Reactor Core Neutron Flux Decomposition for Transient Accuracy

The neutron flux is segmented into shape function and amplitude function components. The shape function describes the spatial distribution pattern while the amplitude function captures the temporal variation and energy dependence. This segmentation allows the complex transient neutron flux problem to be decomposed into manageable parts that can be solved separately and combined, maintaining accuracy while controlling computational complexity.

The method transforms the neutron flux from a single complex parameter into multiple parameters (shape function coefficients and amplitude function values). By changing the parameter representation, the method captures transient effects more accurately without proportionally increasing computational burden, as the shape function can be pre-determined or approximated.

By separating the neutron flux into shape and amplitude functions, the method can use pre-computed or simplified shape functions that capture spatial distribution patterns. This allows rapid calculation of the amplitude function at each time step while maintaining accurate spatial distribution through the shape function, thus preserving both speed and accuracy during transient processes.

The shape function can be determined in advance or updated less frequently than the full neutron flux solution. This preliminary determination of the spatial distribution pattern allows for faster transient calculations, as only the amplitude function needs to be solved at each time step, significantly reducing computational cost while maintaining spatial accuracy.