海域地表水与地下水相互作用下水量与水质运移规律数值模拟研究
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摘要
地下水与地表水的交互作用既是水资源研究的核心和热点,也是陆水相互作用中重要的物理过程。国际水文科学协会(IAHS)和国际水文地质学家协会(IAH)分别于1986年和1994年将地表水和地下水相互作用的问题正式提交会议讨论,于是地表水和地下水相互作用的研究便成了水文学及水文地质学方面研究的热点问题,然而,由于各种条件的限制,现有的模拟或者以单独研究地表水为主,或者以单独研究地下水为主,而且在模拟地表水与地下水耦合作用时,常常将地表水刻画成一维或者二维流,实际上,海域地表水体的流动往往是三维的。随着经济的快速增长和计算机速度的不断扩大,对数值模拟结果精度的要求越来越高,因此,本文旨在将地表水与地下水作为一个整体,进一步研究海域地表水与地下水相互作用下水量与数值分布规律的数值模拟问题。
论文的第一部分在忽略海域地表水流动性的情况下研究地表水与地下水耦合数值模拟。首先,在忽略咸淡水密度差异的条件下,采用有限差分法建立控制方程的差分格式与半解析有限差分格式,讨论有限差分格式对时间网格剖分、空间网格剖分以及初始条件选择的敏感性,同时研究有限差分格式、半解析有限差分格式与解析解的联系与区别；其次,在考虑咸淡水密度差异的情况下,研究密度差异对地下水流场的影响；最后,通过算例对比分析传统有限差分法、半解析有限差分法和解析解,揭示这些模型的应用条件以及范围。结果表明
(1)半解析数值解是采用解析法消去时间项,然后采用数值法计算空间项。数值实验结果表明,空间步长对半解析数值解的影响不敏感,对于传统的数值解,时间步长不同计算结果差异很大,因此,对于海潮波动的数值模拟,时间的剖分对数值结果的影响很大。
(2)在潜水含水层中,当海潮波动相对含水层厚度比较小时,模型的线性化给计算结果带来的误差较小,可以忽略不计,反之,当波动比较大时,误差随着也增大。
(3)求解海潮波动引起地下水流动的问题时,由于海潮的周期性,解析解和半解析数值解都不需要初始条件,然而,采用传统有限差分法求解非稳定流问题,初始条件必不可少,数值模拟结果表明采用平均海平面作为初始条件,效果最佳。
(4)储水系数对海水入侵引起地下水流场变化比较敏感,储水系数越小,忽略咸淡水密度差异造成的误差越大。对于储水系数较大的潜水含水层,海水与淡水的密度差异只影响临海地区的流场,但是在远离海域的地方,流场几乎不受影响。
(5)海水的浓度随着时间的推移慢慢向内陆延伸,但是由于水头海域水头的波动很小,因此浓度的传播很慢。
论文的第二部分对应于本文的第三章,是在考虑地表水流动的情况下,研究海域地表水与地下水耦合数值模拟问题,其中,地表水采用三维的Navier-Stokes方程组来描述。本文在Katerina差分格式的基础上,分析其收敛性条件以及差分方程的特点,针对该差分方程的缺陷,推导了上游加权半隐式半显式差分格式,然后,提出了改进的方法——加权因子预测法,并推导了加权因子的计算公式,最后,通过两个数值算例,验证了改进法的合理性以及有效性,并研究了含水层性质对耦合流场下水质和水量空间分布的影响。结果表明
(1)现有的半显式半隐式有限差分格式虽然计算量小,然而由于其收敛性条件难以把握,很容易造成部分区域质量不守恒或者波动现象,于是,本文提出了加权因子预测法,数值实验表明该法效果很好。
(2)当含水层的渗透性较差和储水系数较大时,地表水与地下水的交互作用比较弱,即地表水水位的强烈变化在含水层中的衰减太快,反之,当储水系数比较小时,地表水与地下水的耦合作用强烈,地表水水位变化在含水层中的衰减变慢。
论文的第三部分对应于本文的第四章,首先建立控制方程的有限差分格式,然后通过数值算例研究污染物在含水层与地表水中的迁移规律,结果表明：与地下水流动速度相比,地表水的流动速度很快,因此,溶质在含水层的传播速度慢,而当运移到地表水体时,传播速度很快。若某地区含水层受到了污染,则尽量将污染物圈定在某个区域内,比如加隔水墙,或者在被污染的含水层附近采用低渗透的介质使污染物的扩散减慢,同时在含水层中注入某些生物化学溶剂,使含水层慢慢净化。
第四部分是应用实例,采用数值模拟手段研究雷州半岛地表水与地下水耦合作用下水质和水量的空间分布规律。首先通过分析总结现有的勘察资料,弄清楚该地区的水文地质背景,并概化出该地区的水文地质概念模型,然后,针对该模型,建立对应的数学模型与数值模型,最后,采用自制模拟程序,模拟该地区的水量与水质的分布规律。数值模拟结果表明,随着海水水位的波动,含水层的水头也在波动,然而,波动的范围很小,即只在距离海域100m处以内的含水层中的水流受影响,远离海岸的地方几乎不受海水潮汐动态的影响。对于海水入侵情况,在刚开始,海域的咸水入侵含水层,然而,随着时间的推移,咸水的入侵速度变慢,到14小时后,入侵基本结束,即咸淡水界面保持稳定。因此,在雷州半岛,如果没有高强度的开采,是不会导致海水入侵问题。
The studies of the interaction between the surface water and groundwater are the key and hot problems, which is also the important physical process in the interaction of the land and water. International Association of Hydrological Sciences (IAHS) in 1986 and International Association of Hydro geologists (IAH) in 1994 submited this topic into the congress, and then it came to the hot problems of the water resource in hydrology and hydrogeology. However, due to the limitation of the computer and other matters, the modeling of the interaction between the surface water and groundwater, always trended to either surface water modeling or groundwater modeling, and the surface water movement is described by the 1-D flow or 2-D flow. In fact, the sea water movement is 3-D. With the development of the economy and the computer, the accuracy of numerical simulation should be higher and higher. Therefore,3-D groundwater and 3-D surface water were coupled to simulate the spatial distribution of water quality and quantity with time in this paper.
