Pub Date : 2023-06-07DOI: 10.1080/23324309.2023.2257670
Guillaume Lambou Ymeli
AbstractThis 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 cylinder. This solution is built by combining the spherical harmonics for volumetric thermal radiations with the D1Q3 scheme of lattice Boltzmann method (LBM) for hyperbolic energy equation where the gradient of static particle distribution function was discretized at implicit time. The accuracy of the proposed model for dealing with radiation/conduction problems is investigated by considering a semitransparent radiative transfer in a cylinder with temperature dependent thermal conductivity and space dependent scattering albedo. The effects of different parameters, such as scattering albedo, refractive index, thermal conductivity, emissivity, optical thickness, and the conduction-radiation parameter on both radiations and temperature distributions for steady and transient states are studied. Results of the present work are benchmarked against those available in the literature with accuracy greater than 98.9% for a large interval of parameter sets and therefore, excellent agreement has been obtained. It also establishes from this study that the proposed layered approach is an efficient and accurate method for radiative analysis in inhomogeneous media while the D1Q3 scheme is suitable to accommodate thermal wave front in non-Fourier analysis.Keywords: Non-Fourier conductionradiationspherical harmonics methodLattice Boltzmann methodsolid cylinder Disclosure statementNo potential conflict of interest was reported by the authors.
{"title":"A Semi-Analytical Description of Radiation Coupled with Thermal Wave Conductive Transfer in Inhomogeneous Solid Cylinder","authors":"Guillaume Lambou Ymeli","doi":"10.1080/23324309.2023.2257670","DOIUrl":"https://doi.org/10.1080/23324309.2023.2257670","url":null,"abstract":"AbstractThis 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 cylinder. This solution is built by combining the spherical harmonics for volumetric thermal radiations with the D1Q3 scheme of lattice Boltzmann method (LBM) for hyperbolic energy equation where the gradient of static particle distribution function was discretized at implicit time. The accuracy of the proposed model for dealing with radiation/conduction problems is investigated by considering a semitransparent radiative transfer in a cylinder with temperature dependent thermal conductivity and space dependent scattering albedo. The effects of different parameters, such as scattering albedo, refractive index, thermal conductivity, emissivity, optical thickness, and the conduction-radiation parameter on both radiations and temperature distributions for steady and transient states are studied. Results of the present work are benchmarked against those available in the literature with accuracy greater than 98.9% for a large interval of parameter sets and therefore, excellent agreement has been obtained. It also establishes from this study that the proposed layered approach is an efficient and accurate method for radiative analysis in inhomogeneous media while the D1Q3 scheme is suitable to accommodate thermal wave front in non-Fourier analysis.Keywords: Non-Fourier conductionradiationspherical harmonics methodLattice Boltzmann methodsolid cylinder Disclosure statementNo potential conflict of interest was reported by the authors.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135493612","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}
Pub Date : 2023-06-07DOI: 10.1080/23324309.2023.2254951
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 study some statistical properties of this distribution. Besides that, we study the estimated value of the diffusion coefficient to present more information about the particle’s motion in the fluid.
{"title":"On Multivariate Distribution of <i>n-</i>Dimensional Brownian Diffusion Particle in the Fluid","authors":"Mohamed Abd Allah El-Hadidy, Alaa Awad Alzulaibani","doi":"10.1080/23324309.2023.2254951","DOIUrl":"https://doi.org/10.1080/23324309.2023.2254951","url":null,"abstract":"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 study some statistical properties of this distribution. Besides that, we study the estimated value of the diffusion coefficient to present more information about the particle’s motion in the fluid.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135494061","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}
Pub Date : 2023-04-16DOI: 10.1080/23324309.2023.2233233
R. D. Garcia, M. 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 and transmission probabilities resulting from Monte Carlo simulations carried out with the MCNP and PHITS codes for iron, concrete and graphite ducts are used as reference solutions. It is concluded that the model built on two basis functions performs well (deviations typically < 10% in magnitude) for iron, the material for which absorption is most important, but less so for the scattering-dominated materials concrete and graphite. It is also concluded that changes in the energy distribution of the incident source have their strongest influence on the results for iron ducts.
