Radiation Transport Problems Research Articles

Реализация бикомпактной схемы для HOLO алгоритма решения задач переноса излучения в среде

Bicompact schemes for the HOLO algorithm for solving the transport equation were applied to solve model problems of radiation transport in a medium (the first and the second Fleck problems). The main idea of HOLO algorithms is to accelerate the convergence of iterative processes due to the joint solving of high order (HO) and low order (LO) kinetic equations. The schemes are constructed by the method of lines on a minimal two-point stencil and have the fourth order of approximation in space. The Runge-Kutta method of the third order of approximation was used for integration over time. Verification and validation of the schemes were carried out. Solutions of the first and the second Fleck problems by the proposed method coincided well with solutions obtained by other methods. A modification of the second Fleck problem was proposed to investigate the dependence of the velocity of the thermal wave front on the absorption coefficient in the optically thick region.

Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes

AbstractThis article focuses on designing efficient iteration algorithms for nonequilibrium three‐temperature heat conduction equations, which are used to formulate the radiative energy transport problem. Based on the framework of relaxation iteration, we design a new accelerated iteration algorithm by reasonable approximation of the Jacobi matrix, according to the characteristics of the discrete scheme for the three‐temperature equations. Adopting the iteration framework, we analyze the advantages and disadvantages of several iteration algorithms commonly used in practice and the new iteration algorithm. Finally, we compare the new iteration algorithm with some other iteration algorithms by solving several nonlinear models, and show that the new algorithm can achieve significant acceleration effect.

High-Order Finite Element Second Moment Methods for Linear Transport

We present high-order, finite element–based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to convert existing discretizations of the VEF moment system to discretizations of the SMM moment system. The moment discretizations are coupled to a high-order Discontinuous Galerkin discretization of the SN transport equations. We show that the resulting methods achieve high-order accuracy on high-order (curved) meshes, preserve the thick diffusion limit, and are effective on a challenging multimaterial problem both in outer fixed-point iterations and in inner preconditioned iterative solver iterations for the discrete moment systems. We also present parallel scaling results and provide direct comparisons to the VEF algorithms from which the SMM algorithms were derived.

Low-cost photoreactors for highly photon/energy-efficient solar-driven synthesis

Low-cost photoreactors for highly photon/energy-efficient solar-driven synthesis

Physics-Informed Neural Network with Fourier Features for Radiation Transport in Heterogeneous Media

Typical machine learning (ML) methods are difficult to apply to radiation transport due to the large computational cost associated with simulating problems to create training data. Physics-informed Neural Networks (PiNNs) are a ML method that train a neural network with the residual of a governing equation as the loss function. This allows PiNNs to be trained in a low-data regime in the absence of (experimental or synthetic) data. PiNNs also are trained on points sampled within the phase-space volume of the problem, which means they are not required to be evaluated on a mesh, providing a distinct advantage in solving the linear Boltzmann transport equation, which is difficult to discretize. We have applied PiNNs to solve the streaming and interaction terms of the linear Boltzmann transport equation to create an accurate ML model that is wrapped inside a traditional source iteration process. We present an application of Fourier Features to PiNNs that yields good performance on heterogeneous problems. We also introduce a sampling method based on heuristics that improves the performance of PiNN simulations. The results are presented in a suite of one-dimensional radiation transport problems where PiNNs show very good agreement when compared to fine-mesh answers from traditional discretization techniques.

Global variance reduction method for Monte Carlo simulation of thermal radiation transport

The implicit Monte Carlo (IMC) method is an important numerical approximation method of simulating the thermal radiative transfer problems under high temperature condition. However, one problem plaguing the IMC method is that the calculation error distributions of the radiation specific intensities are highly asymmetric in space and time. By theoretical analysis and numerical simulations, we find that the error is affected by the records of track in the tallying mesh. Accordingly, a global variance reduction method for implicit Monte Carlo simulation is developed and the corresponding formulas are derived. This method includes three key techniques: 1) the automated dynamic distribution method for the Monte Carlo simulation source particles; 2) the dynamic weight-window technique and the none-bias weight revise algorithm that is suited to the particle distribution method; 3) the analytical estimation variance reduction method of the radiation specific intensity. In view of the above, a three-dimensional simulation code, named IMC3D, is developed to simulate the thermal radiative transfer phenomena. The typical thermal radiative transport problem, known as Marshak wave, is simulated. The simulation results indicate that the global variance reduction method for implicit Monte Carlo makes the statistical errors much more symmetric in space and time and the maximum of error is controllable, thereby increasing the calculation speed approximately 10 times. The new IMC method and code are used for simulating the radiative transportation in hohlraum of ICF successfully.