The first part of this thesis is on numerical simulation of the interaction between the groundwater and surface water as boundary condition of the aquifer, that is the movement of the surface water is ignored in the stress period. Firstly, the traditional finite difference scheme and semi finite difference scheme are established under the condition that the difference of density between the fresh water and salt water is ignored. The influences of the initial condition, time step and spatial step to the results of finite difference method are discussed, and the relations and difference among semi finite difference method, traditional finite difference method and analytical solution were studied. Secondly, the finite difference scheme was established if the density of salt water was considered. By comparing the numerical results from semi finite difference method, traditional finite difference method and analytical solution, the limitations and demerits of these models were obtained by numerical simulations. The results shows
(1) The semi-analytical numerical solution of the groundwater level, which is numerical for the spatial variables and analytical for the time variable. The results from numerical experiments show that the dimension of spatial step does affect the numerical results very much, by comparing the traditional finite difference method, semi finite difference method and analytical method. In contrary, the time step dimension is an important factor to the accuracy of the numerical simulations.
(2) If the tidal amplitude is small in relevant to the aquifer's thickness in the unconfined aquifer, the error caused by the linearization for the nonlinear model can be ignored, or the error is large.
(3) The groundwater flow in coastal aquifer is simulated by the traditional finite difference method, the initial condition is necessary for the unsteady flow. The semi finite difference method and analytical method do not need it, due to the tidal period. By comparing the simulations among traditional finite difference method, semi finite difference method and analytical method, the results show the average sea level is better as the initial head for the unsteady flow.
(4) The storage coefficient is a very sensitive factor for the groundwater level movement caused by the sea intrusion. If it is small, the error, caused by neglecting the difference between the fresh water and salt water, can not be ignored. However, as for the unconfined aquifer where the storage is small, the error exists in the area not far from sea water, and is small for the area far form sea water.
(5) The sea water moves to the inland with time. Due to the fluctuant of sea water, it moves fast at the beginning, but slowly later.
The second part corresponding to the chapter three is about the interaction between the groundwater and surface water whose movement has been considered by the 3-D Navier-Stokes equations. Firstly, the upstream weighted semi implicit finite difference scheme was established, based on the Katerina's numerical method. Secondly, the character of this finite difference scheme was analyzed, and then the improved finite difference method was presented——weighted factor predicting method, and the fomula of the weighted factor was derived. Lastly, the rationality of the improved method was verified by two numerical simulations, at the same time, the influence of the aquifer property to the water quality and quantity distribution spatially was simulated.The results show
(1) The computation of Katerina's numerical method is small to simulate the surface water and groundwater interaction, but the convergent condition is difficult to be satisfied. If it can not be met, mass in region can not be balanced and the water level is fluctuant, more than the maximum or smaller than the minimum. Therefore, the improved numerical method was presented, and the numerical simulations show it is more reasonable.
(2) If the permeability of the aquifer is low, and storage is high, the interaction between the surface water and groundwater is strong, in the contrary, it is not strong and the surface water level fluctuant decrease drastically.
The third part corresponding to the chapter four is about the contaminant transport numerical simulation under the flow field of the groundwater-surface water. Firstly, the finite difference scheme of the solute transport governing equation was established, and then its law in the surface water and groundwater coupling flow field is simulated by the numerical experiments. Results show:the velocity of the surface water flow is very fast, comparing with groundwater flow velocity, so the contaminant moves faster in the surface water than in the groundwater. If some region was polluted, the contaminant should be limited in small zone by some measures, such as impermeable wall, and some biochemistry solvents could be injected into the aquifer, simultaneously, in order to purify the groundwater.
