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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]

In this paper, a unified gas kinetic particle (UGKP) method is developed for radiative transfer in both absorbing and anisotropic scattering media. This numerical method is constructed based on our theoretical work on the model reduction for an anisotropic scattering system. The macroscopic solver of this method directly solves the macroscopic anisotropic diffusion equations, eliminating the need to solve higher-order moment equations. The reconstruction of macroscopic scattering source in the microscopic solver, based on the multiscale equivalent phase function we proposed in this work, has also been simplified as one single scattering process, significantly reducing the computational costs. The proposed method has also the property of asymptotic preserving. In the optically thick regime, the proposed method solves the diffusion limit equations for an anisotropic system. In the optically thin regime, the kinetic processes of photon transport are simulated. The consistency and efficiency of the proposed method have been validated by numerical tests in a wide range of flow regimes. The novel equivalent scattering source reconstruction can be used for various transport processes, and the proposed numerical scheme is widely applicable in high-energy density engineering applications. [ABSTRACT FROM AUTHOR]

The mesoscopic particle transport mechanics is bridged to the macroscopic fluid dynamics through the asymptotic theory. The construction of a concise model in the asymptotic regime is a major objective of kinetic theory. In this work, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are presented for an anisotropic-scattering transport process with arbitrary order of scattering kernel. The prediction of the theoretical model perfectly agrees with the numerical experiments. A clear picture of the diffusion physics is revealed for the neutral particle transport in the asymptotic optically thick regime. [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]

Pinhole imaging is an important test technique to obtain information on the spatial distribution of the radiation field in the target region and has been widely used in nuclear physics and inertial confinement fusion (ICF). Coded-aperture, able to maintain good resolution as well as enhancing signal strength, has become a more frequently used method than pinhole imaging in experimental studies. Thus, implementing Monte Carlo simulations of coded-aperture imaging will improve coded-aperture design, image reconstruction, and other related works. However, the current international mainstream Monte Carlo transport simulation programs do not possess the ability to directly simulate coded-aperture imaging. This paper develops a relatively complete coded-aperture imaging simulation function on the Neutron Photon Transport System code based on the next-event estimation method. With the application of Monte Carlo simulation techniques, such as variance reduction and rejection sampling, it is capable of simulating coded-aperture accurately, flexibly, and efficiently, including problems of multiple shapes and even irregular geometry. The results are consistent with combined pinhole imaging, and the computational efficiency has been improved significantly. [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 detailed derivations of the DSA algorithm in the r - θ - z geometry is given. • A parallel DSA algorithm is implemented in the frame of the KBA algorithm. • Based on the red-black sweep, a half-reduced PCG method has been proposed. • The effectiveness and efficiency of this parallel DSA algorithm has been verified. • The HRB(m)-PCG algorithm has well parallel scalability. A parallel DSA algorithm based on the red-black sweep PCG method is proposed to accelerate the neutron transport calculation in the 3-D cylindrical geometry. This parallel acceleration technique shares the same spatial domain decomposition strategy with the KBA method. The red-black sweep iteration is formed by moving the r - and θ -axial components of the diffusion operator into the right hand side of the diffusion equation. Using the initial values refreshed by several red-black sweep iterations simplifies the matrix-vector multiplication in the CG procedure. Through the homogeneous problems, how the times of the red-black sweep effects the DSA algorithm is analyzed. A wide range of problems including FBR benchmark, PWR Pin-by-pin calculation and PWR shielding calculation have been performed to test the effectiveness and efficiency of the new method. The solution time is reduced by 3 ~ 10 times in different problems. This new acceleration algorithm has well parallel scalability. [ABSTRACT FROM AUTHOR]

• The first-collision source method is developed to solve the adjoint equation. • The effect of reflective boundaries is considered in the ray-tracing procedure. • SC scheme and GMRES algorithm have implemented in 3D x - y - z geometry. • How to form the point source is investigated in the ex-core detector simulation. • The SN-FC method achieves good accuracy and efficiency. Simulation of the ex-core detector response function (DRF) is of great importance for reactor power monitoring, control and protection systems. However, the 3D DRF calculation requires vast majorities of computational resources due to its characteristics such as deep penetration, strong anisotropic scattering, large computational geometry, etc. In this paper, the step characteristics (SC) spatial differencing scheme and GMRES algorithm have been implemented in the 3D S N code to ensure the simulation efficient. The adjoint first-collision (FC) source method is developed to mitigate the ray effect in the DRF simulation. The Kobayashi benchmarks are calculated to verify the correctness of the FC module. Numerical results based on the Kori-1 reactor ex-core detector indicate that the SN-FC method has the comparable accuracy with multi-group Monte-Carlo method but achieves much higher efficiency. [ABSTRACT FROM AUTHOR]