Methodology, applications and performance of the CAD-based geometry type in the serpent 2 Monte Carlo code

The Serpent 2 Monte Carlo code features a CAD-based geometry option for the modeling of complicated and irregular systems. The methodology is based on the STL data format, which is commonly used for computer graphics and 3D printing, and supported by a wide range of software tools. The methodology has been available for several years, but not described in complete detail. This paper presents the geometry routine with its advantages, limitations and known flaws. A brief overview on practical applications and a workflow example involving neutron and photon transport calculations for a spent nuclear fuel storage rack are provided for discussion. It is concluded that the CAD-based geometry type is a convenient option for various neutron and radiation transport problems, and does not suffer from significant deterioration in computational efficiency compared to conventional CSG models. It is also noted, however, that taking full advantage of the methodology requires some level of understanding on the software tools, the STL data format and the Serpent geometry routine to avoid the most common pitfalls.

Experimental imaging and Monte Carlo modeling of ultrafast pulse propagation in thin scattering slabs.

.SignificanceMost radiative transport problems in turbid media are typically associated with mm or cm scales, leading to typical time scales in the range of hundreds of ps or more. In certain cases, however, much thinner layers can also be relevant, which can dramatically alter the overall transport properties of a scattering medium. Studying scattering in these thin layers requires ultrafast detection techniques and adaptations to the common Monte Carlo (MC) approach.AimWe aim to discuss a few relevant aspects for the simulation of light transport in thin scattering membranes, and compare the obtained numerical results with experimental measurements based on an all-optical gating technique.ApproachA thin membrane with controlled scattering properties based on polymer-dispersed nanoparticles is fabricated for experimental validation. Transmittance measurements are compared against a custom open-source MC implementation including specific pulse profiles for tightly focused femtosecond laser pulses.ResultsExperimental transmittance data of ultrafast pulses through a thin scattering sample are compared with MC simulations in the spatiotemporal domain to retrieve its scattering properties. The results show good agreement also at short distances and time scales.ConclusionsWhen simulating light transport in scattering membranes with thicknesses in the orders of tens of micrometer, care has to be taken when describing the temporal, spatial, and divergence profiles of the source term, as well as the possible truncation of step length distributions, which could be introduced by simple strategies for the generation of random exponentially distributed variables.

Development and verification of Geant4-based parallel computing Monte Carlo simulations for nuclear logging applications

Monte Carlo is one of the most common methods to solve radiation transport problems. However, due to its statistical nature, Monte Carlo is time-consuming when applied to large-scale problems. Therefore, parallel computing, a powerful tool in accelerating Monte Carlo calculations, has been receiving increasing attention along with new developments of computing hardware in recent years. This work documents the application of parallel computing in Geant4 simulations pertaining to nuclear logging tools. A user-specific interface is developed to enable Geant4 multithreading functionality for two nuclear logging models and the parallel Monte Carlo performance is evaluated on a designated HPC (high performance computing) platform. Upon the validation of the parallel-mode simulation, the performance of the Geant4-based simulation in multi-threaded mode (G4-MT) and with the G4-MPI native interface to MPI are compared to obtain the best combination of threads and processes on each node. Strong and weak scalabilities on multiple threads are then investigated by computing the speedup and the parallel efficiency of the simulation. The results show that combining multi-threaded and MPI-based execution can significantly reduce execution time in parallel mode. And the paper documents the improvement of Monte Carlo simulation efficiency by optimizing the configuration of computational resources for parallel execution while keeping close-to-linear acceleration.

Monte Carlo sensitivity calculation in fixed source problems with the derivative source method

This paper proposes a new Monte Carlo sensitivity analysis method for fixed source radiation transport problems, which is dubbed the derivative source method (DSM). This method is a variation of the formerly proposed perturbation source method. A transport equation of a derivative particle representing a derivative of a flux with respect to a parameter such as a cross section is derived by differentiating the fixed source radiation transport equation. This paper presents a Monte Carlo algorithm to solve this transport equation. The derivative particle is emitted from a region of interest (ROI) when a radiation particle undergoes a collision in the ROI. The derivative particle is tracked in the same manner as the ordinary radiation particles. The derivative particle that undergoes a collision in the ROI can yield another derivative particle whose derivative order is increased by one from the colliding particle. This higher-order derivative particle can be used for calculating the higher-order derivative of a flux. The differential operator sampling method (DOS), which is commonly used for Monte Carlo sensitivity analyses, suffers from poor performance when an ROI is small. For a small ROI, the efficiency of the DSM can be improved by adding a pseudo scattering cross section in the ROI, thereby increasing the pseudo scatterings and the number of derivative particles emitted from the ROI. The efficiency of the new method is evaluated by comparing the DSM to the DOS. Numerical tests are performed for a two-dimensional geometry containing a small inclusion. The results reveal that the DSM definitely outperforms the DOS for these test problems. The efficiency of the DSM depends strongly on the pseudo scattering cross section added to the inclusion.

