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    Fully meshless solution of the one-dimensional multigroup neutron transport equation with the radial basis function collocation method
    (Pergamon-Elsevier Science Ltd, 2020) Tanbay, Tayfun; Ozgener, B.
    In this paper a fully meshless method is proposed for the numerical solution of the one-dimensional multigroup neutron transport equation with anisotropic scattering. Both first-order and even-parity forms of the transport equation are studied. The radial basis function collocation method is chosen for the spatial treatment, and Legendre polynomials are used to approximate the angular variable. The selection of the Legendre polynomials instead of discrete ordinates approach resulted with a fully meshless algorithm in both independent variables. Multiquadric is utilized as the radial function. Seven problems are considered to evaluate the performance of the method. The results show that the method converges exponentially, and it is possible to obtain high levels of accuracies for the multiplication factor and neutron flux with a good stability in both spatial and angular domains. For the one-group isotropic benchmark problem, discrete ordinates solutions employing discontinuous linear finite elements for the spatial variable are also provided, and a comparison of the methods revealed that the fully meshless method produced more accurate results than the discrete ordinates-finite element scheme when the shape parameter is properly chosen. (C) 2019 Elsevier Ltd. All rights reserved.
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    A Meshless Method Based on Symmetric RBF Collocation for Neutron Diffusion Problems
    (Polish Acad Sciences Inst Physics, 2019) Tanbay, Tayfun; Ozgener, B.
    In this study we have worked on the numerical solution of the multigroup neutron diffusion equation with the symmetric radial basis function collocation method. For the spatial approximation of the neutron flux, multiquadric, inverse multiquadric, and Gaussian basis functions are used as the interpolation functions. To test the performance of the method, both external and fission source problems are considered in two-dimensional Cartesian geometry. The effect of the shape parameter on the convergence and stability of the numerical algorithm is also investigated. The results have shown that, when the multiquadric is chosen, the symmetric RBF collocation method converges exponentially, and it is possible to obtain highly accurate multiplication factors and neutron flux distributions with this algorithm.