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A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-03-25 Joseph M. Coale, Dmitriy Y. Anistratov
A new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion so...
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On Reducing the Collision Time Between a Nanosensor and a Randomly Moving Particle in the Fluid J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-03-23 Mohamed Abd Allah El-Hadidy, Alaa A. Alzulaibani, Faten S. Alamri
The search model suggested in this study uses a unit-speed nanosensor to track the fluid’s randomly linear flow particle, starting at the real line’s origin. The nanosensor oscillates passing throu...
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Neutron Star Evolution in f(Q) Modified Gravity Framework J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-03-22 Samprity Das, Surajit Chattopadhyay, Aroonkumar Beesham
The current study reports the evolution of a Neutron Star in f(Q) modified gravity framework, where f(Q) is chosen in the form f(Q)=Q+aQ, where the non-metricity scalar Q is taken as Q=6H2 and a is...
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Energy-Dependent, Self-Adaptive Mesh h(p)-Refinement of a Constraint-Based Continuous Bubnov-Galerkin Isogeometric Analysis Spatial Discretization of the Multi-Group Neutron Diffusion Equation with Dual-Weighted Residual Error Measures J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-03-09 S. G. Wilson, M. D. Eaton, J. Kópházi
Energy-dependent self-adaptive mesh refinement algorithms are developed for a continuous Bubnov-Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isoge...
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Several Numerical Simulation Methods for the Time-Dependent Schrödinger Equation J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-03-01 Song Luo, Yanhua Cao
The time-dependent Schrödinger equation can be solved using the Houbolt difference scheme or the space-time polynomial particular solutions method, with the former performing well in dissipative pr...
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Studying the Influence of Antimicrobial Resistance on the Probability Distribution of Densities for Synchronization Growing of Different Kinds of Bacteria J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-02-20 Mohamed Abd Allah El-Hadidy, R. Alraddadi
Multiple types of microorganisms impact people with immunological illnesses simultaneously. In the presence of antibiotic resistance and random fluctuations such as rapid changes in the environment...
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Study on Thermal Effect on the SEM Contrast of a Nanorod in a Fast Scanning Mode J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-02-19 Peng Zhang
Modern scanning electron imaging (SEM) frequently adopts the multi-frame stacking technique to minimize the vibration and drift but ignores the electron beam-induced thermal effect (called thermal ...
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An Adjoint Method for High-Resolution EPMA Based on the Spherical Harmonics (PN) Model of Electron Transport J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-02-17 Tamme Claus, Gaurav Achuda, Jonas Bünger, Silvia Richter, Manuel Torrilhon
Electron Probe Microanalysis (EPMA) is a nondestructive technique to determine the chemical composition of material samples in the micro- to nanometer range. Based on intensity measurements of x-ra...
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Fluctuations of Mean-Square Displacement in Presence of Traps: Non-Self-Averaging versus Ensemble Averaging J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-01-30 K. A. Pronin
We consider nonstationary diffusion in a medium with random traps-sinks. We study the self-averaging of the mean-square displacement (MSD) of the ensemble of N particles in the fluctuational long-t...
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A Study on the Finiteness of a Tracking Method with Reduction in the Collision Time between a D-Dimensional Random Walk Particle and One of Multiple Nano-Sensors J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2024-01-22 Mohamed Abd Allah El-Hadidy, Alaa Awad Alzulaibani
In order to detect radionuclides and dangerous substances in a fractured medium with the least amount of time and maximum probability, this paper provides a revolutionary tracking model. It relies ...
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Shallow Moments to Capture Vertical Structure in Open Curved Shallow Flow J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-12-18 I. Steldermann, M. Torrilhon, J. Kowalski
Shallow water models are successfully used for simulating geophysical flows like river floods, tsunamis, sediment transport, or debris flows. Depth-averaged models are in general attractive due to ...
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On Solution Regularity of the Two-Dimensional Radiation Transfer Equation and Its Implication on Numerical Convergence J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-12-13 Dean Wang
In this paper, we deal with the differential properties of the scalar flux ϕ(x) defined over a two-dimensional bounded convex domain, as a solution to the integral radiation transfer equation. Esti...
