1.1. Getting Started#

The ANTS package solves the discrete ordinates neutron transport equation in one-dimensional (slab and sphere), two-dimensional (rectangular), and three-dimensional (rectangular) geometry. Three-dimensional problems are currently limited to fixed source problems.

Problem Types Supported:

  • Fixed source problems: Given an external source and/or boundary source, compute the steady-state flux

  • Time-dependent problems: Solve transient problems with temporal evolution

  • Criticality (k-eigenvalue) problems: Find the effective multiplication factor and fundamental eigenmode

Acceleration Methods:

  • Hybrid methods: Collision-based decomposition for time-dependent problems

  • DMD (Dynamic Mode Decomposition): Reduced-order acceleration for multigroup problems

Discretizations:

  • Spatial: Step characteristic method or diamond difference

  • Angular: Discrete ordinates (product quadrature sets)

  • Energy: Multigroup formulation

  • Time: BDF1 (backward Euler), BDF2, Crank-Nicolson (CN), and TR-BDF2

1.1.1. Installation#

1.1.2. Required Input Data#

To solve a neutron transport problem, you need:

  1. Cross-sectional data for each material: - Total cross section (\(\sigma^{\mathrm{t}}\)) - Scattering matrix (\(\sigma^{\mathrm{s}}\)) - Fission matrix (\(\chi \, \nu \, \sigma^{\mathrm{f}}\))

  2. Geometry specification: spatial cells, material locations, dimensions

  3. Angular quadrature: discrete directions and weights

  4. Source terms: external source and/or boundary conditions

  5. Parameters: problem configuration (geometry type, discretization, time stepping, etc.)

1.1.3. Current Limitations#

  • No beta decay or delayed neutrons

  • No temperature feedback or Doppler effects

1.1.4. Notation#

Throughout the documentation, the following notation is used for problem dimensions:

  • \(I\) : Number of spatial cells in the x direction

  • \(J\) : Number of spatial cells in the y direction

  • \(K\) : Number of spatial cells in the z direction (3D)

  • \(N\) : Number of discrete angles (1D), \(N^2\) total angles (2D), or the total number of ordinates (3D, \(2 N^2\) for angular_xyz(N))

  • \(G\) : Number of energy groups

  • \(T\) : Total elapsed time

  • \(M\) : Number of different materials