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An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao jianxian Qiu School of Mathematical Sciences and Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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Communications on Applied Mathematics and Computation 2024年第1期6卷 605-624页

作者： Feng Zheng jianxian Qiu College of Mathematics and Statistics Fujian Normal UniversityFuzhou350117FujianChina School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen361005FujianChina

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation *** can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary ***,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO *** numerical tests are performed to verify the high resolution and high accuracy of the scheme.

关键词： Finite volume Dimension by dimension HWENO Hyperbolic conservation laws

High-order finite volume methods for solving compressible multicomponent flows

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Science China Mathematics 2024年

作者： Feng Zheng jianxian Qiu School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationFujian Normal University School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling& High-Performance Scientific Computing Xiamen University

In this paper, we propose a high-order finite volume method for solving multicomponent fluid problems. Our method couples the quasi-conservative form with the reconstruction of conservative variables in a characteristic manner. The source term and numerical fluxes are carefully designed to maintain the pressure and velocity equilibrium for the interface-only problem and preserve the equilibrium of physical parameters in a single-component fluid. These ingredients enable our scheme to achieve both high-order accuracy in the smooth region and the high resolution in the discontinuity region of the solution. Extensive numerical tests are performed to verify the high resolution and accuracy of the scheme.

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苦味抑制剂阿魏酸的构效关系

食品科学 2024年第14期45卷 14-22页

作者：方子超周隽涵郑建仙华南理工大学食品科学与工程学院广东广州510640

探索阿魏酸(ferulic acid,FA)羧基取代基团以及丙烯酸碳链长度对苦味抑制作用的影响。本实验使用分子动力学模拟,分析苦味受体与苦味抑制剂FA、4-(2,2,3-三甲基环戊基)丁酸和苦味激活剂安赛蜜相互作用的构象差异,以获得FA对苦味受体的... 详细信息

探索阿魏酸(ferulic acid,FA)羧基取代基团以及丙烯酸碳链长度对苦味抑制作用的影响。本实验使用分子动力学模拟,分析苦味受体与苦味抑制剂FA、4-(2,2,3-三甲基环戊基)丁酸和苦味激活剂安赛蜜相互作用的构象差异,以获得FA对苦味受体的抑制结构F4。基于F4的相互作用模式,构建系列FA衍生物,结合电子舌分析技术,探讨FA苦味抑制构效关系。结果表明在配体与F4相互作用模式相符的前提下,FA羧基取代基团氢键受体的电荷量与苦味抑制强度呈反比;FA丙烯酸碳链长度改性为二碳长度,会导致配体与关键残基相互作用不稳定,导致其苦味抑制强度降低,改性为四碳长度则增强其苦味抑制强度。FA作为新型苦味抑制剂,在改善食品食用品质方面具有开发潜力。

关键词：阿魏酸苦味抑制构效关系分子动力学模拟电子舌

隧道内双块式无砟轨道受力特征及防裂优化措施

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铁道建筑 2024年第6期64卷 50-55页

作者：吴建贤昌九城际铁路股份有限公司南昌330004

针对隧道仰拱施工缝位置双块式无砟轨道道床板在施工阶段裂纹多发进而影响无砟轨道长期使用寿命的问题,建立纵连式和单元式双块式无砟轨道有限元整体模型,分析了不同工况下仰拱施工缝位置道床板的主拉应力,讨论了混凝土收缩以及整体温... 详细信息

针对隧道仰拱施工缝位置双块式无砟轨道道床板在施工阶段裂纹多发进而影响无砟轨道长期使用寿命的问题,建立纵连式和单元式双块式无砟轨道有限元整体模型,分析了不同工况下仰拱施工缝位置道床板的主拉应力,讨论了混凝土收缩以及整体温度荷载作用下混凝土应力状态,并基于分析结果从结构优化以及施工角度提出了双块式无砟轨道裂纹预防措施。结果表明:对于施工缝区域,纵连式道床板主拉应力随基底刚度增大而降低,单元式道床板主拉应力随板长减小而降低;采用植筋措施能够有效降低两种道床板结构在施工缝的应力水平,道床板主拉应力随植筋间距减小而减小。综合考虑,建议实际工程中在道床板跨越施工缝区域采用植筋措施,植筋间隔两根轨枕布置。

关键词：高速铁路双块式无砟轨道数值模拟仰拱施工缝裂纹萌生裂纹预防

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高精度WENO格式的发展与展望

中国科学：数学 2024年第2期54卷 121-138页

作者：朱君舒其望邱建贤南京航空航天大学数学学院南京211106 Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA 厦门大学数学科学学院厦门361005