{"title":"Evaluation of 1D Models for Particle Transport with Wall Migration in Ducts of Rectangular Cross Section","authors":"R. D. Garcia, M. T. Pazianotto, Felipe L. Frigi","doi":"10.1080/23324309.2023.2233233","DOIUrl":"https://doi.org/10.1080/23324309.2023.2233233","url":null,"abstract":"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 and transmission probabilities resulting from Monte Carlo simulations carried out with the MCNP and PHITS codes for iron, concrete and graphite ducts are used as reference solutions. It is concluded that the model built on two basis functions performs well (deviations typically < 10% in magnitude) for iron, the material for which absorption is most important, but less so for the scattering-dominated materials concrete and graphite. It is also concluded that changes in the energy distribution of the incident source have their strongest influence on the results for iron ducts.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"246 - 268"},"PeriodicalIF":0.7,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41493001","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}
Pub Date : 2023-04-16DOI: 10.1080/23324309.2023.2223410
Adam Q. Lam, T. Palmer, T. Brunner, R. 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 a purely-absorbing transport equation and a diffusion solution that accounts for effective scattering, or absorption–reemission. The method aims to improve the implicitness of the traditional implicit Monte Carlo (IMC) method. We derive DAIMC generally for 3D Cartesian geometries, but in this paper, we present results and analysis in 1D slab geometry. These preliminary results indicate that DAIMC implementations may provide more accurate and robust TRT solutions than IMC in certain test problems.
{"title":"A Monte Carlo Thermal Radiative Transfer Solver with Nonlinear Elimination","authors":"Adam Q. Lam, T. Palmer, T. Brunner, R. Vega","doi":"10.1080/23324309.2023.2223410","DOIUrl":"https://doi.org/10.1080/23324309.2023.2223410","url":null,"abstract":"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 a purely-absorbing transport equation and a diffusion solution that accounts for effective scattering, or absorption–reemission. The method aims to improve the implicitness of the traditional implicit Monte Carlo (IMC) method. We derive DAIMC generally for 3D Cartesian geometries, but in this paper, we present results and analysis in 1D slab geometry. These preliminary results indicate that DAIMC implementations may provide more accurate and robust TRT solutions than IMC in certain test problems.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"221 - 245"},"PeriodicalIF":0.7,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545167","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}
Pub Date : 2023-04-16DOI: 10.1080/23324309.2023.2222003
P. 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 transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed, and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.
{"title":"Probability of Initiation in Neutron Transport","authors":"P. Brown","doi":"10.1080/23324309.2023.2222003","DOIUrl":"https://doi.org/10.1080/23324309.2023.2222003","url":null,"abstract":"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 transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed, and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"179 - 220"},"PeriodicalIF":0.7,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42187760","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}
Pub Date : 2023-02-23DOI: 10.1080/23324309.2023.2218843
R. G. Türeci, D. 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 be derived for the interested in this study. The tabulated results are calculated for varying the secondary neutron number and the scattering parameter. Albedo values for the triplet anisotropic scattering are convergent. A special code is used to get the numerical values in Mathematica with high precision This code holds all numerical values and the results of all algebraic process as a rational number. Thus, the round-off errors in machine language are minimized. A second and completely different numerical process is performed with the Polynomial Regression (PR) and the Artificial Neural Network (ANN). The application of the PR and ANN algorithms are studied with the calculated albedo results in this study. This application is only data mining without performing any analytical calculation. Discussion The expectation is to get bigger albedo values than the quadratic AG scattering. But the results are surprising that the triplet and the quadratic albedo results are close to each other. The result of ANN is more successful than PR results. Moreover, the intermediate values that are not in the data set can also be successfully calculated.
