multigroup

Multigroup is a method used in neutron transport and reactor physics to discretize the continuous energy spectrum of neutrons into a finite set of energy groups. For each group, a group-averaged cross section is defined, and the neutron flux within the group is solved. The multigroup approach replaces the continuous-energy Boltzmann transport equation with a set of coupled equations for the group fluxes, enabling practical numerical solutions.

In practice, cross sections are collapsed from detailed energy-dependent libraries into group-averaged values: absorption, fission, and scattering terms become group constants, with scattering connecting different energy groups (from one group to another). The fission source may populate various groups depending on the emitted neutron spectrum. The equations can be solved in diffusion, transport, or Monte Carlo frameworks, but the term multigroup usually refers to deterministic methods like multigroup diffusion or discrete ordinates transport.

Group structure is chosen to capture key physics; common group counts range from a few groups (two- or three-group) for coarse models to 20–70 or more in sophisticated designs. The approach is widely used because it balances accuracy with computational efficiency, particularly in reactor core simulations and shielding analyses. Libraries such as ENDF/B, JEFF, and JENDL provide energy-dependent cross sections which are collapsed into multigroup representations.

Limitations include sensitivity to the chosen group structure and potential loss of fine spectral detail, especially near resonance absorption or sharp thresholds. The accuracy depends on how well the collapsed cross sections reproduce the true energy behavior, and cross sections may be affected by temperature effects or Doppler broadening.