检索结果-南通市图书馆

Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts

Communications on Applied Mathematics and Computation 2024年第2期6卷 907-962页

作者： Dinshaw S.Balsara Deepak Bhoriya chi-Wang shu Harish Kumar Physics Department University of Notre DameNotre DameUSA ACMS Department University of Notre DameNotre DameUSA Division of Applied Mathematics Brown UniversityProvidenceUSA Department of Mathematics Indian Institute of TechnologyDelhiIndia

Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation *** multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable *** makes them quite attractive for several science and engineering ***,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative *** this paper,we perform such an extension which improves the domain of the applicability of such *** extension is carried out by writing the scheme in fluctuation *** use the HLLI Riemann solver of Dumbser and Balsara(***.304:275-319,2016)as a building block for carrying out this *** of the use of an HLL building block,the resulting scheme has a proper supersonic *** use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the *** new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present *** conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied *** examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional *** Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the *** some

关键词： Hyperbolic PDEs Numerical schemes Non-conservative products Stiff source terms Finite difference WENO

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

引用

Communications on Applied Mathematics and Computation 2024年第1期6卷 533-549页

作者： Luciano K.Araki Rafael B.de R.Borges Nicholas Dicati P.da Silva chi-Wang shu Department of Mechanical Engineering Federal University of ParanáCuritiba81531-980ParanáBrazil Mathematics and Statistics Institute Rio de Janeiro State UniversityRio de Janeiro20550-900Rio de JaneiroBrazil Department of Mechanical Engineering State University of MaringáMaringá87020-900ParanáBrazil Division of Applied Mathematics Brown UniversityProvidenceRI02912USA

Capturing elaborated flow structures and phenomena is required for well-solved numerical *** finite difference methods allow simple discretization of mesh and model ***,they need simpler meshes,e.g.,*** inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular ***-resolution and high-order methods can capture elaborated flow structures and *** also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation *** perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)***,we propose to solve a challenging engineering application without turbulence *** aim to verify and validate recent high-resolution and high-order *** check the solver accuracy,we solved vortex and Couette ***,we solved inviscid and viscous nozzle flows for a conical *** employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving *** showed the solver is high-order and captured elaborated flow structures and *** can see oblique shocks in both nozzle *** the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

关键词： High-resolution Compressible Navier-Stokes Free-shock separation Nozzle flow

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Polyphenol components in black chokeberry(Aronia melanocarpa)as clinically proven diseases control factors——an overview

引用

Food Science and Human Wellness 2024年第3期13卷 1152-1167页

作者： Ningxuan Gao chi shu Yuehua Wang Jinlong Tian Yuxi Lang Chenyu Jin Xingyue Cui Hanqian Jiang Shi’an Liu Zhiying Li Wei Chen Hao Xu Bin Li Department of Food Science College of FoodShenyang Agricultural UniversityShenyang 110161China Department of Food Science and Nutrition College of Biosystems Engineering and Food ScienceZhejiang UniversityHangzhou 310058China Chaoyang Beihe Food Co. Ltd.Chaoyang 122100China

The black chokeberry is rich in polyphenols,including flavonoids with anthocyanins,flavanols and lavonols as the main components and a variety of phenolic acids represented by chlorogenic *** of these polyphenols,black chokeberry has the effect of preventing and adjuvant therapy *** study summarized the current research results on the types and contents of functional components in black chokeberry,and analyzed their digestion,absorption and metabolism in human *** this basis,the disease control functions that have been proved effective in clinical research were reviewed and *** studies showed that black chokeberry have good prevention and adjuvant therapy effects on hyperlipidemia,hypertension,diabetes and *** there are different functional components in black chokeberry,its prevention and treatment of the same disease can come from multiple pathways,which provides a more reliable effectiveness for the disease control of different populations.

关键词： Black chokeberry Hyperlipidemia Hypertension Diabetes Inflammation

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

高精度WENO格式的发展与展望

引用

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

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

ANTI-DIFFUSIVE FINITE DIFFERENCE WENO METHODS FOR SHALLOW WATER WITH TRANSPORT OF POLLUTANT

引用

Journal of Computational Mathematics 2006年第3期24卷 239-251页

作者： Zhengfu Xu chi-Wang shu Department of Mathematics Pennsylvania State University University Park PA 16802 USA Division of Applied Mathematics Brown University Providence Rhode Island 02912 USA

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the SaintVenant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution

关键词： Anti-diffusive flux correction Sharpening contact discontinuity High order accuracy Finite difference WENO scheme Saint-Venant system of shallow water Transport of pollutant.

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices

引用

Science china Mathematics 2016年第1期59卷 115-140页

作者： LIU YunXian shu chi-Wang School of Mathematics Shandong University Division of Applied Mathematics Brown University

We consider the drift-diffusion （DD） model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin （LDG） schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit （IMEX） time discretization with the LDG spatial diseretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.

