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变限积分的有限体积法解决对流扩散方程

DOI: 10.3969/j.issn.1006-7043.201410049

Keywords: 变限积分, 高精度, 对流-扩散方程, Fourier分析法, 非稳态, 一维

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Abstract:

针对一维对流扩散方程,基于变限积分的有限体积法,提出一种高精度全离散方法.该方法在控制体内对方程进行变限积分,引入变限因子,然后分别对上下限再进行积分,从而将微分方程转化为积分方程,最后运用插值的方法对目标函数进行近似代替.该方法提高了计算精度,结果得到一维的收敛精度.采用Fourier分析法证明了格式为条件稳定.最后给出了非稳态和稳态2种情况下的数值算例,验证了所提出的格式具有高精度和易于编程计算的优点.

References

[1]  DEHGHAN M.Weighted finite difference techniques for the one-dimensional advection diffusion equation[J]. Appl Math Comput, 2004,147: 307-319.
[2]  ROACHE P J.Computational fluid dynamics[M]. Hermosa Publishers, 1972.
[3]  SPALDING D B. A novel finite difference formulation for differential expressions involving both first and second derivatives[J]. International Journal for Numerical Methods in Engineering, 1972, 4(4): 551-559.
[4]  DEHGHAN M. Numerical solution of the three-dimensional advection-diffusion equation[J]. Applied Mathematics and Computation, 2004, 150(1): 5-19.
[5]  ISENBERG J, GUTFINGER C. Heat transfer to a draining film[J]. International Journal of Heat and Mass Transfer, 1973, 16(2): 505-512.
[6]  PARLANGE J Y. Water transport in soils[J]. Annual Review of Fluid Mechanics, 1980, 12(1): 77-102.
[7]  FATTAH Q N, HOOPES J A. Dispersion in anisotropic, homogeneous, porous media[J]. Journal of Hydraulic Engineering, 1985, 111(5): 810-827.
[8]  CHATWIN P C, ALLEN C M. Mathematical models of dispersion in rivers and estuaries[J]. Annual Review of Fluid Mechanics, 1985, 17(1): 119-149.
[9]  HOLLY J R F M, USSEGLIO-POLATERA J M. Dispersion simulation in two-dimensional tidal flow[J]. Journal of Hydraulic Engineering, 1984, 110(7): 905-926.
[10]  KUMAR N. Unsteady flow against dispersion in finite porous media[J]. Journal of Hydrology, 1983, 63(3): 345-358.
[11]  GUVANASEN V, VOLKER R E. Numerical solutions for solute transport in unconfined aquifers[J]. International Journal for Numerical Methods in Fluids, 1983, 3(2): 103-123.
[12]  KARAHAN H. Unconditional stable explicit finite difference technique for the advection-diffusion equation using spreadsheets[J]. Advances in Engineering Software, 2007, 38(2): 80-86.
[13]  KARAHAN H. Implicit finite difference techniques for the advection-diffusion equation using spreadsheets[J]. Advances in Engineering Software, 2006, 37(9): 601-608.
[14]  SUN H, ZHANG J. A high-order compact boundary value method for solving one-dimensional heat equations[J]. Numerical Methods for Partial Differential Equations, 2003, 19(6): 846-857.
[15]  TIAN Z F. A rational high-order compact ADI method for unsteady convection-diffusion equations[J]. Computer Physics Communications, 2011, 182(3): 649-662.
[16]  HIRSH R S. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique[J]. Journal of Computational Physics, 1975, 19(1): 90-109.
[17]  CIMENT M, LEVENTHAL S H, WEINBERG B C. The operator compact implicit method for parabolic equations[J]. Journal of Computational Physics, 1978, 28(2): 135-166.
[18]  BAZAN F S V. Chebyshev pseudospectral method for computing numerical solution of convection-diffusion equation[J]. Applied Mathematics and Computation, 2008, 200(2): 537-546.
[19]  MOHEBBI A, DEHGHAN M. High-order compact solution of the one-dimensional heat and advection-diffusion equations[J]. Applied Mathematical Modelling, 2010, 34(10): 3071-3084.
[20]  DEHGHAN M. Implicit collocation technique for heat equation with non-classic initial condition[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2006, 7(4): 461-466.
[21]  KARAA S, ZHANG J. High order ADI method for solving unsteady convection-diffusion problems[J]. Journal of Computational Physics, 2004, 198(1): 1-9.
[22]  TIAN Z F, GE Y B. A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems[J]. Journal of Computational and Applied Mathematics, 2007, 198(1): 268-286.
[23]  王红梅. 对流扩散方程的特征有限元方法[D]. 济南:山东大学, 2012.WANG Hongmei. Characteristics finite element methods for convection-diffusion problems[D]. Jinan: Shandong University, 2012.
[24]  丁晓燕, 冯秀芳. 求解二维非定常对流扩散方程的高精度指数型差分方法[J]. 宁夏大学学报: 自然科学版, 2014, 35(1): 6-13.DING Xiaoyan, FENG Xiufang. A high-order exponential method for solving unsteady convection-diffusion equation[J]. Journal of Ningxia University: Natural Science Edition, 2014, 35(1): 6-13.
[25]  秦新强, 王志刚, 王全九, 等. 对流占优扩散方程的楔形基无网格法[J]. 工程数学学报, 2013, 30(5): 721-730.QIN Xinqiang, WANG Zhigang, WANG Quanjiu, et al. Meshless method with ridge basis functions for convection-dominated diffusion equations[J]. Chinese Journal of Engineering Mathematics, 2013, 30(5): 721-730.
[26]  马亮亮. 变系数空间分数阶对流-扩散方程的有限差分解法[J]. 沈阳大学学报: 自然科学版, 2013, 25(4): 341-344.MA Liangliang. Finite difference methods for space fractional convection-diffusion equation with variable coefficients[J]. Journal of Shenyang University: Natural Science, 2013, 25(4): 341-344.
[27]  杨录峰, 李春光. 一种求解对流扩散反应方程的高阶紧致差分格式[J]. 宁夏大学学报: 自然科学版, 2013, 34(2): 101-104.YANG Lufeng, LI Chunguang. A high-order compact finite difference scheme for solving the convection diffusion reaction equations[J]. Journal of Ningxia University: Natural Science Edition, 2013, 34(2): 101-104.

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