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On the Renormalization Maps for the φ-Divergence Moment Closures Applied in Radiative Transfer J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-12-13 M. R. A. Abdelmalik, Z. Cai, T. Pichard
The φ-divergence-based moment method was recently introduced Abdelmalik et al. for the discretization of the radiative transfer equation. At the continuous level, this method is very close to the e...
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Comparison between Van Genuchten and Brooks-Corey Parameterizations in the Solution of Multiphase Problems in Rigid One-Dimensional Porous Media J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-12-13 P. H. S. Slompo, M. A. V. Pinto, M. L. Oliveira
Multiphase problems in porous media involve the complex flow of multiple fluid phases within porous structures, covering areas of Engineering, Medicine, Geology, among others. Understanding these p...
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Application of Approximate Maximum-Entropy Moment Closure to the Wigner Equation J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-11-29 William Morin, Fabien Giroux, James G. McDonald
This paper investigates the potential of moment closures as a possible path to future quantum hydrodynamics models. Moment closures are known to produce accurate predictions of continuum and non-eq...
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Transport Features on Bidirectional Nanofluid Flow with Convective Heating and Variable Darcy Regime J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-11-29 Yusuf Olatunji Tijani, Mojeed Taiwo Akolade, Abdul Rahman Mohd Kasim
The performance of Au and TiO2 nanoparticles in Casson flow propelled by the rotational effect subject to convective heating and variable Darcy phenomenon is presented. As a means to contribute sig...
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Du Fort-Frankel Finite Difference Scheme for Solving of Oxygen Diffusion Problem inside One Cell J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-11-29 Abdellatif Boureghda, Nadjate Djellab
In this paper, we use the well-known Du Fort-Frankel finite difference scheme to solve the oxygen diffusion problem inside one cell which is modeled by an initial moving boundary value problem for ...
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A Semi-Analytical Description of Radiation Coupled with Thermal Wave Conductive Transfer in Inhomogeneous Solid Cylinder J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-09-13 Guillaume Lambou Ymeli
This study presents the analytical layered solution for thermal radiations coupled with non-Fourier conductive heat transfer, formulated from the Cattaneo-Vernotte flux model in inhomogeneous solid...
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On Multivariate Distribution of n-Dimensional Brownian Diffusion Particle in the Fluid J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-09-09 Mohamed Abd Allah El-Hadidy, Alaa Awad Alzulaibani
This work presents the multivariate distribution of an n-dimensional independent Brownian particle’s position at any time t in the fluid. To know the diffusion properties of particle in a fluid, we...
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Development and Benchmarking of Charged Particle Propagation Methods in G4-ASPP J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-08-03 Luke Stegeman, Dan J. Fry, Amir A. Bahadori
A new transport tool that simultaneously accounts for the impacts of external electromagnetic fields and bulk shielding material on charged particle dynamics, G4-ASPP, was developed to streamline a...