Goal-oriented multi-collision source algorithm for discrete ordinates transport calculation

Discretization errors are extremely challenging conundrums of discrete ordinates calculations for radiation transport problems with void regions. In previous work, we have presented a multi-collision source method (MCS) to overcome discretization errors, but the efficiency needs to be improved. This paper proposes a goal-oriented algorithm for the MCS method to adaptively determine the partitioning of the geometry and dynamically change the angular quadrature in remaining iterations. The importance factor based on the adjoint transport calculation obtains the response function to get a problem-dependent, goal-oriented spatial decomposition. The difference in the scalar fluxes from one high-order quadrature set to a lower one provides the error estimation as a driving force behind the dynamic quadrature. The goal-oriented algorithm allows optimizing by using ray-tracing technology or high-order quadrature sets in the first few iterations and arranging the integration order of the remaining iterations from high to low. The algorithm has been implemented in the 3D transport code ARES and was tested on the Kobayashi benchmarks. The numerical results show a reduction in computation time on these problems for the same desired level of accuracy as compared to the standard ARES code, and it has clear advantages over the traditional MCS method in solving radiation transport problems with reflective boundary conditions.

A novel energy balance approach for a verifiable and accurate solution of radiation extinction in purely absorbing particle clouds

We consider the problem of radiation transport through purely absorbing particle clouds. The gold-standard solution of particle-resolved Monte Carlo ray-tracing method to this problem is computationally expensive and therefore solving the radiation transport equation (specifically, the Beer-Bouguer law (BB-law)) on a Eulerian mesh is often preferred. While the absorption coefficient in the real problem is infinite, the BB-law approximates it to be a finite number in the form of number density through a set of assumptions. For particle clouds that do not obey these assumptions, the BB-law predicts an incorrect exponential decay. Also, when the number density is computed using the nearest-neighbor approach, the BB-law solution diverges when the Eulerian mesh size becomes closer to or smaller than the particle size. This numerical divergence is due to the homogenization error. Although the filtering strategy for number density minimizes the homogenization error, it still converges to an incorrect exponential decay for particle clouds that break the BB-law constraints and the cost of the filtering is equivalent to that of the gold-standard solution. In this study, we develop a novel, highly accurate, verifiable and cost-effective solution to the radiation transport equation on a Eulerian domain using an energy balance approach where we derive an expression for the absorption coefficient as a function of particle and Eulerian mesh sizes. We apply our new method to Poisson and turbulent particle clouds that violate all the BB-law constraints and show that the solution is converging upon the mesh refinement, and eventually, we recover the same gold-standard solution for a much cheaper computational cost.

A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations

Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits the applicability of the method. Here we address this conservation issue by solving a low-order equation with closure terms computed via a high-order solution calculated with DLR. We observe that the high-order solution well approximates the closure term, and the low-order solution can be used to correct the conservation bias in the DLR evolution. We also apply the linear discontinuous Galerkin method for the spatial discretization. We then demonstrate with the numerical results that this so-called high-order/low-order (HOLO) algorithm is conservative without sacrificing computational efficiency and accuracy.

Efficiency analysis of multiple detector effects on MCNP 6.2 simulations

An analysis of some variance reduction methods was introduced and compared with the conventional narrow beam geometry for radiation transport problems. Although the Monte Carlo methods provide accurate results in radiation transport problems, their usability requires a high processing infrastructure. Simulation algorithms need miscellaneous mathematical tricks named as variance reduction to achieve precise results with reduced computing resources. These techniques mostly require experience, intuition, and iteration. For this reason, an alternative approach that may be adopted by all users is needed. Proposed method using source-biased quadruplet and octuplet detection geometries need neither additional code nor advanced experience. The designed geometries were tested on various selected materials, energy values and source definitions to prove its availability. The accuracy and the stability of the method were analyzed with all possible parameters such as material and energy dependence (tasks-error/CPU time, detector fluctuation-NPS, relative error-NPS, deviation-NPS, etc.). Besides, to verify the analysis results, some radiography applications were performed. The efficiency of multiple detector usage was found to be dependent on the complexity of the geometry as expected. It may be concluded that the multi-detector usage is efficient for simplified geometries in terms of relative error and computing time. The firstly introduced geometric designs worked steadily over ~10M histories on all trials. For the advised design, up to ~7 times improvement achieved in terms of computing time based on the figure of merit.

