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Discrete Ordinates Method for the Transport Equation Preserving One-Dimensional Spherical Symmetry in Two-Dimensional Cylindrical Geometry

F. Chaland, G. Samba

Nuclear Science and Engineering / Volume 182 / Number 4 / April 2016 / Pages 417-434

Technical Paper /

First Online Publication:March 22, 2016
Updated:April 1, 2016

To calculate instability flows where radiative transport plays a role, it is mandatory to have one-dimensional (1-D) spherical symmetry. To obtain this 1-D symmetry, a new approach for solving the transport equation in the context of the discrete ordinates method is proposed in two-dimensional cylindrical geometry. Based on a new formulation of the spatial transport term, this method allows us to derive a scheme preserving the 1-D symmetry on an equal-angle zoning mesh. We prove this property at both discrete angle and spatial levels. Numerical results show that the scheme based on our method preserves constant solutions and the 1-D symmetry, and it is consistent of order 1.