The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in...The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.展开更多
The China dual-functional lithium–lead test blanket module(DFLL-TBM) is a liquid Li Pb blanket concept developed by the Institute of Nuclear Energy Safety Technology of the Chinese Academy of Sciences for testing in ...The China dual-functional lithium–lead test blanket module(DFLL-TBM) is a liquid Li Pb blanket concept developed by the Institute of Nuclear Energy Safety Technology of the Chinese Academy of Sciences for testing in ITER to validate relevant tritium breeding and shielding technologies. In this study, neutronic calculations of DFLL-TBM were carried out using a massively parallel three-dimensional transport code, Hydra, with the Fusion Evaluated Nuclear Data Library/MG. Hydra was developed by the Nuclear Engineering Computational Physics Lab based on the discrete ordinates method and has been devoted to neutronic analysis and shielding evaluation for nuclear facilities. An in-house Monte Carlo code(MCX) was employed to verify the discretized calculation model used by Hydra for the DFLL-TBM calculations. The results showed two key aspects:(1) In most material zones,Hydra solutions are in good agreement with the reference MCX results within 1%, and the maximal relative difference of the neutron flux is merely 3%, demonstrating the correctness of the calculation model;(2) while the current DFLL-TBM design meets the operation shielding requirement of ITER for 4 years, it does not satisfy the tritium self-sufficiency requirement. Compared to the two-step approach, Hydra produces higher accuracies as it does not rely on the homogenization technique during the calculation process. The parallel efficiency tests of Hydra using the DFLL-TBM model also showed that this code maintains a high parallel efficiency on O(100) processors and, as a result, is able to significantly improve computing performance through parallelization. Parameter studies have been carried out by varying the thickness of the beryllium armor layer and the tritium breeding zone to understand the influence of the beryllium layer and breeding zone thickness on tritium breeding performance. This establishes a foundation for further improvement in the tritium production performance of DFLL-TBM.展开更多
This paper presents a novel approach for evaluating the air impact on urban microclimate and building loads.Traditional software tools,such as TRNSYS and EnergyPlus,often employ the surface-to-surface method for radia...This paper presents a novel approach for evaluating the air impact on urban microclimate and building loads.Traditional software tools,such as TRNSYS and EnergyPlus,often employ the surface-to-surface method for radiation transfer calculations,which neglects the influence of air.To address this limitation,this work integrates the discrete ordinates method(DOM)with the spectral-line weighted-sum-of-gray-gases(SLW)air model to develop a microclimate energy approach.The SLW model uses outdoor temperature and humidity data to compute absorption coefficients,leveraging the air spectrum provided by the HITRAN database.The DOM is then employed to calculate both solar and infrared radiation transfers within the urban environment.A transient simulation is conducted over one year for an urban scene in Suzhou,China.The results indicate that the air impact on radiation transfer increases with rising outdoor temperature and humidity.Overall,the results demonstrate that air effects exert a non-negligible influence on building heating and cooling load calculations,with an impact magnitude comparable to the introduction of an auxiliary thermal source.This study highlights the significance of considering air properties in urban microclimate and building energy simulations for more accurate results.展开更多
The original vector discrete ordinate radiative transfer(VDISORT)model takes into account Stokes radiance vector but derives its solution assuming azimuthal symmetric surface reflective matrix and atmospheric scatteri...The original vector discrete ordinate radiative transfer(VDISORT)model takes into account Stokes radiance vector but derives its solution assuming azimuthal symmetric surface reflective matrix and atmospheric scattering phase matrix,such as the phase matrix derived from spherical particles or randomly oriented non-spherical particles.In this study,a new VDISORT is developed for general atmospheric scattering and boundary conditions.Stokes vector is decomposed into both sinusoidal and cosinusoidal harmonic modes,and the radiance at arbitrary viewing geometry is solved directly by adding two zero-weighted points in the Gaussian quadrature scheme.The complex eigenvalues in homogeneous solutions are also taken into full consideration.The accuracy of VDISORT model is comprehensively validated by four cases:Rayleigh scattering case,the spherical particle scattering case with the Legendre expansion coefficients of 0th-13th orders of the phase matrix(hereinafter L13),L13 with a polarized source,and the randomoriented oblate particle scattering case with the Legendre expansion coefficients of 0th-11th orders of the phase matrix(hereinafter L11).In all cases,the simulated radiances agree well with the benchmarks,with absolute biases less than 0.0065,0.0006,and 0.0008 for Rayleigh,unpolarized L13,and L11,respectively.Since a polarized bidirectional reflection distribution function(pBRDF)matrix is used as the lower boundary condition,VDISORT is now able to handle fully coupled atmospheric and surface polarimetric radiative transfer processes.展开更多
