Norms use the entire 3D domain: L1 = Σ|e|ΔV/V, L2 = √(Σe²ΔV/V), L∞ = max|e|.
Orders are p = log(error coarse / error fine) / log(Δx coarse / Δx fine), measured at the same final time.
Zero norms have no reported order. CGS: positions and cell sizes in cm, time in s, E and its errors in erg/cm³, Fx,Fy,Fz and their errors in erg/(cm² s). CSV numbers use these same units.
The central cell layer moves toward z=0 with refinement; each numerical value is compared to its own matched cell average.
The first-order time update can limit smooth-case convergence. A moving discontinuity can have different orders in different norms.
These figures show measurements; they do not apply the CTest pass/fail thresholds.
Equilibrium sphere
Linearized / diffusion-limit reference; finite-amplitude nonlinear M1 has a model error floor.
Convergence PDF
Energy errors (erg/cm³) and observed orders
32³ cells — level 2
Slice at z = 9.375000e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
64³ cells — level 3
Slice at z = 4.687500e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
Gaussian pulse
Linearized / diffusion-limit reference; finite-amplitude nonlinear M1 has a model error floor.
Convergence PDF
Energy errors (erg/cm³) and observed orders
32³ cells — level 2
Slice at z = 9.375000e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
64³ cells — level 3
Slice at z = 4.687500e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
Streaming front
Exact nonlinear M1 streaming reference.
Convergence PDF
Energy errors (erg/cm³) and observed orders
32³ cells — level 2
Slice at z = 9.375000e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
64³ cells — level 3
Slice at z = 4.687500e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
Streaming wave
Exact nonlinear M1 streaming reference.
Convergence PDF
Energy errors (erg/cm³) and observed orders
32³ cells — level 2
Slice at z = 9.375000e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
64³ cells — level 3
Slice at z = 4.687500e+08 cm. Profiles at y = z = Δx/2.
Paired values CSV · Profiles PDF
· CSV units
Flux slice maps
Fx PDF
Fy PDF
Fz PDF
Radiation conservation
Full-domain integrals Q = ∫(E, Fx, Fy, Fz) dV. The budget residual is
R(t) = Q(t) − Q(0) + B(t) − S(t), where B is cumulative net outward boundary transport
and S is the cumulative signed change actually applied by radiation source updates.
Physical sources and boundary transport can change the radiation totals.
Radiation momentum is ∫F dV / c²; division by c² gives the same relative budget errors.
Normalized errors are |R(t)| / scale(t). For E, scale = max(|E₀|, |E(t)|, |B_E(t)|, |S_E(t)|).
For each flux component, scale also includes c times this energy scale and that component's
|Q₀|, |Q(t)|, |B(t)| and |S(t)|. This remains defined for zero net flux.
A zero scale with zero residual reports zero; no fixed physical-unit floor is used.
Maximum errors cover all recorded timesteps.
Conservation history CSV ·
Budget summary CSV ·
Budget summary JSON ·
CSV units ·
History PNG ·
History PDF
