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The neutron transport equation is usually solved against a stationary background medium. When the background material is moving, the transport equation will need to be modified. Solving the transport equation with moving material is quite complicated, especially for the curved coordinate system because of the double angular redistributions. In this study, the discretization method of the simplified transport equation considering the moving-material effect is implemented in three-dimensional cylindrical geometry. Directly solving this modified transport equation with the standard solution technique is problematic since the advection term introduced by moving material may render the transport solver numerically unstable. The speed ratio λ is defined for stability analysis. A forced-stable method is proposed in this study to achieve good numerical stability for any material speeds and time-step sizes. The accuracy of this new method is verified using manufactured solutions. Steady numerical results demonstrate that the effects introduced by background motion cannot be neglected as the material speed starts to approach one-tenth of the neutron speed. Moreover, transient analysis indicates that the moving background has a considerable impact on the criticality of a system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• The transport equation considering background motions is studied. • Analytic forms of the coupled transport equation are derived. • Methods of transforming equations between different phase spaces are discussed. The neutron transport equation is usually solved against stationary background materials. When the background material is moving, the transport equation will need to be modified. Two historical approaches, "effective" cross-sections and "co-moving" frame, have been used in the past decades. The neutron transport community prefers to use the second method. However, the modified transport equation in the "co-moving" frame is extremely complicated. In this study, we discuss these modifications for non-relativistic neutrons. Transport equations considering background motions have been derived under the three-dimensional (3-D) Cartesian, cylindrical, and spherical coordinates, which can be conveniently reduced to lower-dimensional systems. Moreover, methods of transforming the coupled equation between different phase spaces have been studied. [ABSTRACT FROM AUTHOR]

The deterministic methods are efficient for solving the neutron transport equation (NTE), but suffer from discretization errors. The increasingly complex geometric models make spatial discretization errors the primary source of discretization errors. Considering that spatial discretization errors come from inaccurate geometric shape descriptions and low-accuracy numerical schemes, this paper develops a Discontinuous Galerkin Finite Element Method for the NTE on unstructured polygonal meshes to reduce spatial discretization errors. In this method, the physical modal basis is adopted to handle the polygonal mesh and to achieve high-order accuracy in a uniform and efficient way. The numerical results of various fixed-source and k-eigenvalue benchmarks demonstrate that the method developed in this paper can give accurate solutions on polygonal meshes with high convergence rates. [ABSTRACT FROM AUTHOR]

The discrete ordinates (S N) method is a highly effective and accurate angular discretization method for the neutron transport equation, but suffers from the inherent ray effect in low-scattering regions. The first collision source (FCS) method employing the methods without ray effect to obtain the uncollided flux is a common ray effect mitigation technique. In this paper, a novel FCS method using the spherical harmonics (P N) method to calculate the uncollided flux is proposed. The P N for the first collision source (P N -FCS) method possesses distinctive advantages in several aspects: (1) it can be applied in the problem containing reflective boundary conditions that are difficult to handle with traditional FCS method, (2) it uses the discontinuous Galerkin method to perform spatial discretization, and thus can be easily applied in arbitrary shape and order finite element meshes, (3) it can be effectively calculated in parallel on distributed meshes, (4) the accuracy and computational cost can be flexibly adjusted. Besides, the filter technique is adopted to improve the performance of the P N method in stream-dominated regions. The P N -FCS method has been implemented in two- and three-dimensional neutron transport code and tested by various testing problems. Numerical results show that the P N -FCS method can effectively mitigate the ray effect. • An effective ray effect mitigation method is proposed by combining the first collision source and filtered P N methods. • The methodology can be applied to arbitrary shape and order unstructured meshes with reflective boundary conditions. • The robustness of the methodology is demonstrated in different types and dimensional problems. [ABSTRACT FROM AUTHOR]