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Evaluation of 1D Models for Particle Transport with Wall Migration in Ducts of Rectangular Cross Section J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-07-17 Roberto D. M. Garcia, Maurício T. Pazianotto, Felipe L. Frigi
Abstract Approximate 1D models of particle transport in ducts that make use of an exponential displacement kernel to describe the effect of wall migration are evaluated for ducts of rectangular cross section. The studied models are based on the use of either one or two basis functions to approximate the transverse and azimuthal dependencies of the angular flux in the duct. Thermal-neutron reflection
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A Monte Carlo Thermal Radiative Transfer Solver with Nonlinear Elimination J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-07-03 Adam Q. Lam, Todd S. Palmer, Thomas A. Brunner, Richard M. Vega
Abstract In this paper, we present a new Monte Carlo method for solving the thermal radiative transfer (TRT) equations via the method of nonlinear elimination (NLEM). This method is inspired by the previous application of NLEM to thermal radiation diffusion. Our approach, called diffusion accelerated Implicit Monte Carlo (DAIMC), is a hybrid technique which combines a Monte Carlo method for solving
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Probability of Initiation in Neutron Transport J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-06-21 Peter N. Brown
Abstract We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron
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Study of Forward and Backward Scattering in Two-Region Milne Problem for Non-absorbing Medium Using a Synthetic Kernel J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-06-18 Dalia A. Garbiea, Alia El-Depsy, Mustafa M. Selim, Osama A. Mohamedien
Abstract In this work, the effect of an extremely anisotropic scattering function on the two-region Milne problem is studied. This scattering function divides the neutrons resulting from the collisions into three parts; part ( l)l) which moves backward, part (m) which moves forward, and part (n) which emerge isotropically from the collisions, where ll + m + n = 1. The integral version of the transport
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Half-Space Albedo Problem for Triplet Anlı-Güngör Scattering J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-06-07 R. Gökhan Türeci, Demet Gülderen
Abstract Introduction The Anlı-Güngör (AG) scattering function which is written in triplet form is applied to the half-space albedo problem. The aim of the study is to compare the results of albedo between the triplet AG scattering and quadratic AG scattering. Methods The analytical calculations are performed by HN method. Since the HN method is based on the usage of the Case eigenfunctions, they should
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High-Order Mixed Finite Element Variable Eddington Factor Methods J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-04-21 Samuel Olivier, Terry S. Haut
Abstract We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The mixed finite element VEF discretizations are coupled to a high-order Discontinuous Galerkin (DG) discretization of the discrete ordinates transport equation to form effective linear transport
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On a Response Matrix Solver for Slab-Geometry Neutral Particle Transport Problems in the Discrete Ordinates and Energy Multigroup Formulations Considering Non-Uniform Interior Sources J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-03-30 Leonardo R.C Moraes, Ricardo C. Barros, Richard Vasques
Abstract We present in this work an extension of the Response Matrix (RM) method for the numerical solution of slab-geometry neutral particle transport equation in the discrete ordinates (S N) and energy multigroup formulations considering non-uniform sources. By using the term non-uniform we mean that the particle source is not spatially uniform inside the regions that compose the domain. The extended
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On the Semi-Analytical Solution of Displacement Thickness in a Laminar Streamwise Corner Flow Assisted by Computational Fluid Dynamics Simulation J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-02-02 Eakarach Bumrungthaichaichan, Prajaree Unaprom, Pakapong Sathianchok, Santi Wattananusorn
Abstract In this paper, the new semi-analytical correlation for displacement thickness of laminar fluid flow along an arbitrary-angle corner formed by the intersection of two plates has been proposed because of the discrepancy in displacement thickness for strong interference corner between the present computational fluid dynamics simulation and previous analytical correlation.
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A Deterministic Adjoint-Based Semi-Analytical Algorithm for Fast Response Change Computations in Proton Therapy J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2023-01-27 Tiberiu Burlacu, Danny Lathouwers, Zoltán Perkó
Abstract In this paper we propose a solution to the need for a fast particle transport algorithm in Online Adaptive Proton Therapy capable of cheaply, but accurately computing the changes in patient dose metrics as a result of changes in the system parameters. We obtain the proton phase-space density through the product of the numerical solution to the one-dimensional Fokker-Planck equation and the
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Half-Space Albedo Problem with Pure-Triplet Scattering and Legendre Polynomial Outgoing Flux J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-11-30 A. Z. Bozkır, D. C. Sahni, R. G. Türeci
Abstract In this study, the albedo problem is investigated with three different methods, HN method, FN method, and SVD method. The first two methods are used for the comparison of the SVD method results. Therefore, the main aim of this study is to study of the SVD method for albedo problem. The recently improved method is based on usage of the transformation of the integral part to a sum in the one-speed
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Effect of Temperature Dependent Sink on Peristaltic Transport in a Differentially Heated Vertical Annulus Filled with a Porous Material J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-11-13 A. K. Tiwari, A. K. Singh
Abstract In this article, we have presented a mathematical analysis to study the peristaltic flow through vertical annulus filled with a porous material bounded by two concentric uniform tubes. This analysis can serve as a model which may help in understanding the mechanism of physiological flows and heat transfer in a vertical annulus subject to differentially heating in the presence of a temperature
