The singularities of the transport solution and of its first order derivatives in absence of scattering kernel
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1975
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J. J. Van Binnebeek, « The singularities of the transport solution and of its first order derivatives in absence of scattering kernel », Bulletins de l'Académie Royale de Belgique, ID : 10.3406/barb.1975.57936
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. — The paper denumbrates and classifies the discontinuities of the flux and of its first partial derivatives in a pure transport problem with vacuum boundary conditions, when the cross-section and/or the volume source functions or their partial derivatives suffer discontinuities along some boundaries and when these boundaries have no unique normal at some points. It shows that the flux function ceases to be smooth along pieces of the transport characteristic straight lines tangent to some of the discontinuity surface or passing through an edge of those boundaries. Those singularities are practically important because they generate a slow convergence in the numerical processes, as well as a failure of the usual proofs for the consistency of numerical algorithms.