Using the imaginary coordinate method given by Ref. [1] it has been proved that the maximal Schwarzschild geometry can be described by the Weyl coordinates. It is well known that the metric of the field of. a Schwarzs...Using the imaginary coordinate method given by Ref. [1] it has been proved that the maximal Schwarzschild geometry can be described by the Weyl coordinates. It is well known that the metric of the field of. a Schwarzschild particle m in the Schwarzschild coordinate system展开更多
Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometr...Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L1（X）. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.展开更多
Ⅰ. INTRODUCTIONSince the discrete ordinate method was introduced by Chandrasekhar in 1950, it has been used by many investigators to study radiative transfer problems in atmosphere, and ex tended the description of r...Ⅰ. INTRODUCTIONSince the discrete ordinate method was introduced by Chandrasekhar in 1950, it has been used by many investigators to study radiative transfer problems in atmosphere, and ex tended the description of radiative transfer from homogeneous medium to展开更多
The problems in some previous discrete ordinate method computations of radiative transfer are discussed, and a new manipulation is presented, which overcomes the difficulties in intensity calculations with the discret...The problems in some previous discrete ordinate method computations of radiative transfer are discussed, and a new manipulation is presented, which overcomes the difficulties in intensity calculations with the discrete ordinate method, and can be used to obtain accurate intensities with less streams. Even in strongly anisotropically scattering atmospheres the intensities in all directions including forward and backward directions of the direct radiation can be obtained satisfactorily.展开更多
This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers....This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers.A five-point nodecentered and a four-point cell-centered tailored finite point schemes(TFPS)are introduced.The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system.Numerically,both methods can not only capture the diffusion limit,but also exhibit uniform convergence in the diffusive regime,even with boundary layers.Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy,uniformly with respect to the mean free path.Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.展开更多
Sixteen different vegetation types of grassland and shrubland were selected to study the component and diversity of plant species of riparian plant communities along main channel in the Three-Gorges areas. Species ric...Sixteen different vegetation types of grassland and shrubland were selected to study the component and diversity of plant species of riparian plant communities along main channel in the Three-Gorges areas. Species richness (s), Simpson index (D), and Shannon-Weiner index (H) were used to study the biodiversity and the hierarchical classification was carried out by the methods of TWINSPAN and DCA ordination. The results showed that the components of flora were complex and dominated by the temperate type in the riparian plant communities. Species diversity was not different between the communities, but Shannon-Weiner indexes of different layers in some grassland were significantly different. TWINSPAN and DCA indicated that riparian plant communities distributed along the gradient of moisture.展开更多
基金supported by the National Natural Science Foundation of China(No.11975097)the Fundamental Research Funds for the Central Universities(No.2019MS038).
文摘The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.
基金the National Key Research and Development Program of China(Nos.2018YFB0204301,2017YFB0202104,and 2017YFE0302200)。
文摘The China dual-functional lithium–lead test blanket module(DFLL-TBM) is a liquid Li Pb blanket concept developed by the Institute of Nuclear Energy Safety Technology of the Chinese Academy of Sciences for testing in ITER to validate relevant tritium breeding and shielding technologies. In this study, neutronic calculations of DFLL-TBM were carried out using a massively parallel three-dimensional transport code, Hydra, with the Fusion Evaluated Nuclear Data Library/MG. Hydra was developed by the Nuclear Engineering Computational Physics Lab based on the discrete ordinates method and has been devoted to neutronic analysis and shielding evaluation for nuclear facilities. An in-house Monte Carlo code(MCX) was employed to verify the discretized calculation model used by Hydra for the DFLL-TBM calculations. The results showed two key aspects:(1) In most material zones,Hydra solutions are in good agreement with the reference MCX results within 1%, and the maximal relative difference of the neutron flux is merely 3%, demonstrating the correctness of the calculation model;(2) while the current DFLL-TBM design meets the operation shielding requirement of ITER for 4 years, it does not satisfy the tritium self-sufficiency requirement. Compared to the two-step approach, Hydra produces higher accuracies as it does not rely on the homogenization technique during the calculation process. The parallel efficiency tests of Hydra using the DFLL-TBM model also showed that this code maintains a high parallel efficiency on O(100) processors and, as a result, is able to significantly improve computing performance through parallelization. Parameter studies have been carried out by varying the thickness of the beryllium armor layer and the tritium breeding zone to understand the influence of the beryllium layer and breeding zone thickness on tritium breeding performance. This establishes a foundation for further improvement in the tritium production performance of DFLL-TBM.
