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Nuclear Science and Engineering
Fusion Science and Technology
Study indicates pilot facility could significantly reduce waste volumes
Waste disposal start-up Deep Isolation and fusion tech company SHINE Technologies have announced the completion of a collaborative study assessing the costs of disposing of radioactive byproducts from a pilot spent nuclear fuel recycling facility.
Nuclear Science and Engineering | Volume 193 | Number 12 | December 2019 | Pages 1339-1354
Technical Paper | doi.org/10.1080/00295639.2019.1638660
Articles are hosted by Taylor and Francis Online.
The SN transport equation asymptotically tends to an equivalent diffusion equation in the limit of optically thick systems with small absorption and sources. A spatial discretization of the SN equation is of practical interest if it possesses the optically thick diffusion limit. Such a numerical scheme will yield accurate solutions for diffusive problems if the spatial mesh size is thin with respect to a diffusion length, whereas the mesh cells are thick in terms of a mean free path. Many spatial discretization methods have been developed for the SN transport equation, but only a few of them can obtain the thick diffusion limit under certain conditions. This paper presents a theoretical result that simply states that the mesh size required for a finite difference scheme to attain the diffusion limit is , where is the order of accuracy of spatial discretization, is the “diffusion” mesh size that can be many mean free paths thick, and is a small positive scaling parameter that can be defined as the ratio of a particle mean free path to a characteristic scale length of the system. Numerical results for schemes such as the Diamond Difference method, Step Characteristic method, Step Difference method, Second-Order Upwind method, and Lax-Friedrichs Weighted Essentially Non-Oscillatory method of the third order (LF-WENO3) are presented that demonstrate the validity and accuracy of our analysis.