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[en] Highlights: •A modified α − k power iteration method is presented for computing the time-eigenvalue. •It is not required to provide the initial values of α for the modified method. •Computational experiences validate the validity and efficiency of the new method. -- Abstract: A modified α − k power iteration method is presented for the prediction of time-eigenvalue(α) of the neutron transport equation. By developing a direct relationship between K-eigenvalue and α-eigenvalue, a new formula is introduced to estimate the value of α. Compared with the conventional method, it is not required to provide the initial values of α for the modified method. Since it is always difficult to guess the suitable initial values, the modified method is more convenient for solving time-eigenvalue problems. Computational experiences show that the accuracy of the modified method is the same as the conventional method.
[en] The 3-D steady-state SN neutron-gamma transport theory code ATES3 developed at BARC can be utilized for external source problems such as shielding analysis. A brief description on the use of ATES3 and its validation for international shielding type benchmarks problems is presented in the paper. (author)
[en] Nuclear reactor physics deals with the solution of the neutron transport equation, for which several numerical methods and resulting calculation codes exist. Using parallel programming to multiply the resources available to these codes, it is possible to increase their computational power, thus improving their modelling capabilities. This work focuses on the optimization of neutron transport algorithms by means of parallel programming techniques. For cell calculations, the collision probabilities and heterogeneous response (HRM) methods are considered, including the associated multigroup scheme, as implemented in INVAP’s cell calculation code, CONDOR. The diffusion method in a finite difference formulation, used in CITVAP for core calculations, is optimized as well. The parallel methods obtained are implemented in OpenMP, an application for parallel programming in shared memory computers. (author)
[es]La física de reactores está basada en la resolución de la ecuación de transporte de neutrones, para la cual existen diversos esquemas numéricos y códigos de cálculo que los implementan. La programación en paralelo permite aumentar la velocidad de estos códigos mediante la utilización de múltiples unidades de procesamiento, mejorando la capacidad de modelado. En este trabajo se estudió la paralelización de distintos algoritmos asociados a la ecuación de transporte. Para la etapa de cálculos de celda fueron considerados los métodos de probabilidades de colisión y de respuesta heterogénea (HRM), incluyendo el esquema multigrupo asociado, y su implementación en el código CONDOR, desarrollado en INVAP. El método de difusión en diferencias finitas implementado en el código CITVAP fue analizado para los cálculos de núcleo. La programación de los algoritmos desarrollados se realizó en OpenMP, una herramienta de procesamiento en paralelo en el modelo de memoria compartida. (author)
[en] The theory of multipoint coupled reactors developed by multi-group transport is verified by using the probabilistic transport code MCNP5 and the continuous-energy Monte Carlo reactor physics burnup calculation Serpent code. The verification was performed by calculating the multiplication factors (or criticality factors) and coupling coefficients for a two-region test reactor known as the Deuterium Critical Assembly, DCA. The multiplication factors k_e_f_f calculated numerically and independently from simulations of the DCA by MCNP5 and Serpent codes are compared with the multiplication factors k_e_f_f calculated based on the coupled reactor theory. Excellent agreement was obtained between the multiplication factors k_e_f_f calculated with the Serpent code, with MCNP5, and from the coupled reactor theory. This analysis demonstrates that the Serpent code is valid for the multipoint coupled reactor calculations. (author)
[en] The Integral Transport Matrix Method (ITMM) has been shown to be an effective method for solving the neutron transport equation in large domains on massively parallel architectures. In the limit of very large number of processors, the speed of the algorithm, and its suitability for unstructured meshes, i.e. other than an ordered Cartesian grid, is limited by the construction of four matrix operators required for obtaining the solution in each sub-domain. The existing algorithm used for construction of these matrix operators, termed the differential mesh sweep, is computationally expensive and was developed for a structured grid. This work proposes the use of a new algorithm for construction of these operators based on the construction of a single, fundamental matrix representing the transport of a particle along every possible path throughout the sub-domain mesh. Each of the operators is constructed by multiplying an element of this fundamental matrix by two factors dependent only upon the operator being constructed and on properties of the emitting and incident cells. The ITMM matrix operator construction time for the new algorithm is demonstrated to be shorter than the existing algorithm in all tested cases with both isotropic and anisotropic scattering considered. While also being a more efficient algorithm on a structured Cartesian grid, the new algorithm is promising in its geometric robustness and potential for being applied to an unstructured mesh, with the ultimate goal of application to an unstructured tetrahedral mesh on a massively parallel architecture. (authors)
[en] Two-dimensional time-dependent finite-difference equations of the surface harmonics method (SHM) for the description of the neutron transport are derived for square-lattice reactors. These equations are implemented in the SUHAM-TD code. Verification of the derived equations and the developed code are performed by the example of known test problems, and the potential and efficiency of the SHM as applied to the solution of the time-dependent neutron transport equation in the diffusion approximation in two-dimensional geometry are demonstrated. These results show the substantial advantage of SHM over direct finite-difference modeling in computational costs
[en] Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)
[en] Research highlights: → The critical slab and sphere problem in neutron transport under Case eigenfunction formalism is considered. → These equations reduce to integral expressions involving X functions. → Gauss quadrature is not ideal but DE quadrature is well-suited. → Several fold decrease in computational effort with improved accuracy is realisable. - Abstract: In this paper benchmark numerical results for the one-speed criticality problem with isotropic scattering for the slab and sphere are reported. The Fredholm integral equations of the second kind based on the Case eigenfunction formalism are numerically solved by Neumann iterations with the Double Exponential quadrature.