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The Milne Problem with the Anlı-Güngör Scattering J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-11-08 R. Gökhan Türeci
Abstract Recently developed the Anlı-Güngör scattering function is applied to the Milne problem in this study. It is the function of Legendre polynomials with t parameter which can be called as scattering parameter. The extrapolation distance values are calculated for varying t parameters and varying secondary neutron numbers with the HN method. The numerical results are calculated by 40th approximation
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The Milne Problem for Linear-Triplet Anisotropic Scattering with HN Method J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-11-08 D. Gülderen, D.C. Sahni, R.G. Türeci, A. Aydιn
Abstract The Milne problem is investigated for the linear-triplet anisotropic scattering with HN method in this study. The scattering function is the linear combination of linear anisotropic scattering and triplet anisotropic scattering in Mika’s scattering. The positivity condition is needed to find physical results since the scattering function defines the scattering probabilities. It defines the
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The Ln/Ln0 Method for 1D Neutron Transport in a Slab Medium J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-10-21 B. D. Ganapol
Abstract A new, highly precise benchmark for the monoenergetic 1 D neutron transport equation with isotropic scattering, based on Case’s singular eigenfunctions, is presented. Because of the nature of singular distributions, Case’s analytical solution notoriously resists straightforward numerical computation. To overcome this difficulty, two complementary Lagrange interpolation schemes are constructed
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Analytical Discrete-Ordinates Solutions for Improved 1D Models of Particle Transport in Ducts with Wall Migration J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-09-28 R. D. M. Garcia
Abstract Analytical discrete-ordinates (ADO) solutions are developed for two improved one-dimensional (1D) models of particle transport in ducts that include wall migration. One of the studied models is based on an approximation of the transverse and azimuthal dependencies of the angular flux in terms of two basis functions, while the other uses three. Particle migration in the wall is modeled by an
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“On the Foundation of Transport-Driven Diffusion for Neutron Transport Problems” J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-08-13 Paolo Picca, Roberto Furfaro, Sandra Dulla, Piero Ravetto
Abstract The article presents the foundation of a novel methodology developed for the solution of the neutron transport equation, named the transport driven-diffusion approach, which can be considered as an evolution of the classic multiple collision method. The idea behind this method is based on the expansion of the full solution in terms of the contributions of the particles emitted by successive
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NURBS Enhanced Virtual Element Methods for the Spatial Discretization of the Multigroup Neutron Diffusion Equation on Curvilinear Polygonal Meshes J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-08-05 J. A. Ferguson, J. Kópházi, M. D. Eaton
Abstract The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to
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Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-07-31 William Bennett, Ryan G. McClarren
Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta
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Motion of a Neutrally Buoyant Circular Particle in a Lid-Driven Square Cavity: A Numerical Study J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-07-18 Junjie Hu, Dongke Sun, Shaohua Mao, Hongmei Wu, Songyang Yu, Maosen Xu
Abstract Understanding, predicting and controlling the motion of the solid particles in a confined cavity is significant. The motion of a neutrally buoyant circular particle in a lid-driven square cavity is studied with the lattice Boltzmann method, where the effects of the initial position, particle size and Reynolds number are investigated. The obvious characteristic of the motion of the circular
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Analyzing of the Scattering Coefficients in the Neutron Transport Equation for Critical Systems J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-06-25 Halide Koklu, Okan Ozer
Abstract The scattering function analysis is done by Chebyshev and Legendre polynomials in the neutron transport equation. The effect of the scattering coefficients on the critical thicknesses are presented in tables. The analyses are done for PN, TN, and UN methods up to fourth order of the scattering function. By making calculations, the critical thicknesses are obtained with Mark and Marshak boundary
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Bipolar Hydrodynamical Model for Charge Transport in Graphene Nanoribbons J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-06-20 V. D. Camiola, G. Nastasi
Abstract A hydrodynamical model for charge transport in narrow strips of graphene is here presented. The model takes into account the interactions with the well-known lattice vibrations and with the edge of the strip. The remarkable result is the modulation of the charge current due to the swapping of charge carriers between the conduction and the valence bands, controlled by the Fermi energy variation
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An Improved Model for Light Transport in the Color Conversion Element of Light-Emitting Diodes J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-06-17 Chih-Yang Wu, Dao-Chi Hong
Abstract Light transport with fluorescence in a phosphor layer based on radiative transfer theory is an efficient tool for understanding the performance of a phosphor-converted light-emitting diode. In this work, the models based on radiative transfer theory including light conversion of phosphor particles are developed for calculating the light transport in planar remote phosphor layers. The models
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Corrigendum - Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-06-16 D. C. Sahni
Abstract An important correction in an earlier paper by the author is presented.