{"title":"Half-Space Albedo Problem for Triplet Anlı-Güngör Scattering","authors":"R. G. Türeci, D. Gülderen","doi":"10.1080/23324309.2023.2218843","DOIUrl":"https://doi.org/10.1080/23324309.2023.2218843","url":null,"abstract":"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 be derived for the interested in this study. The tabulated results are calculated for varying the secondary neutron number and the scattering parameter. Albedo values for the triplet anisotropic scattering are convergent. A special code is used to get the numerical values in Mathematica with high precision This code holds all numerical values and the results of all algebraic process as a rational number. Thus, the round-off errors in machine language are minimized. A second and completely different numerical process is performed with the Polynomial Regression (PR) and the Artificial Neural Network (ANN). The application of the PR and ANN algorithms are studied with the calculated albedo results in this study. This application is only data mining without performing any analytical calculation. Discussion The expectation is to get bigger albedo values than the quadratic AG scattering. But the results are surprising that the triplet and the quadratic albedo results are close to each other. The result of ANN is more successful than PR results. Moreover, the intermediate values that are not in the data set can also be successfully calculated.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"143 - 161"},"PeriodicalIF":0.7,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45524114","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}
Pub Date : 2023-02-23DOI: 10.1080/23324309.2023.2219659
Dalia A. Garbiea, A. El-Depsy, M. M. Selim, O. 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 ( which moves backward, part (m) which moves forward, and part (n) which emerge isotropically from the collisions, where + m + n = 1. The integral version of the transport equation is solved using trial functions based on Case’s eigenmodes and exponential integral function. Hence, the solution to the Milne problem is formulated in terms of characteristic quantities such as the extrapolation length and the fractional scalar flux discontinuity. Numerical results for the analytically evaluated quantities are presented. Some of our numerical results are compared with the available published results.
摘要本文研究了极各向异性散射函数对两区Milne问题的影响。这个散射函数把碰撞产生的中子分成三部分;部分(向后移动)，部分(m)向前移动，部分(n)从碰撞中各向同性出现，其中+ m + n = 1。利用基于Case特征模态和指数积分函数的试函数求解输运方程的积分版本。因此，米尔恩问题的解是用外推长度和分数标量通量不连续等特征量来表示的。给出了解析求值量的数值结果。我们的一些数值结果与现有的已发表的结果进行了比较。
{"title":"Study of Forward and Backward Scattering in Two-Region Milne Problem for Non-absorbing Medium Using a Synthetic Kernel","authors":"Dalia A. Garbiea, A. El-Depsy, M. M. Selim, O. A. Mohamedien","doi":"10.1080/23324309.2023.2219659","DOIUrl":"https://doi.org/10.1080/23324309.2023.2219659","url":null,"abstract":"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 ( which moves backward, part (m) which moves forward, and part (n) which emerge isotropically from the collisions, where + m + n = 1. The integral version of the transport equation is solved using trial functions based on Case’s eigenmodes and exponential integral function. Hence, the solution to the Milne problem is formulated in terms of characteristic quantities such as the extrapolation length and the fractional scalar flux discontinuity. Numerical results for the analytically evaluated quantities are presented. Some of our numerical results are compared with the available published results.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"162 - 177"},"PeriodicalIF":0.7,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45139173","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}
Pub Date : 2023-01-11DOI: 10.1080/23324309.2023.2200308
Samuel S. Olivier, T. 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 algorithms that are compatible with high-order (curved) meshes. This combination of VEF and transport discretizations is motivated by the use of high-order mixed finite element methods in hydrodynamics calculations at the Lawrence Livermore National Laboratory (LLNL). Due to the mathematical structure of the VEF equations, the standard Raviart Thomas (RT) mixed finite elements cannot be used to approximate the vector variable in the VEF equations. Instead, we investigate three alternatives based on the use of continuous finite elements for each vector component, a non-conforming RT approach where DG-like techniques are used, and a hybridized RT method. We present numerical results that demonstrate high-order accuracy, compatibility with curved meshes, and robust and efficient convergence in iteratively solving the coupled transport-VEF system and in the preconditioned linear solvers used to invert the discretized VEF equations.
