High accuracy scheme for neutron transport neutron defense problem
Abstract:
The paper considers the problems of calculating the stationary transport of high-energy neutrons from an external source in a hollow metal structure. The spatial grid for calculation consists of tetrahedra, which allows to model complicated geometric shapes of objects. The calculated area is highly heterogeneous, since it consists of metal parts with strong absorption and scattering and practically non-absorbing internal parts. A scheme based on a minimal stencil, within a single tetrahedron for the calculation. The scheme has a high approximation order and is based on characteristic approaches. For a smooth solution and a constant absorption coefficient in each cell, the scheme has a third order of convergence. The cells are traversed using the graph topological sorting algorithm. A new version of the parallelization of the calculation for the OpenMP standard has been proposed. For discretization by an angular variable, a cubature formula of the direct product type over two angles with an algebraic order of accuracy of nine is used. The angular grid is constructed in such a way as to correctly calculate the moments for narrowly directed beams of external radiation. The standard 26-group approximation of the BNAB library is used for energy sampling. A decrease in the neutron flux inside the structure is shown for groups with an energy above 1 MeV. Graphs of the angular distribution inside the structure are given.
Keywords:
transport equation, neutron transport, characteristic scheme, tetrahedral scheme, projection-characteristic method, high order of approximation, compact stencil
Publication language:russian, pages:21
Research direction:
Mathematical modelling in actual problems of science and technics
