Exponential Response Matrix Spectral Nodal Method for the Discrete Ordinates Neutral Particle Transport Model

Abstract

In this work, the response matrix-exponential nodal method is presented to solve fixed source neutral particle transport problems with isotropic scattering and discrete ordinates formulation in two-dimensional Cartesian geometry. The method is based on the response matrix scheme by using the general solution of the transverse integrated SN nodal equations with exponential approximations for the leakage terms. This approach eliminates the need for additional auxiliary equations found in the spectral Green’s function (SGF) schemes, streamlining internodal computation to a matrix-vector multiplication. The formulation includes a lambda parameter possible determined by the medium characteristics, e.g., the scattering ratio coefficient and/or empirical methods. Two model problems with low absorption rates were investigated to analyze the performance of the proposed method. The numerical solutions exhibited superior accuracy for the coarsest spatial grid configurations in both homogeneous and heterogeneous study cases. However, refining the spatial grid revealed a relative loss in accuracy compared to the RM-CN method, potentially due to increased truncation error propagation. Nevertheless, all numerical solutions converge to the reference solution when refining the spatial discretization grid. Comparison of both response matrix schemes demonstrated similar convergence rates and computational efficiency in terms of iterations and CPU consumption.