文摘This paper presents a novel approach for evaluating the air impact on urban microclimate and building loads.Traditional software tools,such as TRNSYS and EnergyPlus,often employ the surface-to-surface method for radiation transfer calculations,which neglects the influence of air.To address this limitation,this work integrates the discrete ordinates method(DOM)with the spectral-line weighted-sum-of-gray-gases(SLW)air model to develop a microclimate energy approach.The SLW model uses outdoor temperature and humidity data to compute absorption coefficients,leveraging the air spectrum provided by the HITRAN database.The DOM is then employed to calculate both solar and infrared radiation transfers within the urban environment.A transient simulation is conducted over one year for an urban scene in Suzhou,China.The results indicate that the air impact on radiation transfer increases with rising outdoor temperature and humidity.Overall,the results demonstrate that air effects exert a non-negligible influence on building heating and cooling load calculations,with an impact magnitude comparable to the introduction of an auxiliary thermal source.This study highlights the significance of considering air properties in urban microclimate and building energy simulations for more accurate results.
基金Supported by the Natural Science Program of China(U2142212)Natural Science Foundation of Hunan Province(2021JC0009)National Key Research and Development Program of China(2022YFC3004200)。
文摘The original vector discrete ordinate radiative transfer(VDISORT)model takes into account Stokes radiance vector but derives its solution assuming azimuthal symmetric surface reflective matrix and atmospheric scattering phase matrix,such as the phase matrix derived from spherical particles or randomly oriented non-spherical particles.In this study,a new VDISORT is developed for general atmospheric scattering and boundary conditions.Stokes vector is decomposed into both sinusoidal and cosinusoidal harmonic modes,and the radiance at arbitrary viewing geometry is solved directly by adding two zero-weighted points in the Gaussian quadrature scheme.The complex eigenvalues in homogeneous solutions are also taken into full consideration.The accuracy of VDISORT model is comprehensively validated by four cases:Rayleigh scattering case,the spherical particle scattering case with the Legendre expansion coefficients of 0th-13th orders of the phase matrix(hereinafter L13),L13 with a polarized source,and the randomoriented oblate particle scattering case with the Legendre expansion coefficients of 0th-11th orders of the phase matrix(hereinafter L11).In all cases,the simulated radiances agree well with the benchmarks,with absolute biases less than 0.0065,0.0006,and 0.0008 for Rayleigh,unpolarized L13,and L11,respectively.Since a polarized bidirectional reflection distribution function(pBRDF)matrix is used as the lower boundary condition,VDISORT is now able to handle fully coupled atmospheric and surface polarimetric radiative transfer processes.
文摘Using the imaginary coordinate method given by Ref. [1] it has been proved that the maximal Schwarzschild geometry can be described by the Weyl coordinates. It is well known that the metric of the field of. a Schwarzschild particle m in the Schwarzschild coordinate system
基金Supported by National Natural Science Foundation of China(Grant No.11201007)
文摘Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L1（X）. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.
文摘Ⅰ. INTRODUCTIONSince the discrete ordinate method was introduced by Chandrasekhar in 1950, it has been used by many investigators to study radiative transfer problems in atmosphere, and ex tended the description of radiative transfer from homogeneous medium to
文摘The problems in some previous discrete ordinate method computations of radiative transfer are discussed, and a new manipulation is presented, which overcomes the difficulties in intensity calculations with the discrete ordinate method, and can be used to obtain accurate intensities with less streams. Even in strongly anisotropically scattering atmospheres the intensities in all directions including forward and backward directions of the direct radiation can be obtained satisfactorily.
基金supported by the NSFC Project No.10971116.M.Tang is supported by Natural Science Foundation of Shanghai under Grant No.12ZR1445400Shanghai Pujiang Program 13PJ1404700+1 种基金supported in part by the National Natural Science Foundation of China under Grant DMS-11101278the Young Thousand Talents Program of China.
文摘This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers.A five-point nodecentered and a four-point cell-centered tailored finite point schemes(TFPS)are introduced.The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system.Numerically,both methods can not only capture the diffusion limit,but also exhibit uniform convergence in the diffusive regime,even with boundary layers.Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy,uniformly with respect to the mean free path.Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.
基金This study was supported by the Chinese Academy of Sciences (A grant KZCX2-406) the National Natural Science Foundation of China (NSFC39970123) and Changbai Mountain Open Research Station.
文摘Sixteen different vegetation types of grassland and shrubland were selected to study the component and diversity of plant species of riparian plant communities along main channel in the Three-Gorges areas. Species richness (s), Simpson index (D), and Shannon-Weiner index (H) were used to study the biodiversity and the hierarchical classification was carried out by the methods of TWINSPAN and DCA ordination. The results showed that the components of flora were complex and dominated by the temperate type in the riparian plant communities. Species diversity was not different between the communities, but Shannon-Weiner indexes of different layers in some grassland were significantly different. TWINSPAN and DCA indicated that riparian plant communities distributed along the gradient of moisture.
