Generalized Energy Condensation Theory

A generalization of multigroup energy condensation theory has been developed. The new method generates a solution within the few-group framework that exhibits the energy spectrum characteristic of a many-group transport solution, without the computational time usually associated with such solutions. This is accomplished by expanding the energy dependence of the angular flux in a set of general orthogonal functions. The expansion leads to a set of equations for the angular flux moments in the few-group framework. The zeroth moment generates the standard few-group equation while the higher-moment equations generate the detailed spectral resolution within the few-group structure. It is shown that by carefully choosing the orthogonal function set (e.g., Legendre polynomials), the higher-moment equations are only coupled to the zeroth-order equation and not to each other. The decoupling makes the new method highly competitive with the standard few-group method since the computation time associated with determining the higher moments becomes negligible as a result of the decoupling. The method is verified in several one-dimensional benchmark problems typical of boiling water reactor configurations with mild to high heterogeneity.