1.3125, 1.325, 1.3375, 1.35, 1.3625, 1.375, 1.3875, 1.4, 1.4125, 1.425, 1.4375, 1.45, 1.4625, 1.475, 1.4875, 1.5 s.
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. Gaussian energy excess above the recorded background uses a labeled logarithmic floor. 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 CSVGaussian analytic diffusion-limit reference binaryFinal numerical Silo (local file; excluded from staged site)