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Higher Order UN Method for the Solution of the Neutron Diffusion Problem J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-05-25 Hakan Öztürk, Ahmet Tuğralı
Abstract The first application of the UN (Chebyshev polynomials of the second kind) method with higher order approximations is performed to solve the neutron diffusion problem in a slab reactor. The moments of equations are carried out by solving neutron transport equation using first the conventional spherical harmonics (PN) and then the UN method. These differential equations with constant coefficients
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Numerical Analysis of the Monte-Carlo Noise for the Resolution of the Deterministic and Uncertain Linear Boltzmann Equation (Comparison of Non-Intrusive gPC and MC-gPC) J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-04-25 Gaël Poëtte
Abstract Monte Carlo-generalized Polynomial Chaos (MC-gPC) has already been thoroughly studied in the literature. MC-gPC both builds a gPC based reduced model of a partial differential equation (PDE) of interest and solves it with an intrusive MC scheme in order to propagate uncertainties. This reduced model captures the behavior of the solution of a set of PDEs subject to some uncertain parameters
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A Transport Theory Route to the Dirac Equation J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-04-18 Gianni Coppa
Abstract Starting from the similarity between the spherical harmonics approximation of order one to the linear transport equation (usually referred as P1 approximation) and the Klein-Gordon equation of the quantum physics, an extended set of equations is introduced, which is proved to be equivalent to the Dirac equation with imaginary mass. Conversely, when a real mass is restored into the extended
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Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2022-02-04 Ryan G. McClarren
Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem
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Stochastic Theory of Neutron Transport in Nuclear Reactor J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-08-03
Abstract The work is an extended version of the report presented at the conference ICTT-26. In the Part I we derive the forward and backward time-dependent linear stochastic equations for probability density of the integer number of neutrons and delayed neutron precursors in distributed model of a nuclear reactor. In the Part II we derive the distributed criticality stochastic equations and obtain
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Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-07-02 D. C. Sahni
Abstract We develop the density transform method for treating particle transport problems in spherical geometry with linearly anisotropic scattering. We consider both, the interior and exterior problems of a homogeneous sphere and show that the transform satisfies an equation that resembles particle transport equation in slab geometry. The boundary conditions for these two problems are different. We
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Hybrid Lattice Boltzmann Simulation of Three-Dimensional Natural Convection J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-06-30 Alexander Nee
Abstract The capability of hybrid lattice Boltzmann–finite difference model in simulation of laminar and turbulent three-dimensional (3D) natural convection was examined. Fluid dynamics was computed by means of the lattice Boltzmann method and the finite difference solver was used for advection-diffusion equation. It was found that both two-dimensional and 3D models reproduced the same thermal fields
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A Response Matrix Method for Slab-Geometry Discrete Ordinates Adjoint Calculations in Energy-Dependent Neutral Particle Transport J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-05-17 Leonardo R. da C. Moraes, Ralph S. Mansur, Carlos A. Moura, Jesús P. Curbelo, Hermes Alves Filho, Ricardo C. Barros
Abstract Presented here is an application of the Response Matrix (RM †) method for adjoint discrete ordinates (S N) problems in slab-geometry applied to energy-dependent neutral particle transport problems. The RM † method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the
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Entropy Generation Rate for Stationary Ballistic-Diffusive Heat Conduction in a Rectangular Flake J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-09 Saad Bin Mansoor, Bekir S. Yilbas
Abstract Thermodynamic irreversibility in low dimensional flake is considered and entropy generation rate in two-dimensional thin film is examined, Equation of phonon radiative transfer is solved for two-dimensional and rectangular diamond flake. Volumetric and total entropy generation rate are evaluated incorporating the formulation of thermal radiation heat transfer. The influence of flake aspect
