Methods for calculating diffusional gas release from spherical grains

Two efficient numerical methods are presented for calculating the diffusion of fission gases in spherical grains under time-varying conditions. The methods, the A-2-step method and the LOAM (Locally Accurate Method), are tested comprehensively against an exact piece-wise solution, using simple test cases and randomly generated power-temperature histories. The performance of the methods is compared with an algorithm reported in the literature. The A-2-step method is found to be the most accurate for release fractions below 10%, and the LOAM the most accurate for release fractions above 10%. By combining the two methods an absolute error of less that 0.3?/o is obtained, over the entire range of release fractions. There is no significant difference in computing times between the methods investigated. The applicability of the LOAM in cases involving a moving grain boundary, or a grain boundary acting as an imperfect sink, is discussed.