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Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model 非平衡扩散模型的两组辐射转移基准
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2022-02-04 DOI: 10.1080/23324309.2022.2032757
R. McClarren
{"title":"Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model","authors":"R. McClarren","doi":"10.1080/23324309.2022.2032757","DOIUrl":"https://doi.org/10.1080/23324309.2022.2032757","url":null,"abstract":"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. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Stochastic Theory of Neutron Transport in Nuclear Reactor 核反应堆中子输运的随机理论
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-07-29 DOI: 10.1080/23324309.2021.1942062
R. Y. Nesterenko
{"title":"Stochastic Theory of Neutron Transport in Nuclear Reactor","authors":"R. Y. Nesterenko","doi":"10.1080/23324309.2021.1942062","DOIUrl":"https://doi.org/10.1080/23324309.2021.1942062","url":null,"abstract":"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 the analytical solutions for asymptotic neutron number probability density function for a reactor in a close-to-critical state.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46285183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hybrid Lattice Boltzmann Simulation of Three-Dimensional Natural Convection 三维自然对流的混合晶格玻尔兹曼模拟
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-06-07 DOI: 10.1080/23324309.2021.1942061
A. Nee
{"title":"Hybrid Lattice Boltzmann Simulation of Three-Dimensional Natural Convection","authors":"A. Nee","doi":"10.1080/23324309.2021.1942061","DOIUrl":"https://doi.org/10.1080/23324309.2021.1942061","url":null,"abstract":"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. The Nusselt numbers were in a good agreement with benchmark data with the Rayleigh number up to Computation speed of developed hybrid model was more than two times higher in comparison with conventional computational fluid dynamics (CFD) vorticity–vector potential formulation.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1942061","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47955940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering 具有线性各向异性散射的球几何粒子输运问题的密度变换方法
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-06-07 DOI: 10.1080/23324309.2021.1938610
D. Sahni
{"title":"Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering","authors":"D. Sahni","doi":"10.1080/23324309.2021.1938610","DOIUrl":"https://doi.org/10.1080/23324309.2021.1938610","url":null,"abstract":"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 also work out the density transform method for linearly anisotropic scattering for a region of arbitrary shape.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1938610","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44857912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A Response Matrix Method for Slab-Geometry Discrete Ordinates Adjoint Calculations in Energy-Dependent Neutral Particle Transport 能量相关中性粒子输运中板几何离散坐标伴随计算的响应矩阵方法
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-04-16 DOI: 10.1080/23324309.2021.1914661
L.R.C. Moraes, R. S. Mansur, C. A. Moura, J. P. Curbelo, H. A. Filho, R. Barros
{"title":"A Response Matrix Method for Slab-Geometry Discrete Ordinates Adjoint Calculations in Energy-Dependent Neutral Particle Transport","authors":"L.R.C. Moraes, R. S. Mansur, C. A. Moura, J. P. Curbelo, H. A. Filho, R. Barros","doi":"10.1080/23324309.2021.1914661","DOIUrl":"https://doi.org/10.1080/23324309.2021.1914661","url":null,"abstract":"Abstract Presented here is an application of the Response Matrix (RM ) method for adjoint discrete ordinates (S ) 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 analytical solution of the energy multigroup adjoint S equations. The main contribution of this work is to analyze the application of the RM method to problems where it is required to solve the energy multigroup adjoint S equations multiple times. This is the case of two classes of problems that can be taken care of through the adjoint technique: (i) source-detector problems; and (ii) the estimation of interior neutron source distributions that drive a subcritical system at a prescribed power density level. The efficiency (speed and accuracy) of the RM code is compared to the conventional Diamond Difference code.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1914661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41753799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Three-Dimensional Numerical Study of a Fluid-Kinetic Model for Respiratory Aerosols with Variable Size and Temperature 变粒径变温度呼吸性气溶胶流体动力学模型的三维数值研究
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-04-05 DOI: 10.1080/23324309.2021.1906705
L. Boudin, D. Michel
{"title":"Three-Dimensional Numerical Study of a Fluid-Kinetic Model for Respiratory Aerosols with Variable Size and Temperature","authors":"L. Boudin, D. Michel","doi":"10.1080/23324309.2021.1906705","DOIUrl":"https://doi.org/10.1080/23324309.2021.1906705","url":null,"abstract":"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 air is described through a system of partial differential equations: the incompressible Navier–Stokes equations for the air velocity, convection-diffusion equations on its temperature, and water vapor mass fraction. The aerosol distribution function obeys a Vlasov-type equation and depends on the standard kinetic variables, but also on radius and temperature variables. After discussing again the implementation strategy, we perform numerical experiments, mainly in a branched structure looking like the trachea and the first lung generation. This allows the presentation of various statistics on the aerosol behavior in terms of particle deposition, temperature, and size variation of the droplets. We observe that the outcome appears coherent with the two-dimensional case. Finally, we discuss several assumptions which may lead to model simplifications, such as the fact that the water vapor mass fraction in the air may be considered to be constant throughout the branched structure in standard breathing conditions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1906705","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43915716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gray Phonon Transport Prediction of Thermal Conductivity in Lithium Aluminate with Higher-Order Finite Elements on Meshes with Curved Surfaces 曲面网格上铝酸锂热导率的高阶有限元灰色声子输运预测
