地下水溶质运移数值模拟中减少误差的新方法

梅一; 吴吉春

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地下水溶质运移数值模拟中减少误差的新方法

梅一, 吴吉春

文章导航 > 水科学进展 > 2009 > 20(5): 639-645

梅一, 吴吉春. 地下水溶质运移数值模拟中减少误差的新方法[J]. 水科学进展, 2009, 20(5): 639-645.

引用本文:

梅一, 吴吉春. 地下水溶质运移数值模拟中减少误差的新方法[J]. 水科学进展, 2009, 20(5): 639-645.

MEI Yi, WU Ji-chun. New method for reducing the numerical error in solving the problem of contaminant transport in ground water[J]. Advances in Water Science, 2009, 20(5): 639-645.

Citation:

MEI Yi, WU Ji-chun. New method for reducing the numerical error in solving the problem of contaminant transport in ground water[J]. Advances in Water Science, 2009, 20(5): 639-645.

地下水溶质运移数值模拟中减少误差的新方法

梅一,
吴吉春

南京大学水科学系, 江苏, 南京, 210093

基金项目: 国家自然科学基金资助项目(40725010;40672160)

详细信息

作者简介:
梅一(1983- ),男,四川成都人,硕士研究生,主要研究方向为地下水数值模拟.E-mail:njumeiyi@gmail.com

中图分类号: P641.2

New method for reducing the numerical error in solving the problem of contaminant transport in ground water

MEI Yi,
WU Ji-chun

Department of Hydrosciences, Nanjing University, Nanjing 210093, China

Funds: The study is financially supported by the National Natural Science Foundation of China(No.40725010;40672160).

摘要: 地下水中污染物运移的数值模拟方法一直是学界的研究热点问题.而如何减少与消除对流-弥散方程数值解中浓度陡锋面附近的数值振荡与数值弥散,更是研究的前沿与难点.提出了一种地下水溶质运移数值模拟中减少数值弥散的新方法.该方法的核心思想是在水动力弥散系数上加上一个数值弥散估算值,得到一个修正弥散系数,用其替代方程中有明确物理意义的水动力弥散系数进行计算.并提出了一个参数——数值弥散因子(μ_NDF),可以根据研究需要进行参数分区并适当调节该因子的大小,从而达到控制数值振荡,减小数值弥散的目的.从一维到二维的多个数值算例的模拟计算结果表明,该方法能在消除数值振荡的基础上,较好地减少数值弥散,达到满意的精度.
- 数值振荡 /
- 数值弥散 /
- 对流-弥散方程 /
- 有限差分 /
- 地下水溶质运移
Abstract: The numerical simulation of the contaminant transport in subsurface porous media have been a hotspot for years.It is always considered to be tough to deal with the problems regarding the numerical dispersion and the oscillation around sharp front area of contaminants.This paper presents a new method which can reduce the numerical dispersion in the numerical modeling of the contaminant transport in groundwater.The core of the new method is adding a new numerical dispersion estimation term to the hydrodynamic dispersion coefficient and obtaining a modified hydrodynamic dispersion coefficient(MHDC).We use MHDC instead of the traditional hydrodynamic dispersion coefficient and put forward a new parameter of numerical dispersion factor(μ_NDF).The research area can be divided into different μ_NDF areas,and their values can be adjusted according to our needs.In this way,we can control the numerical oscillation and diminishing the numerical dispersion.The Simulated results of several examples from one-dimension problems to two-dimension problem indicate that the new method can considerably reduce the numerical dispersion on the basis of diminishing the numerical oscillation and obtain more precise simulation results.Hence,the new method is simple in theory,convenient in application and worth popularizing.
- numerical oscillation /
- numerical dispersion /
- convection-dispersion equations /
- finite different method /
- ground-water contamination transport

