Ray Effect Mitigation for the Discrete Ordinates Method through Quadrature Rotation

Solving the radiation transport equation is a challenging task, due to the high dimensionality of the solution's phase space. The commonly used discrete ordinates (S$_N$) method suffers from ray effects which result from a break in rotational symmetry from the finite set of directions chosen by S$_N$. The spherical harmonics (P$_N$) equations, on the other hand, preserve rotational symmetry, but can produce negative particle densities. The discrete ordinates (S$_N$) method, in turn, by construction ensures non-negative particle densities. In this paper we present a modified version of the S$_N$ method, the rotated S$_N$ (rS$_N$) method. Compared to S$_N$, we add a rotation and interpolation step for the angular quadrature points and the respective function values after every time step. Thereby, the number of directions on which the solution evolves is effectively increased and ray effects are mitigated. Solution values on rotated ordinates are computed by an interpolation step. Implementation details are provided and in our experiments the rotation/interpolation step only adds 5% to 10% to the runtime of the S$_N$ method. We apply the rS$_N$ method to the line-source and a lattice test case, both being prone to ray-effects. Ray effects are reduced significantly, even for small numbers of quadrature points. The rS$_N$ method yields qualitatively similar solutions to the S$_N$ method with less than a third of the number of quadrature points, both for the line-source and the lattice problem. The code used to produce our results is freely available and can be downloaded

Quasi-Random Discrete Ordinates Method for Transport Problems

The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves the main characteristics of the discrete ordinates method, but it has the advantage of providing mitigated ray effect solutions. The QRDOM is discussed in details for applications to one-group transport problems with isotropic scattering in rectangular domains. The method is tested against benchmark problems for which DOM solutions are known to suffer from the ray effects. The numerical experiments indicate that the QRDOM provides accurate results and it demands less discrete ordinates per source iteration when compared against the classical DOM.Comment: 14 pages, 6 figure

Investigation of a discrete ordinates method for neutron noise simulations in the frequency domain

During normal operations of a nuclear reactor, neutron flux measurements show small fluctuations around mean values, the so-called neutron noise. These fluctuations may be driven by a variety of perturbations, e.g., mechanical vibrations of core components. From the analysis of the neutron noise, anomalous patterns can be identified at an early stage and corrected before they escalate. For this purpose, the modelling of the reactor transfer function, which describes the core response to a possible perturbation and is based on the neutron transport equation, is often required. In this thesis a discrete ordinate method is investigated to solve the neutron noise transport equation in the frequency domain. When applying the method, two main issues need to be considered carefully, i.e., the performance of the numerical algorithm and possible numerical artifacts arising from the discretization of the equation. For an efficient numerical scheme, acceleration techniques are tested, namely, the synthetic diffusion acceleration and various forms of the coarse mesh finite difference method. To reduce the possible numerical artifacts, the impact of the order of discrete ordinates and the use of a fictitious source method are studied. These analyses serve to develop the higher-order neutron noise solver NOISE-SN. The solver is compared with different solvers and used to simulate neutron noise experiments carried out in the research reactor CROCUS (at EPFL). The solver NOISE-SN is shown to provide results that are consistent with the results obtained from other higher-order codes and can reproduce features observed in neutron noise experiments

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

acceptedVersio

Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multiscale photon transport. In this method, the photon free streaming and scattering processes are treated in an un-splitting way. The duality descriptions, namely the simulation particle and distribution function, are utilized to describe the photon. By accurately recovering the governing equations of the unified gas-kinetic scheme (UGKS), the UGKWP preserves the multiscale dynamics of photon transport from optically thin to optically thick regime. In the optically thin regime, the UGKWP becomes a Monte Carlo type particle tracking method, while in the optically thick regime, the UGKWP becomes a diffusion equation solver. The local photon dynamics of the UGKWP, as well as the proportion of wave-described and particle-described photons are automatically adapted according to the numerical resolution and transport regime. Compared to the $S_n$ -type UGKS, the UGKWP requires less memory cost and does not suffer ray effect. Compared to the implicit Monte Carlo (IMC) method, the statistical noise of UGKWP is greatly reduced and computational efficiency is significantly improved in the optically thick regime. Several numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the UGKWP method. In comparison to the $S_n$ -type UGKS and IMC method, the UGKWP method may have several-order-of-magnitude reduction in computational cost and memory requirement in solving some multsicale transport problems.Comment: 27 pages, 15 figures. arXiv admin note: text overlap with arXiv:1810.0598