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一维土柱试验的数学模型
引用本文:李功胜,姚德,秦惠增,杨富贵,刘洪亮,王孝勤. 一维土柱试验的数学模型[J]. 山东理工大学学报:自然科学版, 2007, 21(3): 1-6
作者姓名:李功胜  姚德  秦惠增  杨富贵  刘洪亮  王孝勤
作者单位:山东理工大学,数学学院应用数学所,山东,淄博,255049;山东理工大学,环境科学技术研究所,山东,淄博,255049;山东理工大学,材料科学与工程学院,山东,淄博,255049;山东省淄博地质环境监测站,山东,淄博,255091;淄博市水资源管理办公室,山东,淄博,255032
摘    要:主要讨论了一维土柱试验模型及其反问题.考虑到溶质在土壤及地下水中迁移的非线性行为,认为通常模型中的阻滞因子应改为与溶质浓度相关的泛函,而零阶产出项应为与时间、空间及溶质浓度相关的非线性项,进而提出了一类新的描述一维土柱试验的非线性数学模型.对于模型参数的识别问题,给出了两类典型的确定阻滞因子与源(汇)项系数的土柱试验反问题.最后,以淄博张店孝妇河-张冉原状土柱试验为例,应用所建立的数学模型对试验结果做了初步的阐释.

关 键 词:一维土柱试验  数学模型  非线性吸附  非线性源(汇)项作用  反问题
文章编号:1672-6197(2007)05-000106
修稿时间:2006-10-09

One-dimensional mathematical model for soil-column experiment
LI Gong-sheng,YAO De,QIN Hui-zeng,YANG Fu-gui,LIU Hong-liang,WANG Xiao-qin. One-dimensional mathematical model for soil-column experiment[J]. Journal of Shandong University of Technology:Science and Technology, 2007, 21(3): 1-6
Authors:LI Gong-sheng  YAO De  QIN Hui-zeng  YANG Fu-gui  LIU Hong-liang  WANG Xiao-qin
Affiliation:1. Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, China~ 2. Institute of Environmental Science and Technology, Shandong University of Technology, Zibo 255049, China~ 3. School of Material Science and Engineering, Shandong University of Technology, Zibo 255049, China; 4. Inspecting Station of Geology and Environment in Zibo, Zibo 255091, China; 5. Zibo Water Resources Management Office, Zibo 255032, China
Abstract:One-dimensional soil-column experiment models and inverse problems are discussed in this paper.Due to nonlinear behaviors of solute transport in soil and groundwater,the ordinary retardation factor should be a nonlinear function of solute concentration,and the zero production term should be modified to a nonlinear term related with solute concentration,and then a new mathematical model with nonlinear terms is proposed.Furthermore,two kinds of inverse problems for soil-column experiments are discussed.Finally,an original soil-column experi ment in Zhangdian of Ziboisinvestigated,and a reasonable explanationforthe testing results is obtained with the help of the mathematical model.
Keywords:one-dimensional soil-column experiment  mathematical model  nonlinear adsorp-tion  nonlinear source(sink) reactions  inverse problems
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