A deterministic continuous-energy neutron transport calculation method based on hybrid basis function expansion

The Boltzmann neutron transport equation is capable of describing the neutron transport process. The deterministic methods for solving the equation have demonstrated their superior computational efficiency to stochastic methods. However, the treatment of the energy variable remains critically reliant on the multi-group approximation. Its inherent limitations contain a dependence on problem-specific representative energy spectra and the necessity for complex and problem-dependent resonance calculations. Accordingly, this work presents a novel continuous-energy deterministic neutron transport methodology based on basis function expansion for different energy ranges and their coupling effects. Neutron energy spectra are represented using different orthogonal basis sets: polynomial bases for non-resonant energy ranges and wavelet bases for resonant energy ranges. It enables the accurate resolution of complex spectral behavior across the entire energy domain and obviates the need for representative spectra and resonance calculation. Preliminary validation studies performed on a series of uniform medium problems demonstrate its feasibility and accuracy.