discrete1.fixed1d module

Fixed source 1D transport problems.

This module provides solvers for fixed source (non-fissile) 1D transport problems using discrete ordinates methods. It includes source iteration and dynamic mode decomposition techniques.

discrete1.fixed1d.dynamic_mode_decomp(xs_total, xs_scatter, xs_fission, external, boundary, medium_map, delta_x, angle_x, angle_w, bc_x, chi=None, geometry=1, angular=False, edges=0, R=2, K=10)

Solve fixed source problem using dynamic mode decomposition.

Uses dynamic mode decomposition for reduced-order approximation of scalar flux in fixed source transport problems.

Parameters:

• xs_total (numpy.ndarray) – Total macroscopic cross section (cells, groups).

• xs_scatter (numpy.ndarray) – Scattering cross section (cells, groups).

• xs_fission (numpy.ndarray) – Fission cross section (cells, groups).

• external (numpy.ndarray) – External source (steps/1, cells, angles, groups).

• boundary (numpy.ndarray) – Boundary conditions (steps/1, 2, angles, groups).

• medium_map (numpy.ndarray) – Material region map (cells,).

• delta_x (numpy.ndarray) – Cell widths (cells,).

• angle_x (numpy.ndarray) – Discrete ordinates (angles,).

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

• bc_x (int) – Boundary condition type (0=vacuum, 1=reflective).

• geometry (int, optional) – Geometry type (1=slab, 2=cylindrical, 3=spherical).

• angular (bool, optional) – If True, return angular flux instead of scalar.

• edges (int, optional) – If 1, return fluxes at cell edges; if 0, at cell centers.

• R (int, optional) – Number of modes to retain.

• K (int, optional) – Number of snapshots for decomposition.

Returns:

Scalar flux at cell centers (cells, groups) if angular=False and edges=0, otherwise returns angular or edge flux as specified.

Return type:

numpy.ndarray

discrete1.fixed1d.known_source_calculation(flux, xs_total, xs_scatter, external, boundary, medium_map, delta_x, angle_x, angle_w, bc_x, geometry, angular, edges)

Calculate angular flux or edge flux from scalar flux.

Computes angular flux at cell centers/edges or scalar flux at cell edges from a known scalar flux solution.

Parameters:

• flux (numpy.ndarray) – Scalar flux at cell centers (cells, groups).

• xs_total (numpy.ndarray) – Total macroscopic cross section (cells, groups).

• xs_scatter (numpy.ndarray) – Scattering cross section (cells, groups).

• external (numpy.ndarray) – External source (cells, angles, groups).

• boundary (numpy.ndarray) – Boundary conditions (2, angles, groups).

• medium_map (numpy.ndarray) – Material region map (cells,).

• delta_x (numpy.ndarray) – Cell widths (cells,).

• angle_x (numpy.ndarray) – Discrete ordinates (angles,).

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

• bc_x (int) – Boundary condition type (0=vacuum, 1=reflective).

• geometry (int) – Geometry type (1=slab, 2=cylindrical, 3=spherical).

• angular (bool) – If True, return angular flux; if False, return scalar flux.

• edges (int) – If 1, return flux at cell edges; if 0, at cell centers.

Returns:

Angular flux (cells, angles, groups) if angular=True, or scalar flux at edges (cells+1, groups) if angular=False and edges=1.

Return type:

numpy.ndarray

discrete1.fixed1d.source_iteration(xs_total, xs_scatter, xs_fission, external, boundary, medium_map, delta_x, angle_x, angle_w, bc_x, chi=None, geometry=1, angular=False, edges=0)

Solve fixed source problem using source iteration.

Uses the multi-group source iteration method to solve for scalar flux (and optionally angular flux or edge fluxes) in a fixed source transport problem.

Parameters:

• xs_total (numpy.ndarray) – Total macroscopic cross section (cells, groups).

• xs_scatter (numpy.ndarray) – Scattering cross section (cells, groups).

• xs_fission (numpy.ndarray) – Fission cross section (cells, groups).

• external (numpy.ndarray) – External source (steps/1, cells, angles, groups).

• boundary (numpy.ndarray) – Boundary conditions (steps/1, 2, angles, groups).

• medium_map (numpy.ndarray) – Material region map (cells,).

• delta_x (numpy.ndarray) – Cell widths (cells,).

• angle_x (numpy.ndarray) – Discrete ordinates (angles,).

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

• bc_x (int) – Boundary condition type (0=vacuum, 1=reflective).

• geometry (int, optional) – Geometry type (1=slab, 2=cylindrical, 3=spherical).

• angular (bool, optional) – If True, return angular flux instead of scalar.

• edges (int, optional) – If 1, return fluxes at cell edges; if 0, at cell centers.

Returns:

Scalar flux at cell centers (cells, groups) if angular=False and edges=0, otherwise returns angular or edge flux as specified.

Return type:

numpy.ndarray