Affine reduced-order model for radiation transport problems in cylindrical coordinates

This article focuses on parametric reduced-order models to decrease the computational cost of large-scale neutron transport problems in the atmosphere. The atmospheric humidity content and neutron source spectrum are considered as uncertain parameters throughout the problem. We first present our full-order model, including an axisymmetric SN transport methodology, a geopotential model for computing the thermophysical properties of the atmosphere, and a support vector regression method for rapidly generating one-group cross sections at every point. Then, reduction of the full-order problem using the POD-Galerkin and least-squares POD-Petrov-Galerkin methods is presented. The reduced-order models implemented introduce mean relative errors between 0.06% and 0.4% with acceleration factors between 3.6×103-8.4×104, respectively.

Optimization and parallelization of the discrete ordinate method for radiation transport simulation in OpenFOAM: Hierarchical combination of shared and distributed memory approaches.

This paper describes the reduction in memory and computational time for the simulation of complex radiation transport problems with the discrete ordinate method (DOM) model in the open-source computational fluid dynamics platform OpenFOAM. Finite volume models require storage of vector variables in each spatial cell; DOM introduces two additional discretizations, in direction and wavelength, making memory a limiting factor. Using specific classes for radiation sources data, changing the store of fluxes and other minor changes allowed a reduction of 75% in memory requirements. Besides, a hierarchical parallelization was developed, where each node of the standard parallelization uses several computing threads, allowing higher speed and scalability of the problem. This architecture, combined with optimization of some parts of the code, allowed a global speedup of x15. This relevant reduction in time and memory of radiation transport opens a new horizon of applications previously unaffordable.

On the Generalization of the Response Matrix Spectral Nodal Method for Neutral Particle SN Source–Detector Problems in Slab Geometry

A generalization of the Response Matrix spectral nodal method is applied to fixed–source discrete ordinates (SN ) radiative transfer and neutron transport problems in slab geometry. This method is extended to forward and adjoint energy multigroup problems with anisotropic scattering including the upscattering events. We present the numerical methodology which generates SN solutions absolutely free from spatial truncation errors. To discuss the efficiency of the method, we offer a number of numerical results for two typical test problems.

USING ARTIFICIAL NEURAL NETWORKS TO ACCELERATE TRANSPORT SOLVES

Discontinuous Finite Element Methods (DFEM) have been widely used for solving SN radiation transport problems in participative and non-participative media. In this method, small matrix-vector systems are assembled and solved for each cell, angle, energy group, and time step while sweeping through the computational mesh. In practice, these systems are generally solved directly using Gaussian elimination, as computational acceleration for solving this small systems are often inadequate. Nonetheless, the computational cost of assembling and solving these local systems, repeated for each cell in the phase-space, can amount to a large fraction of the total computing time. In this paper, a Machine Learning algorithm is designed to accelerate the solution of local systems. This one is based on Artificial Neural Networks (ANNs). Its key idea is training an ANN with a large set of solutions to random one-cell transport problems and, then, replacing the assembling and solution of the local systems by the feedforward evaluation of the trained ANN. It is observed that the optimized ANNs are able to reduce the compute times by a factor of ~ 3:6 per source iteration, while introducing mean absolute errors between 0:5 – 2% in transport solutions.

The Sobolev approximation for radiation transport with line overlap and continuous opacity

The radiation transport problem in the plane–parallel medium with the large velocity gradient is considered. The Sobolev approximation is used. The effects of continuum absorption and line overlap are taken into account. The photon loss probability functions are calculated and tabulated. Two calculations are performed – for the Gaussian spectral line profile and for the rectangular profile. It is shown that at particular choice of the rectangular profile width the results of the calculations are very close. The evaluated photon loss probability functions may be used in the calculations of energy level populations of OH molecule in the interstellar gas flows.

Tensor Expansions of the Angular Particle Distribution

We establish a relation between the class of symmetric spherical tensors and even/odd polynomials. The expansions of the scattering operator of photons or neutrons in a series of symmetric spherical tensors are obtained. Among them are expansions that have a higher rate of uniform convergence in comparison with expansions in spherical functions and Legendre polynomials. It is shown that, in problems of radiation transport in a substance with predominant forward or backward scattering, it is advisable to use expansions in the system of Chebyshev polynomials and tensors.