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

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...

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Vydáno v:Science and technology of nuclear installations Ročník 2024; číslo 1
Hlavní autoři: Rivas-Ortiz, Iram B., Sanchez-Dominguez, Dany, Marrero Iglesias, Susana, Ambrósio, Paulo Eduardo
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York John Wiley & Sons, Inc 2024
Wiley
Témata:
Accuracy
Approximation
Boundary conditions
Eigenvalues
Green's functions
Mathematical analysis
Matrices (mathematics)
Methods
Neutral particles
Scattering
Truncation errors
ISSN:1687-6075, 1687-6083
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Shrnutí: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 S N 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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ISSN:1687-6075
1687-6083
DOI:10.1155/2024/9459039