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-03-18 DOI: 10.1080/23324309.2021.1900258
N. Whitman, T. Palmer, P. Greaney, S. Hosseini, D. Burkes, D. Senor
{"title":"Gray Phonon Transport Prediction of Thermal Conductivity in Lithium Aluminate with Higher-Order Finite Elements on Meshes with Curved Surfaces","authors":"N. Whitman, T. Palmer, P. Greaney, S. Hosseini, D. Burkes, D. Senor","doi":"10.1080/23324309.2021.1900258","DOIUrl":"https://doi.org/10.1080/23324309.2021.1900258","url":null,"abstract":"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 (PRT) equation was spatially discretized using the continuous finite element method and angularly discretized using the discrete ordinates method. The solution discretization methodology was verified using a method of manufactured solution (MMS) spatial convergence test case and compared favorably to previous work. The angular phonon radiances, heat flux, and temperatures computed in this work compare favorably to previous literature in silicon thin films. Using local values of the temperature gradient and heat flux, the thermal conductivity as a function of position in a one-dimensional perfect crystal was evaluated using a Fourier’s Law representation and compared to kinetic theory. Our results show that in the interior of the simulation domain, our transport-based prediction of thermal conductivity converged on the kinetic theory estimation. We also find that near isothermal boundaries, the transport solution deviated from kinetic theory, implying non-equilibrium behavior in the thin-film limit and agreed with previous studies.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1900258","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46672825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework 蒙特卡罗框架下Keilson-Storer主方程的最优控制
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-03-14 DOI: 10.1080/23324309.2021.1896552
Jan Bartsch, G. Nastasi, A. Borzì
{"title":"Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework","authors":"Jan Bartsch, G. Nastasi, A. Borzì","doi":"10.1080/23324309.2021.1896552","DOIUrl":"https://doi.org/10.1080/23324309.2021.1896552","url":null,"abstract":"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 in the collision kernel of this model is to drive an ensemble of particles to acquire a desired mean velocity and to achieve a desired final velocity configuration. For this purpose, a KS optimality system characterizing the solution of the proposed optimal control problem is derived and used to construct a gradient-based optimization strategy in the framework of MC methods. This task requires to accommodate the resulting adjoint KS model in a form that is consistent with the kinetic formulation. Results of numerical experiments successfully validate the proposed control framework.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1896552","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46655335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Numerical Solution of the Azimuth-Dependent Fokker-Planck Equation in 1D Slab Geometry 一维平板几何中方位相关Fokker-Planck方程的数值解
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-03-01 DOI: 10.1080/23324309.2021.1896554
Ó. López Pouso, N. Jumaniyazov
{"title":"Numerical Solution of the Azimuth-Dependent Fokker-Planck Equation in 1D Slab Geometry","authors":"Ó. López Pouso, N. Jumaniyazov","doi":"10.1080/23324309.2021.1896554","DOIUrl":"https://doi.org/10.1080/23324309.2021.1896554","url":null,"abstract":"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 an artificial absorption coefficient which is singular at the poles. Two numerical schemes capable of dealing with the singularities are proposed: one that is considered as the main scheme, and a second ‘security’ scheme which is used to verify that the results obtained by means of the first one are reliable. Numerical experiments showing second order of convergence are conducted and discussed.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1896554","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47446366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Homogeneous B 1 Model as Polynomial Eigenvalue Problem 多项式特征值问题的齐次B1模型
IF 0.7 4区 工程技术
Journal of Computational and Theoretical Transport Pub Date : 2021-02-23 DOI: 10.1080/23324309.2021.1885446
D. Tomatis, Johan Cufe
{"title":"The Homogeneous B 1 Model as Polynomial Eigenvalue Problem","authors":"D. Tomatis, Johan Cufe","doi":"10.1080/23324309.2021.1885446","DOIUrl":"https://doi.org/10.1080/23324309.2021.1885446","url":null,"abstract":"Abstract The homogeneous version of the B 1 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 can be easily transformed into an ordinary linear generalized eigenproblem of size equal to the initial one multiplied by the polynomial degree used for the approximation of a transcendental function. This procedure avoids recurring to numerical root-finding methods supported by extra eigenvalue problems. The solution of the fundamental buckling with increasing approximation order is compared to the reference value obtained by inverse iterations.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1885446","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43895299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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