[1]	孙讷正.地下水污染:数学模型和数值方法[M].北京:地质出版社,1989:81.(SUN Ne-zheng.Mathematical modeling of groundwater pollution[M].Beijing:Geological Publishing House,1989:81.(in Chinese))
[2]	ZHENG C,WANG P.MT3DMS:A modular three-dimensional multispecies transport model for simulation of advection,dispersion,and chemical reactions of contaminants in groundwater systems[R].Washington DC:U S Army Corps of Engineers.1999:1-10.
[3]	成建梅,胡进武.饱和水流溶质运移问题数值解法综述[J].水文地质工程地质,2003,30(2):99-106.(CHENG Jian-mei,HU Jin-wu.A review of numerical method for contaminant transport in saturated groundwater[J].Hydrogeology and Engineering Geology,2003,30(2):99-106.(in Chinese))
[4]	PINDER G F,GRAY W G.Finite element simulation in surface and subsurface hydrology[M].New York:Academic Press,1977:148.
[5]	HOSSAIN M A,BARBER M E.Optimized Petrov-Galerkin model for advective-dispersive transport[J].Applied Mathematics and Computation,2000,115(1):1-10.
[6]	薛禹群,谢春红.地下水数值模拟[M].北京:科学出版社,2007:58-60.(XUE Yu-qun,XIE Cun-hong.Numerical simulation for groundwater[M].Beijing:Science Press,2007:58-60.(in Chinese))
[7]	水鸿寿.一维流体力学差分方法[M].北京:国防工业出版社,1998:318.(SHUI Hong-shou.Differential methods for one dimensional fluid mechanics[M].Beijing:National Defense & Industry Press,1998:318.(in Chinese))
[8]	ZHENG C,BENNETT G D.Applied contaminant transport modeling[M].San Francisco:Wiley Inter-Science,2002:123.
[9]	NOORISHAD J,TSANG C F,PERROCHET P,et al.A perspective on the numerical solution of convection-dominated transport problems:A price to pay for the easy way out[J].Water Resources Research,1992,28(2),551-561.
[10]	WANG H Q,LACROIX M.Optimal weighting in the finite difference solution of the convection-dispersion equation[J].Journal of Hydrology,1997,200(1/2/3/4),228-242.
[11]	钱家忠,汪家权,葛晓光,等.我国北方型裂隙岩溶水流及污染物运移数值模拟研究进展.水科学进展,2003,14(4):509-512.(QIAN Jia-zhong,WANG Jia-quan,GE Xiao-guang.Advances in research for numerical simulation of contaminant transport and flow in North China type fracture-karst media[J].Advances in Water Science,2003,14(4):509-512.(in Chinese))

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地下水溶质运移数值模拟中减少误差的新方法

梅一,
吴吉春

南京大学水科学系, 江苏, 南京, 210093

基金项目: 国家自然科学基金资助项目(40725010;40672160)

作者简介:
梅一(1983- ),男,四川成都人,硕士研究生,主要研究方向为地下水数值模拟.E-mail:njumeiyi@gmail.com

收稿日期: 2008-08-24
刊出日期: 2009-09-25

中图分类号: P641.2

关键词:

摘要: 地下水中污染物运移的数值模拟方法一直是学界的研究热点问题.而如何减少与消除对流-弥散方程数值解中浓度陡锋面附近的数值振荡与数值弥散,更是研究的前沿与难点.提出了一种地下水溶质运移数值模拟中减少数值弥散的新方法.该方法的核心思想是在水动力弥散系数上加上一个数值弥散估算值,得到一个修正弥散系数,用其替代方程中有明确物理意义的水动力弥散系数进行计算.并提出了一个参数——数值弥散因子(μ_NDF),可以根据研究需要进行参数分区并适当调节该因子的大小,从而达到控制数值振荡,减小数值弥散的目的.从一维到二维的多个数值算例的模拟计算结果表明,该方法能在消除数值振荡的基础上,较好地减少数值弥散,达到满意的精度.

English Abstract

New method for reducing the numerical error in solving the problem of contaminant transport in ground water

MEI Yi,
WU Ji-chun

Department of Hydrosciences, Nanjing University, Nanjing 210093, China

Funds: The study is financially supported by the National Natural Science Foundation of China(No.40725010;40672160).

Received Date: 2008-08-24
Publish Date: 2009-09-25

Keywords:

Abstract: The numerical simulation of the contaminant transport in subsurface porous media have been a hotspot for years.It is always considered to be tough to deal with the problems regarding the numerical dispersion and the oscillation around sharp front area of contaminants.This paper presents a new method which can reduce the numerical dispersion in the numerical modeling of the contaminant transport in groundwater.The core of the new method is adding a new numerical dispersion estimation term to the hydrodynamic dispersion coefficient and obtaining a modified hydrodynamic dispersion coefficient(MHDC).We use MHDC instead of the traditional hydrodynamic dispersion coefficient and put forward a new parameter of numerical dispersion factor(μ_NDF).The research area can be divided into different μ_NDF areas,and their values can be adjusted according to our needs.In this way,we can control the numerical oscillation and diminishing the numerical dispersion.The Simulated results of several examples from one-dimension problems to two-dimension problem indicate that the new method can considerably reduce the numerical dispersion on the basis of diminishing the numerical oscillation and obtain more precise simulation results.Hence,the new method is simple in theory,convenient in application and worth popularizing.

梅一, 吴吉春. 地下水溶质运移数值模拟中减少误差的新方法[J]. 水科学进展, 2009, 20(5): 639-645.

引用本文:

梅一, 吴吉春. 地下水溶质运移数值模拟中减少误差的新方法[J]. 水科学进展, 2009, 20(5): 639-645.

MEI Yi, WU Ji-chun. New method for reducing the numerical error in solving the problem of contaminant transport in ground water[J]. Advances in Water Science, 2009, 20(5): 639-645.

Citation:

MEI Yi, WU Ji-chun. New method for reducing the numerical error in solving the problem of contaminant transport in ground water[J]. Advances in Water Science, 2009, 20(5): 639-645.