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Destruction of Ukrainian dam threatens Zaporizhzhia
A Soviet-era dam downstream from the Zaporizhzhia nuclear power plant in southeastern Ukraine collapsed last evening, causing the water level of the Kakhovka Reservoir north of the dam to drop and raising new concerns over the already jeopardized safety of the Russian-occupied nuclear facility, Europe’s largest. The reservoir supplies water for, among other things, Zaporizhzhia’s cooling systems.
Loren Roberts, Dmitriy Y. Anistratov
Nuclear Science and Engineering | Volume 165 | Number 2 | June 2010 | Pages 133-148
Technical Paper | doi.org/10.13182/NSE08-48
Articles are hosted by Taylor and Francis Online.
A family of nonlinear weighted flux (NWF) methods for solving the transport equation in two-dimensional (2-D) Cartesian geometry is considered. The low-order equations of these methods are defined by means of special linear-fractional factors that are determined by the high-order transport solution. An asymptotic diffusion limit analysis is performed on methods with a general weight function. The analysis revealed conditions on the weight necessary for an accurate approximation of the diffusion equation in this limit. We study methods with weights defined by linear and bilinear functions of directional cosines. As a result, we developed 2-D NWF methods formulated with the low-order equations that give rise to the diffusion equation in optically thick diffusive regions if their factors are calculated by means of the leading-order transport solution. The inherent asymptotic boundary conditions for the NWF methods are analyzed. Numerical results are presented to confirm theoretical results and demonstrate performance of the proposed methods.