Adaptive Angular Resolution for the Finite Element-Spherical Harmonics Method

摘要

The finite element-spherical harmonics (FE-P_N) method based on the second order, even-parity form of transport equation is capable describing highly complex and heterogeneous spatial systems. However, the required order of angular expansion to accurately represent the angular flux distribution may vary widely between regions. Thus, uniform refinement of the spherical harmonics expansions is not cost effective, and the adaptive strategy is desired. This provides a strategy to minimize both computational costs and storage to reach the required accuracy. In this work, we present an adaptive angular refinement algorithm for the FE-P_n method. The refinement strategy developed is based on the hierarchical p-adaptivity and has been implemented in the code EVENT. Its performance and accuracy has been tested by comparing the results against uniform angular refinement. Preliminary numerical results show the great potential on the use of the adaptive angular expansions.