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The Direct Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Marching for Linear Convection-Diffusion Problems

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Communications on Applied Mathematics and Computation 2022年第1期4卷 271-292页

作者： haijin wang Qiang Zhang School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Mathematics Nanjing UniversityNanjing 210093China

In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion *** the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are *** the time discretization,the convection term is treated explicitly and the diffusion term *** the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size ***-mal error estimate is also obtained by the aid of a special global *** experiments are given to verify the stability and accuracy of the proposed schemes.

关键词： Direct discontinuous Galerkin method Implicit-explicit scheme Stability analysis Energy method Convection-diffusion problem

Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems

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Science China Mathematics 2020年第1期63卷 183-204页

作者： haijin wang Qiang Zhang Shiping wang Chi-wang Shu School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Mathematics Nanjing UniversityNanjing 210093China College of Shipbuilding Engineering Harbin Engineering UniversityHarbin 150001China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)*** basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx *** give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order *** optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations.

关键词： local discontinuous Galerkin explicit-implicit-null time discretization nonlinear diffusion stability error estimates

Thermal management for thermoset automated fiber placement based on infrared heater structure arrangement

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Chinese Journal of Aeronautics 2022年第1期35卷 173-183页

作者： Han wang Weiwei wang haijin wang Huiyue DONG Yinglin KE A State Key Laboratory of Fluid Power and Mechatronic System School of Mechanical EngineeringZhejiang UniversityHangzhou 310027China Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province School of Mechanical EngineeringZhejiang UniversityHangzhou 310027China

Layup temperature is a vital factor that affects the production quality of automated fiber placement for thermoset *** high quality production,this paper proposes a new prediction model of layup temperature by considering the structure of infrared heater of automatic fiber placement *** model was first verified by comparing with the temperature results of layup *** a prediction on the effects of heater structure arrangement on layup temperature was conducted in the *** research shows that the length of infrared tube and the radian of reflective-film have significant influences,rather than other *** to this investigation,a heater structure-based heating strategy was presented in the paper to efficiently achieve constant temperature control in variable speed layup process.

关键词： Automated fiber placement Heating strategy optimization Infrared heater structure Thermal management Variable speed

ANALYSIS OF THE IMPLICIT-EXPLICIT ULTRA-WEAK DISCONTINUOUS GALERKIN METHOD FOR CONVECTION-DIFFUSION PROBLEMS

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Journal of Computational Mathematics 2024年第1期42卷 1-23页

作者： haijin wang Anping Xu Qi Tao School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Beijing Computational Science Research Center Beijing 100193China

In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion ***,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete *** fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size ***,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete *** experiments are displayed to verify the theoretical results.

关键词： The ultra-weak discontinuous Galerkin method Convection-diffusion Implicitexplicit time discretization Stability Error estimate

Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

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Communications on Applied Mathematics and Computation 2024年第1期6卷 257-278页

作者： Xuechun Liu haijin wang Jue Yan Xinghui Zhong School of Mathematical Sciences Zhejiang UniversityHangzhou310027ZhejiangChina School of Science Nanjing University of Posts and TelecommunicationsNanjing210023JiangsuChina Department of Mathematics Iowa State UniversityAmes50011IAUSA

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion *** apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical *** on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔ*** observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)*** experiments are provided to verify the theoretical results.

关键词： Direct discontinuous Galerkin(DDG)method with interface correction Symmetric DDG method Superconvergence Fourier analysis Eigen-structure

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Mn在2297铝锂合金中的微合金化作用

稀有金属材料与工程 2018年第3期47卷 871-877页

作者：桑冯建郑子樵王海金中南大学湖南长沙410083

利用金相显微镜、拉伸测试、SEM、TEM、STEM-HAADF等手段研究了微量Mn的添加对2297铝锂合金微观组织与力学性能的影响。结果表明,Mn在2297铝锂合金中主要以AlCuMn棒状弥散粒子和Al(CuMnFe)粗大相形式存在,并且相比Mn-free合金,2297合金... 详细信息

利用金相显微镜、拉伸测试、SEM、TEM、STEM-HAADF等手段研究了微量Mn的添加对2297铝锂合金微观组织与力学性能的影响。结果表明,Mn在2297铝锂合金中主要以AlCuMn棒状弥散粒子和Al(CuMnFe)粗大相形式存在,并且相比Mn-free合金,2297合金中粗大相尺寸较小、分布均匀,因而合金的抗拉强度得到提高。研究表明,Mn的添加没有影响Al_3Zr粒子的析出行为,尽管析出了AlCuMn棒状弥散相,但整体上没有改变2297合金的再结晶程度。

关键词： 2297铝锂合金 Mn Al3Zr 再结晶

2297-T87铝合金厚板力学性能的各向异性与厚向不均匀性

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稀有金属材料与工程 2016年第5期45卷 1196-1202页

