Adaptive Two-zone Method Applied to the Fission Gas Release under an Irradiation-induced Re-solution Condition

Numerous models have been developed to predict the fission gas release where the flux of gas atoms to the grain boundaries is described by a diffusion equation. Among the numerical solution methods, the variational principle has been regarded as a suitable method in the sense of its accuracy and efficiency. The assumption of a perfect sink for a grain boundary results in a steep gradient near the outer layer of the grain at an early stage of a FGR. A suitable re-meshing technique in combination with proper trial functions is needed to treat such a steep gradient by relocating the finite element nodes. The adaptivity, however, should be implemented with the number of meshes as small as possible due to the high number of the FGR calculations during a fuel performance analysis. The two-zone method by Matthews and Wood, is most appropriate since it requires two elements with three degrees of freedom to model the spherical grain. On the other hand, it is known to have a lower accuracy for a low release. In our previous work, we proposed an adaptive two-zone approach to provide an accuracy comparable to that of the FEM with very fine meshes at an early stage as well as at a higher release. In this paper, the adaptive two-zone method is applied to the FGR problem under an irradiation-induced resolution boundary condition