We propose an improved algorithm of generating scattering matrices based on the Monte Carlo method. The new algorithm can greatly improve convergence compared to the traditional approach of the collision estimator. The formula for estimating statistical errors in the new algorithm is given. How the new algorithm benefits the convergence without investing large neutron samples is analyzed, and we also point out that with properly partitioned energy groups, the precision of scattering matrices can get close to that of total scattering cross sections. The new algorithm has been implemented in the neutron transport code NPTS and validated with a number of critical benchmark problems. [ABSTRACT FROM AUTHOR]

In the paper, an improved two-grid scheme based on shifted-inverse power method is proposed to solve the elliptic eigenvalue problems. With this new scheme, the solution of the elliptic eigenvalue problem on a fine grid T h is reduced to the solution of the elliptic eigenvalue problem and the recovered eigenfunction on a much coarser grid T H , and the solution of an elliptic boundary value problem and the recovered solution on the fine grid T h . Theoretical analysis shows that the scheme allows a much coarser mesh to achieve the superconvergence rate. Finally, some numerical experiments are carried out to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

• Next event estimation for neutron transport in moving objects. • Directional emission probabilities based on nuclear data in different frames. • The effect of the motion of the pellet material on the pinhole imaging. The next event estimation is one of the important algorithms employed in Monte Carlo simulations for particle transport. It finds wide applications in point flux, image flux, and variance reduction techniques. With the advancement of transport simulations for moving objects, the next event estimation for moving target nuclei has yet to be realized. The next event estimation requires the calculation of directional emission probabilities based on the outgoing distribution provided by nuclear data. When the target nucleus is in motion, determining the outgoing direction in the coordinate system prescribed by nuclear data and calculating the emission probability in that direction becomes more intricate. In this study, regarding the outgoing distributions in different coordinate systems, we present a systematic approach to calculate the next event estimation for moving targets. The accuracy of this method is verified through the energy and angle distributions of surface current tallies in the test model. Applying the new method, we conducted pinhole imaging simulations for a moving radiator, quantitatively comparing the differences in simulation results with and without considering motion. [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]

• A monte carlo simulation method is proposed specifically for thick pinhole imaging. • Thick pinhole imaging algorithm is improved by more than 10 times in efficiency. • A biased sampling method is designed for calculating the direct contributions. • The convergence of the scatter contributions is significantly accelerated. • The computational efficiency is independent of the imaging distance. Thick pinhole imaging, as an important diagnostic tool, is widely used in the research of inertial confinement fusion (ICF). Particles for pinhole imaging in this kind of applications have high penetrating power, which requires high attenuation material to be used for the shielding of the imaging system. Monte Carlo simulation is an effective approach for theoretical studies of thick pinhole imaging, due to the complex interactions of neutrons or photons within the materials. However, existing Monte Carlo programs can hardly support high-precision simulations in a satisfactory efficiency for thick pinhole imaging. In this paper, a thick pinhole imaging simulation method is proposed and has been implemented in the Monte Carlo code NPTS. The effect on the statistical variances of flux image tally caused by the scores from different emission events and different imaging trajectories has been considered sufficiently. The new method realizes the variance reduction of the image tally by reducing score fluctuations of each particle. The correctness of this method is verified by the calculations of a typical model. Compared to the tally of Flux Image Radiograph (FIR), more than tenfold increase in efficiency has been performed by the new method. And more importantly, the efficiency is no longer affected by the distance between sources and the pinhole shielding. [ABSTRACT FROM AUTHOR]

The next-event-estimation method, though commonly employed in Monte Carlo simulations, will underestimate point flux with reflecting, white, or periodic surfaces. This paper proposed a modification on the traditional next event estimation method to improve the calculation of point flux with reflecting surfaces. The new method has been implemented in the Monte Carlo transport code, NPTS (Neutron Photon Transport System). Several numerical cases are presented, and the results show that the modified next event estimation method works well with reflecting surfaces. The point flux calculated by the modified method is independent of reflecting surfaces. [ABSTRACT FROM AUTHOR]

Monte Carlo programs are increasingly considered the most accurate tool for simulating particle transport problems. The neutron-photon transport simulation capabilities of domestic particle transport Monte Carlo softwares are relatively advanced, while the electron transport simulation functions have not been well developed yet. This paper independently developed the functions of electron transport and photon-electron transport in the CH (condensed history technique) scheme based on the NPTS (Neutron Photon Transport System) program, and implemented the multi-coupling transport simulation of neutrons, photons, and electrons, which can meet the needs of actual applications. Several test models were run on both NPTS and the popular programs such as EGS and RMC to verify the correctness of NPTS. In addition, an energy deposition tally is developed. It is shown both theoretically and experimentally that the energy deposition calculation by NPTS are more accurate than RMC. [ABSTRACT FROM AUTHOR]