Fuel assemblies have a decisive impact on the performance and safety of nuclear reactors.Helical fuel has huge potential for application in small module reactors(SMRs)due to its advantages in volume power density and ...Fuel assemblies have a decisive impact on the performance and safety of nuclear reactors.Helical fuel has huge potential for application in small module reactors(SMRs)due to its advantages in volume power density and safety.Typical helical fuel elements are usually trilobal or cruciform in cross-section.The fuel rods are helically twisted in the axial direction,eliminating the need for spacer grids as the fuel rods are self-supporting.In this paper,a refined subchannel division approach is proposed based on the crossflow mechanism of helical fuel assemblies.Then,a refined helical fuel mixing model framework,including the helical fuel distributed resistance method and directed crossflow method,is developed and implemented in a helical fuel rod bundle to investigate the mixing characteristics.Validation is provided by a 5×5 helical fuel bundle mixing experiment.The refined model predicts about 92.7%of the data with the±10%error range.Compared with existing helical fuel mixing models,the refined mixing model has higher axial accuracy and radial spatial resolution,and can accurately predict the twist angledependent crossflow rate and entry effect.Meanwhile,the refined helical fuel mixing model framework is universal and can be effectively used for the mixing prediction of arbitrary geometric helical fuel after the calibration of coefficients.展开更多
3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic m...3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.展开更多
In this paper,we propose a novel Hermite weighted essentially non-oscillatory(HWENO)fast sweeping method to solve the static Hamilton-Jacobi equations efficiently.During the HWENO reconstruction procedure,the proposed...In this paper,we propose a novel Hermite weighted essentially non-oscillatory(HWENO)fast sweeping method to solve the static Hamilton-Jacobi equations efficiently.During the HWENO reconstruction procedure,the proposed method is built upon a new finite difference fifth order HWENO scheme involving one big stencil and two small stencils.However,one major novelty and difference from the traditional HWENO framework lies in the fact that,we do not need to introduce and solve any additional equations to update the derivatives of the unknown functionϕ.Instead,we use the currentϕand the old spatial derivative ofϕto update them.The traditional HWENO fast sweeping method is also introduced in this paper for comparison,where additional equations governing the spatial derivatives ofϕare introduced.The novel HWENO fast sweeping methods are shown to yield great savings in computational time,which improves the computational efficiency of the traditional HWENO scheme.In addition,a hybrid strategy is also introduced to further reduce computational costs.Extensive numerical experiments are provided to validate the accuracy and efficiency of the proposed approaches.展开更多
We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind sche...We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.展开更多
The equilibriummetric forminimizing a continuous congested trafficmodel is the solution of a variational problem involving geodesic distances.The continuous equilibrium metric and its associated variational problem ar...The equilibriummetric forminimizing a continuous congested trafficmodel is the solution of a variational problem involving geodesic distances.The continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrop’s equilibrium.We propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous formulation.The method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium metric and the resulting geodesic distances.The geodesic distance needed for the state equation is computed by solving a factored eikonal equation,and the adjoint state equation is solved by a fast sweeping method.Numerical examples demonstrate that the proposed adjoint state method produces desired equilibrium metrics and outperforms the subgradient marching method for computing such equilibrium metrics.展开更多
We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented met...We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented method is a complete avoidance of irrational numbers that appear when using the sweeping method in the classical way for solving the problem at hand. Therefore, it is worth mentioning that the efficiency of the proposed method is only assured for low-degree curves.展开更多
