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带间断扩散系数热传导方程的新型自适应数值解法 被引量:5

A New Adaptive Numerical Solver for Heat Conduction Equation with Discontinuous Diffusion Coefficient
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摘要 本文研究带间断扩散系数热传导方程在大变形网格上的高精度数值模拟方法.该方法在算每条边上的能流时采用了本文提出的"孪生逼近"方法,提高了扩散系数间断处能流的计算精度,给出了"孪生逼近"的误差分析.应用该方法于二维大变形网格上热传导问题计算,构造了网格边上能流的一种自适应高精度计算方法,其中自适应指的是自适应选取模板和自适应选取权重大小.数值试验表明该方法能适应网格大变形和扩散系数间断的困难情况. In this paper,a high accuracy numerical simulative method is studied for heat conduction equations with discontinuous diffusion coefficient on large fluid distortion grids. This method applies a so-called "twin-fitting" approximate method proposed in this paper to the calculation of fluxes on edges,then improves calculational accuracy of fluxes on edges with discontinuous diffusion coefficient,at last is given some related error analysis.In two dimension case,an adaptive and high accuracy method is constructed to calculate fluxes on edges,here the "adaptive" means to determine the stencils and the weights adaptively. Numerical experiments show that this method can be accommodated to large fluid distortion grids and the difficult case of discontinuous diffusion coefficient.
出处 《应用数学学报》 CSCD 北大核心 2010年第5期942-960,共19页 Acta Mathematicae Applicatae Sinica
基金 国家973(2005CB321700) 国家自然科学基金重点(10931004) 青年科学基金(11001024)资助项目
关键词 最小二乘法 热传导方程 差分离散 自适应数值模拟 least square method heat conduction equation difference discretization adaptive numerical simulation
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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.
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  • 9Hermeline 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.
  • 10Zhukov 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.

同被引文献59

  • 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
  • 3Kershaw D S. Differencing of the Diffusion Equation in Lagrangian Hydrodynamic Codes. J. Comput. Phys., 1981, 39:375-395.
  • 4Morel 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.
  • 5Shashkov M J. Conservative Finite-difference Methods on General Grids. CRC Press: Boca Raton, FL., 1996.
  • 6Shashkov M J, Steinberg S. Solving Diffusion Equation with Rough Coefficients in Rough Grids. J. Comput. Phys., 1996, 129:383 405.
  • 7Morel 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.
  • 8Hermeline F. A Finite Volume Method for The Approximation of Diffusion Operators on Distorted Meshes. J. Comput. Phys., 2000, 160:481-499.
  • 9Hermeline 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.
  • 10Zhukov 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.

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