Gaussian Pulse: M1 RK1 and FLD backward Euler

Saved-state movies

• L0 · M1 RK1
• L0 · FLD backward Euler
• L1 · M1 RK1
• L1 · FLD backward Euler

Movies use stored numerical states, held without solution interpolation.

Level 0

M1 RK1: complete results, parameters and reference discussion

FLD backward Euler: complete results, parameters and reference discussion

matched. No other refinement level or physical time is substituted for a missing partner.

Matched profile coordinates and values (CSV)

FLD minus M1: model discrepancy on the saved slice

M1 RK1: model-specific reference diagnostics

linearized analytic reference. Fourier telegraph-equation reference for isotropic, linearized radiation moments. Nonlinear M1 can retain a closure-model error at finite amplitude.

Area-weighted reference errors on this model’s original leaf slice.

Source slice CSV · Run metadata

FLD backward Euler: model-specific reference diagnostics

periodic constant-diffusion analytic reference. Each retained Fourier mode decays as exp[-D |k|² t], with D = c/(3χ) and reference flux -D grad(E). It uses the same filtered initial energy as the M1 run, while M1 has its separate telegraph reference. This is an analytic diffusion-limit reference, not an exact solution of nonlinear flux-limited diffusion.

Area-weighted reference errors on this model’s original leaf slice.

Source slice CSV · Run metadata

Model discrepancy and input hashes (JSON)

Level 1

M1 RK1: complete results, parameters and reference discussion

FLD backward Euler: complete results, parameters and reference discussion

matched. No other refinement level or physical time is substituted for a missing partner.

Matched profile coordinates and values (CSV)

FLD minus M1: model discrepancy on the saved slice

M1 RK1: model-specific reference diagnostics

linearized analytic reference. Fourier telegraph-equation reference for isotropic, linearized radiation moments. Nonlinear M1 can retain a closure-model error at finite amplitude.

Area-weighted reference errors on this model’s original leaf slice.

Source slice CSV · Run metadata

FLD backward Euler: model-specific reference diagnostics

periodic constant-diffusion analytic reference. Each retained Fourier mode decays as exp[-D |k|² t], with D = c/(3χ) and reference flux -D grad(E). It uses the same filtered initial energy as the M1 run, while M1 has its separate telegraph reference. This is an analytic diffusion-limit reference, not an exact solution of nonlinear flux-limited diffusion.

Area-weighted reference errors on this model’s original leaf slice.

Source slice CSV · Run metadata

Model discrepancy and input hashes (JSON)

How these comparisons are measured

All field values retain their saved units. Central profiles share x coordinates and the positive row adjacent to y = z = 0. Adaptive leaf-cell averages are prolonged as constants onto the finest common Cartesian x-y partition, without extrapolation or time interpolation. Different leaf sizes may average different z extents adjacent to the plane. These are saved finite-volume slices.

Slice L₁ is mean absolute discrepancy, L₂ is root-mean-square discrepancy, and L∞ is maximum absolute discrepancy, with area weighting. These are two-dimensional diagnostics; separately labeled solver reference norms cover the full volume. Each model is measured against its own saved reference. A diffusion-limit error includes departures of the nonlinear closure from that limit.