加权本质无振荡(weighted essentially non-oscillatory, WENO)格式是用于求解双曲守恒律方程和对流占优问题的一类高精度数值方法. WENO格式设计的思想是在解的光滑区域中获得高阶数值精度,而在解的间断附近保持本质无振荡的性质.以这... 详细信息

加权本质无振荡(weighted essentially non-oscillatory, WENO)格式是用于求解双曲守恒律方程和对流占优问题的一类高精度数值方法. WENO格式设计的思想是在解的光滑区域中获得高阶数值精度,而在解的间断附近保持本质无振荡的性质.以这种思想设计的有限差分和有限体积高精度WENO格式在计算流体力学等领域中得到了广泛应用.本文首先回顾WENO格式设计的基本思想和性质,简要介绍近年来WENO格式研究方面的一些进展,并阐述US-WENO (unequal-sized WENO)格式、MR-WENO (multi-resolution WENO)格式和HWENO (Hermite WENO)格式的构造策略.此外,本文还介绍高精度WENO格式在结构网格和非结构网格上的一些进展,展望这些高精度格式在多个领域中的应用以及未来的发展趋势.

关键词：计算流体力学本质无振荡格式加权本质无振荡格式 US-WENO格式 MR-WENO格式 HWENO格式

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某超限地铁控制中心结构设计

山西建筑 2024年第15期50卷 53-57页

作者：张建先北京城建设计发展集团股份有限公司厦门分公司福建厦门361004

对某地铁控制中心进行结构超限情况判断,结构存在扭转不规则、楼板不连续、凹凸不规则、尺寸突变、构件间断等多项不规则项。针对结构的不规则项,设定合理的结构抗震性能目标,通过不同的结构分析软件研究结构在多遇地震、设防地震、罕... 详细信息

对某地铁控制中心进行结构超限情况判断,结构存在扭转不规则、楼板不连续、凹凸不规则、尺寸突变、构件间断等多项不规则项。针对结构的不规则项,设定合理的结构抗震性能目标,通过不同的结构分析软件研究结构在多遇地震、设防地震、罕遇地震的受力性能,通过弹性时程分析和动力弹塑性分析进一步分析结构的地震反应,发现结构的薄弱位置,对薄弱位置进行相应的加强,使结构设计满足预定的性能目标。

关键词：超限结构设计结构不规则性能目标时程分析动力弹塑性

HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS

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Journal of Computational Mathematics 2007年第2期25卷 131-144页

作者： jianxian Qiu Department of Mathematics Nanjing University Nanjing 210093 China

In this paper, we use Hermite weighted essentially non-oscillatory （HWENO） schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes （HWENO-RK） of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.

关键词： WENO scheme Hermite interpolation Hamilton-Jacobi equation Lax-Wendroff type time discretization High order accuracy.

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公铁混层布置双层箱桁组合梁建造技术

土木工程与管理学报 2024年第4期41卷 63-68页

作者：吴建贤昌九城际铁路股份有限公司江西南昌330002

昌九高铁扬子洲赣江公铁大桥西支主桥为49+144+320+144+49 m双塔竖琴索面半漂浮体系斜拉桥,公铁混层对称布置,下层桥面中间布置双线无砟轨道高速铁路,两侧布置双向4车道城市主干路,上层桥面布置双向8车道城市快速路。主梁采用双层带挑... 详细信息

昌九高铁扬子洲赣江公铁大桥西支主桥为49+144+320+144+49 m双塔竖琴索面半漂浮体系斜拉桥,公铁混层对称布置,下层桥面中间布置双线无砟轨道高速铁路,两侧布置双向4车道城市主干路,上层桥面布置双向8车道城市快速路。主梁采用双层带挑臂箱桁组合梁,结构形式新颖,构造较复杂,为研究其受力性能,建立精细化实体节段模型开展局部应力分析,并结合沿途水运条件,研究了主梁运输方案及对应的安装方案。计算结果表明:带挑臂箱桁组合梁设计合理,上、下层桥面板局部应力较小,节点位置未出现较大的应力集中现象,公路桥面横桥向挠跨比满足规范要求;带挑臂箱桁组合梁桥面空间布置合理,具有良好的经济性,可为今后公铁混层合建桥梁提供借鉴。

关键词：公铁两用桥公铁混层带挑臂箱桁组合梁建造技术