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

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.