Octo-TIGER radiation results

All norms/orders CSV · Conservation CSV · Movies

Norms use the full 3D domain: L1 = Σ|e|ΔV/V; L2 = √(Σe²ΔV/V); L∞ = max|e|. Orders compare matching physical times and configurations. Zero errors have no reported order.

equilibrium_sphere

Steady diffusion-limit reference; finite-flux nonlinear M1 can have a model error floor.

N	E L1	E L2	E L∞	p(L1)	p(L2)	p(L∞)
32	2.019307e-05	5.151584e-05	6.424667e-04	—	—	—
64	4.417055e-06	1.156422e-05	3.464097e-04	2.192704e+00	2.155348e+00	8.911424e-01

32³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	-6.682576e-17	6.682576e-17	1.143749e-16
fx	c * abs(initial_energy)	-2.929058e-21	2.929058e-21	3.024223e-21
fy	c * abs(initial_energy)	6.401787e-20	6.401787e-20	6.714955e-20
fz	c * abs(initial_energy)	3.943254e-20	3.943254e-20	4.048357e-20

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64³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	1.542133e-17	1.542133e-17	1.111621e-16
fx	c * abs(initial_energy)	4.431688e-22	4.431688e-22	1.908576e-21
fy	c * abs(initial_energy)	1.955632e-21	1.955632e-21	2.278035e-20
fz	c * abs(initial_energy)	7.130733e-21	7.130733e-21	1.764282e-20

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gaussian_pulse

Linearized telegraph-equation reference; finite-amplitude nonlinear M1 can have a model error floor. Energy excess uses a logarithmic display with a labeled floor; signed errors and fluxes remain linear.

N	E L1	E L2	E L∞	p(L1)	p(L2)	p(L∞)
32	2.983871e-07	3.652412e-07	9.418889e-07	—	—	—
64	8.208545e-08	1.002996e-07	2.674582e-07	1.861987e+00	1.864534e+00	1.816243e+00

32³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	-1.667907e-16	1.667907e-16	1.667907e-16
fx	c * abs(initial_energy)	8.975796e-23	8.975796e-23	1.113501e-22
fy	c * abs(initial_energy)	-3.360795e-23	3.360795e-23	1.154977e-22
fz	c * abs(initial_energy)	-1.417159e-22	1.417159e-22	1.974124e-22

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64³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	0.000000e+00	0.000000e+00	1.667907e-16
fx	c * abs(initial_energy)	-1.268104e-23	1.268104e-23	1.214705e-22
fy	c * abs(initial_energy)	-1.219528e-23	1.219528e-23	4.936945e-23
fz	c * abs(initial_energy)	4.303502e-23	4.303502e-23	1.093190e-22

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streaming_front

Exact nonlinear M1 streaming reference.

N	E L1	E L2	E L∞	p(L1)	p(L2)	p(L∞)
32	8.321504e-02	1.450355e-01	4.179089e-01	—	—	—
64	4.231950e-02	1.015654e-01	4.205968e-01	9.755217e-01	5.139971e-01	-9.249390e-03

32³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	-5.004000e-16	5.004000e-16	5.004000e-16
fx	abs(initial_component)	1.911724e-16	1.911724e-16	3.823448e-16
fy	c * abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00
fz	c * abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00

Budget summary CSV · Raw history CSV · Fraction history CSV

64³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	0.000000e+00	0.000000e+00	1.668000e-16
fx	abs(initial_component)	-1.911724e-16	1.911724e-16	1.911724e-16
fy	c * abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00
fz	c * abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00

Budget summary CSV · Raw history CSV · Fraction history CSV

streaming_wave

Exact nonlinear M1 streaming reference.

N	E L1	E L2	E L∞	p(L1)	p(L2)	p(L∞)
32	2.385068e-01	2.684704e-01	3.902711e-01	—	—	—
64	6.439468e-02	7.202155e-02	1.155435e-01	1.889017e+00	1.898262e+00	1.756041e+00

32³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00
fx	abs(initial_component)	1.788254e-16	1.788254e-16	1.788254e-16
fy	abs(initial_component)	0.000000e+00	0.000000e+00	0.000000e+00
fz	abs(initial_component)	0.000000e+00	0.000000e+00	1.788254e-16

Budget summary CSV · Raw history CSV · Fraction history CSV

64³ cells

Central cell layer at z=dx/2. Paired values CSV · Profiles PDF

Flux maps

Radiation conservation

R = Q(t) − Q(0) + B(t) − S(t). B is cumulative outward transport; S is the signed source change. Flux integrals divided by c² give radiation momentum. All plotted totals and residuals are fractions of the fixed initial magnitude |Q(0)|. Zero/negligible initial flux (|Q(0)| ≤ 64ε c|E₀|) uses the labeled fallback c|E₀|. Neither denominator changes during the run.

Field	Scale	Final R/scale	Final |R|/scale	Maximum |R|/scale
er	abs(initial_energy)	0.000000e+00	0.000000e+00	0.000000e+00
fx	abs(initial_component)	0.000000e+00	0.000000e+00	0.000000e+00
fy	abs(initial_component)	0.000000e+00	0.000000e+00	0.000000e+00
fz	abs(initial_component)	0.000000e+00	0.000000e+00	0.000000e+00

Budget summary CSV · Raw history CSV · Fraction history CSV