线损是电力企业的一项综合性技术经济指标,它反映了供电企业的运营管理水平．通过分析配电网线损管理的现状,对其工作流程进行了详细的阐述．并对线损理论计算方法如均方根电流法、平均电流法、最大电流法和等值电阻法等进行了初步探索...线损是电力企业的一项综合性技术经济指标,它反映了供电企业的运营管理水平．通过分析配电网线损管理的现状,对其工作流程进行了详细的阐述．并对线损理论计算方法如均方根电流法、平均电流法、最大电流法和等值电阻法等进行了初步探索．采用了前推回代法,通过二叉树理论构造数据结构,利用 C 语言实现线损计算软件编程．展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12135008,12075150,and 12275174)the Shanghai Rising-Star Program (Grant No.22QA1404500)the Jingying Project of China National Nuclear Corporation。
文摘Fuel assemblies have a decisive impact on the performance and safety of nuclear reactors.Helical fuel has huge potential for application in small module reactors(SMRs)due to its advantages in volume power density and safety.Typical helical fuel elements are usually trilobal or cruciform in cross-section.The fuel rods are helically twisted in the axial direction,eliminating the need for spacer grids as the fuel rods are self-supporting.In this paper,a refined subchannel division approach is proposed based on the crossflow mechanism of helical fuel assemblies.Then,a refined helical fuel mixing model framework,including the helical fuel distributed resistance method and directed crossflow method,is developed and implemented in a helical fuel rod bundle to investigate the mixing characteristics.Validation is provided by a 5×5 helical fuel bundle mixing experiment.The refined model predicts about 92.7%of the data with the±10%error range.Compared with existing helical fuel mixing models,the refined mixing model has higher axial accuracy and radial spatial resolution,and can accurately predict the twist angledependent crossflow rate and entry effect.Meanwhile,the refined helical fuel mixing model framework is universal and can be effectively used for the mixing prediction of arbitrary geometric helical fuel after the calibration of coefficients.
基金The authors thank the funds supported by the China National Nuclear Corporation under Grants Nos.WUQNYC2101 and WUHTLM2101-04National Natural Science Foundation of China(42074132,42274154).
文摘3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.
基金supported by the NSF (Grant No.DMS-1753581)supported by NSFC (Grant No.12071392).
文摘In this paper,we propose a novel Hermite weighted essentially non-oscillatory(HWENO)fast sweeping method to solve the static Hamilton-Jacobi equations efficiently.During the HWENO reconstruction procedure,the proposed method is built upon a new finite difference fifth order HWENO scheme involving one big stencil and two small stencils.However,one major novelty and difference from the traditional HWENO framework lies in the fact that,we do not need to introduce and solve any additional equations to update the derivatives of the unknown functionϕ.Instead,we use the currentϕand the old spatial derivative ofϕto update them.The traditional HWENO fast sweeping method is also introduced in this paper for comparison,where additional equations governing the spatial derivatives ofϕare introduced.The novel HWENO fast sweeping methods are shown to yield great savings in computational time,which improves the computational efficiency of the traditional HWENO scheme.In addition,a hybrid strategy is also introduced to further reduce computational costs.Extensive numerical experiments are provided to validate the accuracy and efficiency of the proposed approaches.
基金partially supported by ONR Grant N00014-02-1-0090ARO MURI Grant W911NF-07-1-0185NSF Grant DMS0811254
文摘We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.
基金supported by NSF 0810104 and NSF 1115363Leung was supported in part by Hong Kong RGC under Grant GRF603011HKUST RPC under Grant RPC11SC06.
文摘The equilibriummetric forminimizing a continuous congested trafficmodel is the solution of a variational problem involving geodesic distances.The continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrop’s equilibrium.We propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous formulation.The method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium metric and the resulting geodesic distances.The geodesic distance needed for the state equation is computed by solving a factored eikonal equation,and the adjoint state equation is solved by a fast sweeping method.Numerical examples demonstrate that the proposed adjoint state method produces desired equilibrium metrics and outperforms the subgradient marching method for computing such equilibrium metrics.
基金Project (No. MTM2005-08690-C02-02) partially supported by the Spanish Ministry of Science and Innovation Grant
文摘We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented method is a complete avoidance of irrational numbers that appear when using the sweeping method in the classical way for solving the problem at hand. Therefore, it is worth mentioning that the efficiency of the proposed method is only assured for low-degree curves.
文摘线损是电力企业的一项综合性技术经济指标,它反映了供电企业的运营管理水平．通过分析配电网线损管理的现状,对其工作流程进行了详细的阐述．并对线损理论计算方法如均方根电流法、平均电流法、最大电流法和等值电阻法等进行了初步探索．采用了前推回代法,通过二叉树理论构造数据结构,利用 C 语言实现线损计算软件编程．
