An analytical approach for solving a nodal formulation of two-dimensional fixed-source neutron transport problems with linearly anisotropic scattering

The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

“…The and parameters in Equations ( 6) and ( 7) are arbitrary constants to be determined according to the boundary conditions of the spatial discretization node. Differently from previous spectral nodal methods that one can find in the literature [5][6][7][8], the methodology as presented in this work uses the most recent estimates of the incoming angular fluxes in the node interfaces, to compute the values of and , and then, the outgoing fluxes of the analyzed node are calculated by using the conventional discretized spatial balance equations without introducing any additional approximation. Due to the spectral analysis performed, the constant approximations for the transverse leakage terms and the modifications of the original iterative scheme, the present method is termed Modified Spectral Deterministic-Constant Nodal (MSD-CN) method.…”

“…These methodologies have been applied to develop coarse-mesh nodal methods for two-dimensional problems. These methods are based on the nodal general solution of the one-dimensional transverse integrated equations with approximations for the transverse leakage terms [5][6][7][8].…”

“…Analogously to the companion methods [5][6][7][8], the present method is based on transverse integration of the two-dimensional equations and the transverse leakage terms are assumed to be constant along the edges of the spatial discretization nodes. This new method is referred to as the Modified Spectral Deterministic-Constant Nodal (MSD-CN) method and it uses an iterative algorithm essentially different from the sweeping schemes used in the recent spectral-nodal methods.…”