Pub Date : 2021-06-07DOI: 10.1080/23324309.2021.1942061
A. 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. 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.
{"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":"50 1","pages":"280 - 296"},"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}
Pub Date : 2021-06-07DOI: 10.1080/23324309.2021.1938610
D. 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 also work out the density transform method for linearly anisotropic scattering for a region of arbitrary shape.
{"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":"50 1","pages":"249 - 279"},"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}
Pub Date : 2021-04-16DOI: 10.1080/23324309.2021.1914661
L.R.C. Moraes, R. S. Mansur, C. A. Moura, J. P. Curbelo, H. A. Filho, R. Barros
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.
{"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":"50 1","pages":"159 - 179"},"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}
Pub Date : 2021-04-05DOI: 10.1080/23324309.2021.1906705
L. Boudin, D. 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 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.
{"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":"50 1","pages":"507 - 527"},"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}
Pub Date : 2021-03-18DOI: 10.1080/23324309.2021.1900258
N. Whitman, T. Palmer, P. Greaney, S. Hosseini, D. Burkes, D. 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 (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.
{"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":"50 1","pages":"483 - 506"},"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}
Pub Date : 2021-03-14DOI: 10.1080/23324309.2021.1896552
Jan Bartsch, G. Nastasi, A. 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 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.
{"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":"50 1","pages":"454 - 482"},"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}
Pub Date : 2021-03-01DOI: 10.1080/23324309.2021.1896554
Ó. López Pouso, N. 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 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.
{"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":"50 1","pages":"102 - 133"},"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}
Pub Date : 2021-02-23DOI: 10.1080/23324309.2021.1885446
D. Tomatis, Johan Cufe
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.
{"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":"50 1","pages":"220 - 235"},"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}
Pub Date : 2021-02-23DOI: 10.1080/23324309.2021.1896553
S. Mansoor, B. 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 ratio (width to height) on the entropy generation rate is explored while keeping the Diamond flake area constant for all aspect ratios considered. The findings reveal that the entropy generation rate increases with increasing aspect ratio for fixed boundary conditions.
{"title":"Entropy Generation Rate for Stationary Ballistic-Diffusive Heat Conduction in a Rectangular Flake","authors":"S. Mansoor, B. Yilbas","doi":"10.1080/23324309.2021.1896553","DOIUrl":"https://doi.org/10.1080/23324309.2021.1896553","url":null,"abstract":"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 ratio (width to height) on the entropy generation rate is explored while keeping the Diamond flake area constant for all aspect ratios considered. The findings reveal that the entropy generation rate increases with increasing aspect ratio for fixed boundary conditions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"87 - 101"},"PeriodicalIF":0.7,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1896553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45464733","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 : 2021-01-17DOI: 10.1080/23324309.2020.1851722
J. 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 Existence results of solutions for the due initial value problem are formulated by applying variational methods. In addition, some regularity results of solutions are verified in scales of relevant anisotropic mixed-norm Sobolev spaces.
{"title":"On Global Existence and Regularity of Solutions for a Transport Problem Related to Charged Particles","authors":"J. Tervo","doi":"10.1080/23324309.2020.1851722","DOIUrl":"https://doi.org/10.1080/23324309.2020.1851722","url":null,"abstract":"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 Existence results of solutions for the due initial value problem are formulated by applying variational methods. In addition, some regularity results of solutions are verified in scales of relevant anisotropic mixed-norm Sobolev spaces.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"180 - 219"},"PeriodicalIF":0.7,"publicationDate":"2021-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1851722","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44079821","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：