A hybrid Analytical Discrete Ordinates-Response Matrix Constant Nodal method for one-speed X, Y-geometry transport problems

Moraes, Leonardo R.C.; Patel, Japan K.; Barros, Ricardo C.; Vasques, Richard

doi:10.1016/j.pnucene.2023.104985

Progress in Nuclear Energy

2024

DOI: 10.1016/j.pnucene.2023.104985

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A hybrid Analytical Discrete Ordinates-Response Matrix Constant Nodal method for one-speed X, Y-geometry transport problems

Leonardo R.C. Moraes,

Japan K. Patel,

Ricardo C. Barros

et al.

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

Rivas-Ortiz,

Sanchez-Dominguez,

Marrero Iglesias

et al. 2024

Science and Technology of Nuclear Installations

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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.

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

Rivas-Ortiz,

Sanchez-Dominguez,

Marrero Iglesias

et al. 2024

Science and Technology of Nuclear Installations

View full text Add to dashboard Cite

show abstract

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A hybrid Analytical Discrete Ordinates-Response Matrix Constant Nodal method for one-speed X, Y-geometry transport problems

Cited by 1 publication

References 21 publications

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

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

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