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Variational Determination of the Neutron Integral Transport Equation Eigenvalues Using Space Asymptotic Trial Functions
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The An method in monokinetic neutron transport theory: Convergence and numerical applications
No full textThe convergence of the approximate method, referred to as An, to study the solution of the monokinetic transport equation is fully investigated, when it is applied to the description of the neutron population in both infinite and finite media. The basic features of the method and the analytical and numerical implications are then analysed, in plane and curved geometries. The approximation is inserted within the other today available approximate methods panorama, such as discrete ordinates, SN and PN and its particular features are briefly pointed out. Finally, some typical numerical applications and results to study its performance and reliability are presented, such as calculations of critical dimensions, of Green functions in the infinite medium, and of space neutron distributions in infinite bodies injected by cylindrically symmetric sources
Solution of some 2D transport problems by a high order AN–SP2N?1 method
No full textA collection of classical 2D transport problems (the escape probability from prisms of various shapes, the current-to-flux ratio of a wedge-shaped reflector, the transport and asymptotic flux as well as the extrapolation length near a corner) are solved by means of the boundary element version of a high order AN method, an equivalent form of the odd order simplified spherical harmonics (SP2N?1) method. The use of a high order approximation is motivated by the fact that all the above problems can be made to fulfil the condition of constant total mean free path, which makes AN–SP2N?1 to be equivalent, in turn, to the classical odd order spherical harmonics (P2N?1) method, so that for these problems AN–SP2N?1 shares with the latter method the property that, by increasing the order 2N ? 1, the error can be made as small as we want. A second purpose of the paper is to show that the boundary element approach can handle such highly singular boundary integrals as those implied by the partial derivatives of the asymptotic flux at the boundary
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