作者：王海金郑子樵范雪松中南大学湖南长沙410083

通过拉伸试验、金相显微镜、X射线衍射、扫描电镜和透射电镜分析研究了85 mm厚的2297-T87铝合金厚板力学性能的各向异性与厚度方向的不均匀性。结果表明:在2297-T87合金厚板L方向上力学性能沿厚度层呈不均匀性,从表层到中心强度逐渐提高... 详细信息

通过拉伸试验、金相显微镜、X射线衍射、扫描电镜和透射电镜分析研究了85 mm厚的2297-T87铝合金厚板力学性能的各向异性与厚度方向的不均匀性。结果表明:在2297-T87合金厚板L方向上力学性能沿厚度层呈不均匀性,从表层到中心强度逐渐提高,而LT方向性能变化不明显;织构沿厚度方向分布不均匀,厚板中心主要是β纤维成分和部分的Goss织构;而表层除了少量变形织构,还存在再结晶织构;T/8厚度为大量的剪切织构;T/4厚度层是一个过渡层,同时存在少量再结晶织构、剪切织构和β纤维。同一厚度层不同方向的力学性能各向异性较为明显,强度和塑性的变化趋势一致:L>LT>ST。这种各向异性与晶粒结构和第二相粒子有关。

关键词： 2297-T87合金厚板各向异性不均匀性力学性能织构

基于ArcGIS与多因子模型的光伏电站选址评估

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太阳能学报 2023年第11期44卷 120-130页

作者：王海金唐若笠周雨诗张彦武汉理工大学船海与能源动力工程学院武汉430063 武汉理工大学交通与物流工程学院武汉430063

该文基于中国光伏资源的时空分布,研究并提出一种基于ArcGIS与多因子评价的光伏电站选址及发电潜力预测模型。利用ArcGIS软件与层次分析法,综合考虑多种影响大型光伏电站建设的因素,对不同地势和土地类型赋予不同的光伏利用系数,得到大... 详细信息

该文基于中国光伏资源的时空分布,研究并提出一种基于ArcGIS与多因子评价的光伏电站选址及发电潜力预测模型。利用ArcGIS软件与层次分析法,综合考虑多种影响大型光伏电站建设的因素,对不同地势和土地类型赋予不同的光伏利用系数,得到大型光伏电站建设适宜度、光伏潜力与光伏电站选址的多因子评价模型。基于该模型得出中国光伏发电潜力并给出光伏电站选址建议。评估结果表明,全国年光伏总发电量约为570.07×10^(6)kWh,其中新疆为年光伏总发电量最高的省份。中国较为适宜建设光伏电站的地区主要为西北部地区,其中适宜区面积为1.08×10^(6)km^(2),最适宜区面积为2.10×10^(5)km^(2),研究可结果将为中国光伏产业长期的规划与建设提供可靠的理论依据。

关键词：光伏组件光伏电站选址层次分析法地理信息系统

铺放工艺参数对预浸料丝束曲线铺贴质量的影响

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复合材料学报 2021年第6期38卷 1795-1808页

作者：蔡立成彭啸汪海晋丁会明徐强浙江大学机械工程学院杭州310012 杭州艾美依航空制造装备有限公司复合材料部门杭州311200

为研究铺放工艺参数对复合材料预浸料丝束曲线铺贴质量的影响规律及作用机制,首先自主设计并搭建了可模拟铺丝机曲线铺贴运动的试验平台,进行了变铺放工艺参数与变铺放半径的预浸料丝束曲线铺贴试验。通过测量计算有效贴合长度比、褶皱... 详细信息

为研究铺放工艺参数对复合材料预浸料丝束曲线铺贴质量的影响规律及作用机制,首先自主设计并搭建了可模拟铺丝机曲线铺贴运动的试验平台,进行了变铺放工艺参数与变铺放半径的预浸料丝束曲线铺贴试验。通过测量计算有效贴合长度比、褶皱角度及曲率半径比,并结合变铺放工艺参数的单因素剥离试验对铺放质量进行了表征。结果表明:曲线铺贴质量与预浸料丝束黏结力及弯曲刚度密切相关;随铺放温度、压力和张力增大、铺放速率减小,丝束黏结力上升,曲线铺贴质量提高;铺放温度升高引起的丝束弯曲刚度下降可提升曲线铺贴准确性,但过高的铺放温度会导致丝束黏性下降,曲线铺贴缺陷显著;铺放张力会改变丝束的受力状态,进而影响曲线铺贴路径的准确性;此外,曲线铺贴半径越小,铺放质量对工艺参数的变化越敏感。

关键词：自动铺丝工艺参数曲线铺贴剥离试验预浸料黏结力行为