摘要将高阶混合有限元离散化技术及其相关的预条件迭代求解方法应用于两个空间维度的可变Eddington因子(VEF)方程。将混合有限元VEF离散化与离散坐标输运方程的高阶间断伽辽金(DG)离散化相耦合，形成与高阶(曲线)网格兼容的有效线性输运算法。劳伦斯利弗莫尔国家实验室(LLNL)在流体力学计算中使用了高阶混合有限元方法，从而激发了VEF和输运离散化的结合。由于VEF方程的数学结构，标准的Raviart - Thomas (RT)混合有限元不能近似求解VEF方程中的矢量变量。相反，我们研究了基于对每个矢量组件使用连续有限元的三种替代方案，一种使用类似dg技术的非一致性RT方法，以及一种杂交RT方法。我们给出的数值结果表明，在迭代求解耦合输运-VEF系统和用于反演离散VEF方程的预条件线性求解器中，具有高阶精度、与曲面网格兼容、鲁棒性和高效收敛性。
{"title":"High-Order Mixed Finite Element Variable Eddington Factor Methods","authors":"Samuel S. Olivier, T. Haut","doi":"10.1080/23324309.2023.2200308","DOIUrl":"https://doi.org/10.1080/23324309.2023.2200308","url":null,"abstract":"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 algorithms that are compatible with high-order (curved) meshes. This combination of VEF and transport discretizations is motivated by the use of high-order mixed finite element methods in hydrodynamics calculations at the Lawrence Livermore National Laboratory (LLNL). Due to the mathematical structure of the VEF equations, the standard Raviart Thomas (RT) mixed finite elements cannot be used to approximate the vector variable in the VEF equations. Instead, we investigate three alternatives based on the use of continuous finite elements for each vector component, a non-conforming RT approach where DG-like techniques are used, and a hybridized RT method. We present numerical results that demonstrate high-order accuracy, compatibility with curved meshes, and robust and efficient convergence in iteratively solving the coupled transport-VEF system and in the preconditioned linear solvers used to invert the discretized VEF equations.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"79 - 142"},"PeriodicalIF":0.7,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48483562","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}
Pub Date : 2023-01-02DOI: 10.1080/23324309.2023.2171063
E. Bumrungthaichaichan, Prajaree Unaprom, Pakapong Sathianchok, S. 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.
{"title":"On the Semi-Analytical Solution of Displacement Thickness in a Laminar Streamwise Corner Flow Assisted by Computational Fluid Dynamics Simulation","authors":"E. Bumrungthaichaichan, Prajaree Unaprom, Pakapong Sathianchok, S. Wattananusorn","doi":"10.1080/23324309.2023.2171063","DOIUrl":"https://doi.org/10.1080/23324309.2023.2171063","url":null,"abstract":"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.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"42 - 54"},"PeriodicalIF":0.7,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43023049","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}
Pub Date : 2023-01-02DOI: 10.1080/23324309.2023.2194294
L.R.C. Moraes, R. Barros, R. 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 ) 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 RM method, differently from the conventional RM method, is based on the solution of “source-independent” auxiliary problems (Green’s functions). The solution of these auxiliary problems is used in conjunction with the given non-uniform source to generate the sweeping matrices for the extended RM method. Numerical results with respect to both uniform and non-uniform source problems are given to illustrate the efficiency of the offered extended RM method.
{"title":"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","authors":"L.R.C. Moraes, R. Barros, R. Vasques","doi":"10.1080/23324309.2023.2194294","DOIUrl":"https://doi.org/10.1080/23324309.2023.2194294","url":null,"abstract":"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 ) 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 RM method, differently from the conventional RM method, is based on the solution of “source-independent” auxiliary problems (Green’s functions). The solution of these auxiliary problems is used in conjunction with the given non-uniform source to generate the sweeping matrices for the extended RM method. Numerical results with respect to both uniform and non-uniform source problems are given to illustrate the efficiency of the offered extended RM method.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"52 1","pages":"55 - 77"},"PeriodicalIF":0.7,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42286540","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}
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