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Numerical Solution of the Azimuth-Dependent Fokker-Planck Equation in 1D Slab Geometry J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-16 Óscar López Pouso, Nizomjon Jumaniyazov
Abstract This paper is devoted to solve the steady monoenergetic Fokker-Planck equation in the 1D slab when the incoming fluxes and the source term are allowed to depend on the azimuth θ. The problem is split into a collection of θ-independent problems for the Fourier coefficients of the full solution. The main difficulty is that, except for the zeroth Fourier coefficient, each of these problems contains
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On the Generalization of the Response Matrix Spectral Nodal Method for Neutral Particle SN Source–Detector Problems in Slab Geometry J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-17 Jesús P. Curbelo, Odair P. da Silva, Ricardo C. Barros
Abstract 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
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Three-Dimensional Numerical Study of a Fluid-Kinetic Model for Respiratory Aerosols with Variable Size and Temperature J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-04-05 Laurent Boudin, David Michel
Abstract In this paper, we extend to the three-dimensional case the numerical study previously performed in a two-dimensional framework for a complex coupled fluid-kinetic model describing respiratory aerosols. The specificity of this model lies in the fact that it takes into account the airway humidity and the resulting hygroscopic effects on the aerosol droplets, namely their size variation. The
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Gray Phonon Transport Prediction of Thermal Conductivity in Lithium Aluminate with Higher-Order Finite Elements on Meshes with Curved Surfaces J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-18 Nicholas H. Whitman, Todd S. Palmer, P. Alex Greaney, S. Aria Hosseini, Douglas E. Burkes, David J. Senor
Abstract We present a method for predicting thermal conductivity by deterministically solving the Boltzmann transport equation for gray phonons by utilizing arbitrary higher-order continuous finite elements on meshes which may also be unstructured and utilize curved surfaces. The self-adjoint angular flux (SAAF) formulation of the gray, steady-state, single relaxation time, phonon radiative transport
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Modified Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-17 J.J. Kuczek, J.K. Patel, R. Vasques
Abstract This paper introduces a new acceleration technique for the convergence of the solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO) acceleration scheme. The Fokker-Planck equation, which is an asymptotic limit of the transport equation in highly forward-peaked settings, is modified and used for acceleration;
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Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-03-14 Jan Bartsch, Giovanni Nastasi, Alfio Borzì
Abstract This paper is devoted to the formulation and numerical solution by Monte Carlo (MC) methods of an optimal control problem governed by the linear space-homogeneous Keilson-Storer (KS) master equation. The KS master equation is a representative model of the class of linear Boltzmann equations with many applications ranging from spectroscopy to transport theory. The purpose of the optimal control
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The Homogeneous B1 Model as Polynomial Eigenvalue Problem J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-02-23 Daniele Tomatis, Johan Cufe
Abstract The homogeneous version of the B1 leakage model is a non-linear eigenvalue problem which is generally solved iteratively by a root-finding algorithm, combined to the supplementary eigenvalue problem of the multiplication factor. This problem is widely used for ordinary cross section preparation in reactor analysis. Our work approximates this problem with a polynomial eigenvalue problem, which
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On Global Existence and Regularity of Solutions for a Transport Problem Related to Charged Particles J. Comput. Theor. Transp. (IF 0.7) Pub Date : 2021-01-17 Jouko Tervo
Abstract The paper considers a class of linear Boltzmann transport equations which models charged particle transport, for example in dose calculation of radiation therapy. The equation is an approximation of the exact transport equation containing hyper-singular integrals in its collision terms. The paper confines to the global case where the spatial domain G is the whole space R3. Existence results