Nuclear Science and Engineering · 1961 · 192 citations · 5 references
EngineeringPhysicsFluid DynamicsNuclear PhysicsTransport PhenomenaBoltzmann Transport EquationNeutron ScatteringNeutron TransportNeutron Transport TheoryTransport PropertiesAnisotropic Scattering EffectsEigenvalue Neutron Transport ProblemsLegendre PolynomialsNeutron DiffusionNeutron Diffusion ApproximationNeutron Transport EquationNeutron Transport Modeling
The paper presents a general procedure for solving the one‑velocity Boltzmann equation in plane geometry. The method assumes the scattering function can be expanded as a finite series of Legendre polynomials. The authors derive a complete set of eigenfunctions for the Boltzmann equation, prove their orthogonality and completeness, and illustrate solutions for basic neutron diffusion problems. Supported in part by the Office of Naval Research, U.S.
AbstractThe general procedure of solving the one-velocity Boltzmann equation in the case of plane geometry is presented. It is assumed that the scattering function can be expanded into the finite series of Legendre polynomials. The complete set of eigenfunctions of the Boltzmann equation is found. The orthogonality and completeness of the eigenfunctions are proved. By way of illustration, solutions of some basic problems of neutron diffusion are given. Notes* Supported in part by the Office of Naval Research, U. S. Navy.
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