检索结果-南通市图书馆

A Posteriori Stabilized Sixth-Order finite volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2023年第2期5卷 751-775页

作者： Gaspar J.Machado Stéphane Clain Raphaël Loubère Centre of Physics and Department of Mathematics University of MinhoCampus of Azurém4800-058 GuimaraesPortugal CNRS and Institut de Mathématiques de Bordeaux(IMB) Universitéde BordeauxTalenceFrance

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic *** accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of *** supplemented this scheme with a stencil construction allowing to reduce even further the numerical *** stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial *** on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious ***,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

关键词： finite volume MOOD Adaptive stencil Steady-state solution Euler equations High order

New Superconvergent Structures with Optional Superconvergent Points for the finite volume Element Method

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2023年第5期33卷 1332-1356页

作者： XiangWang Yuqing Zhang Zhimin Zhang School of Mathematics Jilin UniversityChangchun 130012China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

New superconvergent structures are proposed and analyzed for the finite volume element(FVE)method over tensorial meshes in general dimension d(for d≥2);we call these orthogonal superconvergent *** this framework,one has the freedom to choose the superconvergent points of tensorial k-order FVE schemes(for k≥3).This flexibility contrasts with the superconvergent points(such as Gauss points and Lobatto points)for current FE schemes and FVE schemes,which are *** orthogonality condition and the modified M-decomposition(MMD)technique that are developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the FVE *** experiments are provided to validate our theoretical results.

关键词： Superconvergence finite volume orthogonality condition tensorial mesh rectangular mesh

finite volume NUMERICAL ANALYSIS FOR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2005年第2期23卷 165-176页

作者： XiaCui LaboratoryofComputationalPhysics InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009-26Beijing100088China

In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of R^d (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L^2 and H^1 spacial norm convergence properties are obtained.

关键词： finite volume Parabolic convection diffusion equations Numerical analysis

finite volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2014年第4期15卷 959-980页

作者： Jun Zhu Jianxian Qiu College of Science Nanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina School of Mathematical Sciences Xiamen UniversityXiamen 361005FujianChina.

In this paper,we present a new type of Hermite weighted essentially nonoscillatory(HWENO)schemes for solving the Hamilton-Jacobi equations on the finite volume *** cell averages of the function and its first one(in one dimension)or two(in two dimensions)derivative values are together evolved via time approaching and used in the *** the major advantages of the new HWENO schemes are their compactness in the spacial field,purely on the finite volume framework and only one set of small stencils is used for different type of the polynomial *** numerical tests are performed to illustrate the capability of the methodologies.

关键词： HWENO scheme finite volume Hamilton-Jacobi equation

SIMULATION OF VISCOELASTIC FLUID FLOWS IN EXPANSION GEOMETRY USING finite volume APPROACH

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Chinese Journal of Polymer Science 2013年第12期31卷 1599-1612页

作者： Morteza Azizi Ahmad Ramazani S.A Habib Etemadi M Ehsan Shirzaei S Department of Chemical and Petroleum Engineering Sharif University of Technology

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.

关键词： Expansion flow Simulation finite volume OpenFOAM Viscoelastic Fluids.

MULTISTEP finite volume APPROXIMATIONS TO THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE ON GENERAL 2D OR 3D MESHES

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

Journal of Computational Mathematics 2007年第4期25卷 485-496页

作者： Min Yang School of Mathematics and Information Science Yantai University Yantai 264005 China

In this paper, we consider a hydrodynamic model of the semiconductor device. The approximate solutions are obtained by a mixed finite volume method for the potential equation and multistep upwind finite volume methods for the concentration equations. Error estimates in some discrete norms are derived under some regularity assumptions on the exact solutions.

关键词： Semiconductor device Unstructured meshes finite volume Multistep method,Error estimates.

finite volume SUPERCONVERGENCE APPROXIMATION FOR ONE-DIMESIONAL SINGULARLY PERTURBED PROBLEMS

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

Journal of Computational Mathematics 2013年第5期31卷 488-508页

作者： Waixiang Cao Zhimin Zhang Qingsong Zou School of Mathematics and Computational Science Sun Yat-sen University Guangzhou 510275 China Beijing Cornputational Science Research Center Beijing 100084 ChinaDepartment of Mathematics Wayne State University Detroit MI 48202 USA School of MathemaLics and Computational Science and Guangdong Province Key Laboratory of Computational Science Sun Yat-sen University Guangzhou 510275 China

We analyze finite volume schemes of arbitrary order r for the one-dimensional singu- larly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as （N-11n（N 4- 1））r, where 2N is the number of subinter- vals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order （N-11n（N ＋ 1））2r, while at the Gauss points, the derivative error super-converges with order （N-11n（N ＋ 1））r＋1. All the above conver- gence and superconvergence properties are independent of the perturbation parameter e. Numerical results are presented to support our theoretical findings.

关键词： finite volume High Order Superconvergence Convection-Diffsuion.

CONVERGENCE OF finite volume SCHEMES FOR HAMILTON-JACOBI EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2015年第3期33卷 227-247页

作者： Kwangil Kim Yonghai Li School of Mathematics Jilin University Changchun 130012 China Department of Mathematics University of Science Pyongyang DPR Korea

We study numerical methods for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. We first propose a new class of abstract monotone approximation schemes and get a convergence rate of 1/2 . Then, according to the abstract convergence results, by newly constructing monotone finite volume approximations on interior and boundary points, we obtain convergent finite volume schemes for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. Finally give some numerical results.

关键词： Hamilton-Jacobi equations Dirichlet boundary conditions finite volume Monotone schemes.

A Vertex-Centered and Positivity-Preserving finite volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2020年第1期13卷 220-252页

作者： Shuai Su Jiming Wu Graduate School of China Academy of Engineering Physics Beijing 100088China Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China

Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons,ions and *** this paper,we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal *** vertex unknowns are treated as primary ones for which the finite volume equations are *** edgemidpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns,which makes the final scheme a pure vertex-centered *** comparison,most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the ***,the conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex ***,the new scheme effectively alleviates the nu-merical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion *** experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted *** the problem without analytic solution,the contours of the nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.

关键词： 2-D 3-T radiation diffusion equations vertex-centered scheme positivity-preserving finite volume