期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

带间断扩散系数热传导方程的高精度数值模拟方法研究 被引量：4

High Accuracy Numerical Method for Heat Conduction Equation With Discontinuous Diffusion Coefficient
原文传递
导出
摘要 针对热传导方程在间断扩散系数处的数值求解困难,作者已经提出了"孪生逼近"自适应方法.本文以一维问题为例,推广热传导方程解的内蕴连续性到高阶,进而研究构造了更高精度,更经济的"孪生逼近"算法,并用数值结果进行了检验. For the numerical difficulties on discontinuous diffusion coefficient of heat conduction equations,the so-called＂twin-fitting＂adaptive method has been proposed.In this paper,the intrinsic properties of heat conduction equations are extended to high order,and a kind of＂twin-fitting＂algorithm which is more accurate and more economic is constructed, at last numerical experiments validate the algorithm＇s advantages.
作者 宋淑红 王双虎
机构地区 北京应用物理与计算数学研究所 北京应用物理与计算数学研究所计算物理实验室 北京大学应用物理与技术研究中心
出处 《应用数学学报》 CSCD 北大核心 2011年第2期229-239,共11页 Acta Mathematicae Applicatae Sinica
基金 国家自然科学基金重点项目(10931004) 青年科学基金项目(11001024)资助项目
关键词 热传导方程 间断扩散系数 差分离散 heat conduction equation discontinuous diffusion coefficient difference discretization
分类号 O551.3 [理学—热学与物质分子运动论]
  • 相关文献

参考文献14

  • 1Kershaw D S. Differencing of the Diffusion Equation in Lagrangian Hydrodynamic Codes. J. Comput. Phys., 1981, 39:375-395.
  • 2Morel J E, Dendy J E, Hall M L, White S W. A Cell-centered Lagrangian-mesh Diffusion Differencing Scheme. J. Comput. Phys., 1992, 103:286-299.
  • 3Shashkov M J. Conservative Finite-difference Methods on General Grids. CRC Press: Boca Raton, FL., 1996.
  • 4Shashkov M J, Steinberg S. Solving Diffusion Equation with Rough Coefficients in Rough Grids. J. Comput. Phys., 1996, 129:383 405.
  • 5Morel J E, Roberts R M, Shashkov M J. A Local Support-operators Diffusion Discretization Scheme for Quadrilateral r-z Meshes. J. Comput. Phys., 1998, 144:17 51.
  • 6Hermeline F. A Finite Volume Method for The Approximation of Diffusion Operators on Distorted Meshes. J. Comput. Phys., 2000, 160:481-499.
  • 7Hermeline F. Approxiamtion of 2-D and 3-D Diffusion Operators with Variable Full Tensor Coefficients on Arbitrary Meshes. Comput. Meth. Appl. Mech. Engrg., 2007, 196:2497 2526.
  • 8Zhukov V T, Feodoritova O B. Difference Schemes for the Heat Condunction Equation Based on Local Least-squares Approximations, Preprint No. 97, IPMathem. Akad. Nauk S. S. S. R., Moscow, 1989.
  • 9Aavatsmark I, Barkve T, Bee Ф, Aannseth T. Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods. SIAM J. Sci. Comput., 1998, 19:1700-1716.
  • 10Aavatsmark I, Barkve T, Boe Ф, Aannseth T. Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part II: Discussion and Numerical Results. SIAM J. Sci. Comput., 1998, 19:1717-1736.

二级参考文献14

  • 1Lipnikov K, Shashkov M, Yotov I. Local Flux Mimetic Finite Difference Methods. Technical Report LA-UR-05-8364, Los Alamos National Laboratory, 2005.
  • 2Li D Y, Chen G N. An Introduction to Difference Methods of Parabolic Equations. Beijing: Science Press, 1995.
  • 3Hermeline F. A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes. J. Comput. Phys., 2000, 160:481-499.
  • 4Hermeline F. Approxiamtion of 2-D and 3-D Diffusion Operators with Variable Full Tensor Coefficients on Arbitrary Meshes. Comput. Meth. Appl. Mech. Engrg., 2007, 196:2497-2526.
  • 5Zhukov V T, Feodoritova O B. Difference Schemes for the Heat Condunction Equation Based on Local Least-squares Approximations. Preprint No. 97, IPMathem. Akad. Nauk S.S.S.R., Moscow, 1989.
  • 6Aavatsmark I, Barkve T, Bee φ, Aannseth T. Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods. SIAM J. Sci. Comput., 1998, 19: 1700-1716.
  • 7Aavatsmark I, Barkve T, Bφe φ, Aannseth T. Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part II: Discussion and Numerical Results. SIAM J. Sci. Comput., 1998, 19:1717-1736.
  • 8Aavatsmark I. An Introduction to Multipoint Flux Approximations for Quadrilateral Grids. Comput. Geosci., 2002, 6:405 432.
  • 9Samarskii A A. The Theory of Difference Schemes. Marcel Dekker. Inc.: New York-Basel, 2001.
  • 10Kershaw D S. Differencing of the Diffusion Equation in Lagrangian Hydrodynamic Codes. J. Comput. Phys., 1981, 39:375-395.

共引文献4

同被引文献46

  • 1王彩华.一维对流扩散方程的一类新型高精度紧致差分格式[J].水动力学研究与进展（A辑）,2004,19(5):655-663. 被引量：21
  • 2葛永斌,田振夫,詹咏,吴文权.求解扩散方程的一种高精度隐式差分方法[J].上海理工大学学报,2005,27(2):107-110. 被引量：19
  • 3Mohebbi A, Dehghan M. High order compact solution of the one dimensional heat and advec- tion-diffusion equations JJ. Appl Math Modell, 2010, 34(10) : 3071-3084.
  • 4Evans D J, Abdullah A R. Alternating group explicit methods for the diffusion equations [ J ]. Appl Math Modelling, 1985, 9(3) : 201-205.
  • 5Krylov N V. Nonlinear Elliptic and Parabolic Equations of Second Order[ MJ. Springer, 1987.
  • 6Ladyenskaja A O, Solonnikov V A, Ural' ceva N N. Linear and Quasi-Linear Equations of Parabolic Typel M]. Smith S trans. Translations of Mathematical Monographs, Vol 23, 1958.
  • 7Kershaw D S. Differencing of the Diffusion Equation in Lagrangian Hydrodynamic Codes. J. Comput. Phys., 1981, 39:375-395.
  • 8Morel J E, Dendy J E, Hall M L, White S W. A Cell-centered Lagrangian-mesh Diffusion Differencing Scheme. J. Comput. Phys., 1992, 103:286-299.
  • 9Shashkov M J, Steinberg S. Solving Diffusion Equation with Rough Coefficients in Rough Grids. J. Comput. Phys., 1996, 129:383-405.
  • 10Shashkov M J. Conservative Finite-difference Methods on General Grids. CRC Press, Boca Raton, FL., 1996.

引证文献4

二级引证文献3

应用数学学报
2011年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部