关键词： local discontinuous Galerkin method semi-discrete implicit-explicit scheme error estimate semi- conductor

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

DISSIPATIVE NUMERICAL METHODS FOR THE HUNTER-SAXTON EQUATION

引用

Journal of Computational Mathematics 2010年第5期28卷 606-620页

作者： Yan Xu chi-Wang shu Department of Mathematics University of Science and Technology of China Hefei 230026 China Division of Applied Mathematics Brown University Providence RI 02912 USA

In this paper, we present further development of the local discontinuous Galerkin （LDG） method designed in [21] and a new dissipative discontinuous Galerkin （DG） method for the HuntermSaxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].

关键词： Discontinuous Galerkin method Local discontinuous Galerkin method dissi-pation Hunter-Saxton equation Stability.

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

ANALYSIS OF SHARP SUPERCONVERGENCE OF LOCAL DISCONTINUOUS GALERKIN METHOD FOR ONE-DIMENSIONAL LINEAR PARABOLIC EQUATIONS

引用

Journal of Computational Mathematics 2015年第3期33卷 323-340页

作者： Yang Yang chi-Wang shu Department of Mathematical Sciences Michigan Technological University Houghton MI 49931. Division of Applied Mathematics Brown University Providence RI 02912.

In this paper, we study the superconvergence of the error for the local discontinuous Galerkin （LDG） finite element method for one-dimensional linear parabolic equations when the alternating flux is used. We prove that if we apply piecewise k-th degree polynomials, the error between the LDG solution and the exact solution is （k ＋ 2）-th order superconvergent at the Radau points with suitable initial discretization. Moreover, we also prove the LDG solution is （k ＋ 2）-th order superconvergent for the error to a particular projection of the exact solution. Even though we only consider periodic boundary condition, this boundary condition is not essential, since we do not use Fourier analysis. Our analysis is valid for arbitrary regular meshes and for P^k polynomials with arbitrary k ≥ 1. We perform numerical experiments to demonstrate that the superconvergence rates proved in this paper are sharp.

关键词： Superconvergence Local discontinuous Galerkin method Parabolic equation Lnitial discretization Error estimates Radau points.

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

STRONG STABILITY PRESERVING PROPERTY OF THE DEFERRED CORRECTION TIME DISCRETIZATION

引用

Journal of Computational Mathematics 2008年第5期26卷 633-656页

作者： Yuan Liu chi-Wang shu Mengping Zhang Department of Mathematics University of Science and Technology of China Hefei 230026 China Division of Applied Mathematics Brown University Providence RI 02912 USA Department of Mathematics University of Science and Technology of China Hefei 230026 China

In this paper, we study the strong stability preserving （SSP） property of a class of deferred correction time discretization methods, for solving the method-of-lines schemes approximating hyperbolic partial differen... 详细信息

关键词： Strong stability preserving Deferred correction time discretization.

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

NUMERICAL BOUNDARY CONDITIONS FOR THE FAST SWEEPING HIGH ORDER WENO METHODS FOR SOLVING THE EIKONAL EQUATION

引用

Journal of Computational Mathematics 2008年第3期26卷 336-346页

作者： Ling Huang chi-Wang shu Mengping Zhang Department of Mathematics University of Science and Technology of China Hefei Anhui 230026 China Division of Applied Mathematics Brown University Providence RI 02912 USA Department of Mathematics University of Science and Technology of China Hefei 230026 China

High order fast sweeping methods have been developed recently in the literature to solve static Hamilton-Jacobi equations efficiently. Comparing with the first order fast sweeping methods, the high order fast sweeping methods are more accurate, but they often require additional numerical boundary treatment for several grid points near the boundary because of the wider numerical stencil. It is particularly important to treat the points near the inflow boundary accurately, as the information would flow into the computational domain and would affect global accuracy. In the literature, the numerical solution at these boundary points are either fixed with the exact solution, which is not always feasible, or computed with a first order discretization, which could reduce the global accuracy. In this paper, we discuss two strategies to handle the inflow boundary conditions. One is based on the numerical solutions of a first order fast sweeping method with several different mesh sizes near the boundary and a Richardson extrapolation, the other is based on a Lax-Wendroff type procedure to repeatedly utilizing the PDE to write the normal spatial derivatives to the inflow boundary in terms of the tangential derivatives, thereby obtaining high order solution values at the grid points near the inflow boundary. We explore these two approaches using the fast sweeping high order WENO scheme in [18] for solving the static Eikonal equation as a representative example. Numerical examples are given to demonstrate the performance of these two approaches.

关键词： Fast sweeping method WENO scheme Boundary condition

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：