discrete1.multi_group_0d module

Infinite medium multigroup solver.

This module provides multigroup-level driver routines that orchestrate outer iterations over energy groups and angles (discrete ordinates).

Public routines include: - source_iteration: standard multigroup source iteration - discrete_ordinates: discrete ordinates for one group

The multigroup drivers expect arrays shaped as used by the rest of the package (angular and group axes as described in function docstrings).

discrete1.multi_group_0d.discrete_ordinates_aniso(flux_old, xs_total, xs_self_scatter, xs_scatter_w, off_scatter, external, angle_x, angle_w, P, P_weights)

Angular sweep for anisotropic scattering.

This function returns the updated scalar flux array evaluated at a specific energy group.

Parameters:

• flux_old (float) – Previous iterate of the scalar flux.

• xs_total (float) – Total macroscopic cross sections per material.

• xs_self_scatter (float) – Within-group Legendre scatter moments

• xs_scatter_w (numpy.ndarray, shape (L+1,)) – Precomputed (2l+1) * xs_self_scatter.

• off_scatter (float) – Off-diagonal scatter correction/source term (shape: n_cells,).

• external (numpy.ndarray) – External source array (n_angles, n_groups).

• angle_x (numpy.ndarray) – Angular ordinates (n_angles,).

• angle_w (numpy.ndarray) – Quadrature weights (n_angles,).

• P (numpy.ndarray, shape (L+1, angles)) – Precomputed P[l, n] = P_l(mu_n).

• P_weights (numpy.ndarray, shape (L+1, angles)) – Precomputed w_n * P_l(mu_n).

Returns:

Updated scalar flux for energy group.

Return type:

float

discrete1.multi_group_0d.discrete_ordinates_iso(flux_old, xs_total, xs_scatter, off_scatter, external, angle_x, angle_w)

Angular sweep for isotropic scattering.

This function returns the updated scalar flux array evaluated at a specific energy group.

Parameters:

• flux_old (float) – Previous iterate of the scalar flux.

• xs_total (float) – Total macroscopic cross sections per material.

• xs_scatter (float) – Scatter cross section used in source evaluation.

• off_scatter (float) – Off-diagonal scatter correction/source term (shape: n_cells,).

• external (numpy.ndarray) – External source array (n_angles, n_groups).

• angle_x (numpy.ndarray) – Angular ordinates (n_angles,).

• angle_w (numpy.ndarray) – Quadrature weights (n_angles,).

Returns:

Updated scalar flux for energy group.

Return type:

float

discrete1.multi_group_0d.source_iteration(flux_old, xs_total, xs_scatter, external, angle_x, angle_w, P=None, P_weights=None)

Multigroup source iteration solver - dispatches to iso or aniso variant.

Performs outer iterations over energy groups using inner discrete ordinates sweeps for each group. Off-diagonal scatter (up- and down-scatter) contributions are handled via an “off_scatter” accumulator that uses the previous and current flux iterates.

Parameters:

• flux_old (numpy.ndarray) – Initial scalar flux guess with shape (n_groups,).

• xs_total (array_like) – Total cross sections (n_groups,).

• xs_scatter (array_like) – Scatter cross sections (n_groups, n_groups).

• external (numpy.ndarray) – External source array (n_angles, n_groups) or with singleton dimensions where appropriate.

• angle_x (array_like) – Angular ordinates (n_angles,).

• angle_w (array_like) – Quadrature weights (n_angles,).

• P (numpy.ndarray, shape (L+1, angles), optional) – Precomputed Legendre polynomials. Required for anisotropic.

• P_weights (numpy.ndarray, shape (L+1, angles), optional) – Precomputed w_n * P_l(mu_n). Required for anisotropic.

Returns:

Converged scalar flux.

Return type:

numpy.ndarray, shape (n_groups,)

discrete1.multi_group_0d.source_iteration_aniso(flux_old, xs_total, xs_scatter, external, angle_x, angle_w, P, P_weights)

Multigroup source iteration for anisotropic scattering.

Identical workflow to source_iteration_iso() but each group sweep uses the full Legendre expansion of the scatter kernel. The within-group anisotropic correction is applied inside the angular sweep; only the L=0 moment drives the off-diagonal scatter term.

Parameters:

• flux_old (numpy.ndarray) – Initial scalar flux guess with shape (n_groups,).

• xs_total (array_like) – Total cross sections (n_groups,).

• xs_scatter (array_like) – Scatter cross sections (n_groups, n_groups).

• external (numpy.ndarray) – External source array (n_angles, n_groups) or with singleton dimensions where appropriate.

• angle_x (array_like) – Angular ordinates (n_angles,).

• angle_w (array_like) – Quadrature weights (n_angles,).

• P (numpy.ndarray, shape (L+1, n_angles)) – Precomputed Legendre polynomials P[l, n] = P_l(mu_n).

• P_weights (numpy.ndarray, shape (L+1, n_angles)) – Precomputed w_n * P_l(mu_n) used for flux moment accumulation.

Returns:

Converged scalar flux array with shape (n_groups,).

Return type:

numpy.ndarray

discrete1.multi_group_0d.source_iteration_iso(flux_old, xs_total, xs_scatter, external, angle_x, angle_w)

Multigroup source iteration solver for isotropic scattering.

Performs outer iterations over energy groups using inner discrete ordinates sweeps for each group. Off-diagonal scatter (up- and down-scatter) contributions are handled via an “off_scatter” accumulator that uses the previous and current flux iterates.

Parameters:

• flux_old (numpy.ndarray) – Initial scalar flux guess with shape (n_groups,).

• xs_total (array_like) – Total cross sections (n_groups,).

• xs_scatter (array_like) – Scatter cross sections (n_groups, n_groups).

• external (numpy.ndarray) – External source array (n_angles, n_groups) or with singleton dimensions where appropriate.

• angle_x (array_like) – Angular ordinates (n_angles,).

• angle_w (array_like) – Quadrature weights (n_angles,).

Returns:

Converged scalar flux array with shape (n_groups,).

Return type:

numpy.ndarray