The fourth part is about the practical application. Using the numerical method, the special distributions of the water quality and water quantity were simulated under the interaction of surface water and groundwater in Lei Zhou Peninsula. Firstly, the hydraulic background in this area should be made clear through arranging and analyzing the data from the field investigation. Secondly, hydrageological conceptual model was generalized, and the corresponding mathematic model and numerical model were built. Lastly, the special distribution of the water quality and water quantity was simulated by computer programs written by myself. The results show hydraulic head in aquifer in 100m from sea changes with the fluctuant of surface water, and it is almost not affected by the sea water tidal movement in the aquifer more than 100m from sea. As for the sea water intrusion, salt water moves into the aquifer in the beginning, but the interface of the salt water and fresh water does not move later. In Leizhou Peninsula, if the exploitation is not strong, the sea water does not move into the aquifer.
论文的第一部分在忽略海域地表水流动性的情况下研究地表水与地下水耦合数值模拟。首先,在忽略咸淡水密度差异的条件下,采用有限差分法建立控制方程的差分格式与半解析有限差分格式,讨论有限差分格式对时间网格剖分、空间网格剖分以及初始条件选择的敏感性,同时研究有限差分格式、半解析有限差分格式与解析解的联系与区别；其次,在考虑咸淡水密度差异的情况下,研究密度差异对地下水流场的影响；最后,通过算例对比分析传统有限差分法、半解析有限差分法和解析解,揭示这些模型的应用条件以及范围。结果表明
(1)半解析数值解是采用解析法消去时间项,然后采用数值法计算空间项。数值实验结果表明,空间步长对半解析数值解的影响不敏感,对于传统的数值解,时间步长不同计算结果差异很大,因此,对于海潮波动的数值模拟,时间的剖分对数值结果的影响很大。
(2)在潜水含水层中,当海潮波动相对含水层厚度比较小时,模型的线性化给计算结果带来的误差较小,可以忽略不计,反之,当波动比较大时,误差随着也增大。
(3)求解海潮波动引起地下水流动的问题时,由于海潮的周期性,解析解和半解析数值解都不需要初始条件,然而,采用传统有限差分法求解非稳定流问题,初始条件必不可少,数值模拟结果表明采用平均海平面作为初始条件,效果最佳。
(4)储水系数对海水入侵引起地下水流场变化比较敏感,储水系数越小,忽略咸淡水密度差异造成的误差越大。对于储水系数较大的潜水含水层,海水与淡水的密度差异只影响临海地区的流场,但是在远离海域的地方,流场几乎不受影响。
(5)海水的浓度随着时间的推移慢慢向内陆延伸,但是由于水头海域水头的波动很小,因此浓度的传播很慢。
论文的第二部分对应于本文的第三章,是在考虑地表水流动的情况下,研究海域地表水与地下水耦合数值模拟问题,其中,地表水采用三维的Navier-Stokes方程组来描述。本文在Katerina差分格式的基础上,分析其收敛性条件以及差分方程的特点,针对该差分方程的缺陷,推导了上游加权半隐式半显式差分格式,然后,提出了改进的方法——加权因子预测法,并推导了加权因子的计算公式,最后,通过两个数值算例,验证了改进法的合理性以及有效性,并研究了含水层性质对耦合流场下水质和水量空间分布的影响。结果表明
(1)现有的半显式半隐式有限差分格式虽然计算量小,然而由于其收敛性条件难以把握,很容易造成部分区域质量不守恒或者波动现象,于是,本文提出了加权因子预测法,数值实验表明该法效果很好。
(2)当含水层的渗透性较差和储水系数较大时,地表水与地下水的交互作用比较弱,即地表水水位的强烈变化在含水层中的衰减太快,反之,当储水系数比较小时,地表水与地下水的耦合作用强烈,地表水水位变化在含水层中的衰减变慢。
论文的第三部分对应于本文的第四章,首先建立控制方程的有限差分格式,然后通过数值算例研究污染物在含水层与地表水中的迁移规律,结果表明：与地下水流动速度相比,地表水的流动速度很快,因此,溶质在含水层的传播速度慢,而当运移到地表水体时,传播速度很快。若某地区含水层受到了污染,则尽量将污染物圈定在某个区域内,比如加隔水墙,或者在被污染的含水层附近采用低渗透的介质使污染物的扩散减慢,同时在含水层中注入某些生物化学溶剂,使含水层慢慢净化。
第四部分是应用实例,采用数值模拟手段研究雷州半岛地表水与地下水耦合作用下水质和水量的空间分布规律。首先通过分析总结现有的勘察资料,弄清楚该地区的水文地质背景,并概化出该地区的水文地质概念模型,然后,针对该模型,建立对应的数学模型与数值模型,最后,采用自制模拟程序,模拟该地区的水量与水质的分布规律。数值模拟结果表明,随着海水水位的波动,含水层的水头也在波动,然而,波动的范围很小,即只在距离海域100m处以内的含水层中的水流受影响,远离海岸的地方几乎不受海水潮汐动态的影响。对于海水入侵情况,在刚开始,海域的咸水入侵含水层,然而,随着时间的推移,咸水的入侵速度变慢,到14小时后,入侵基本结束,即咸淡水界面保持稳定。因此,在雷州半岛,如果没有高强度的开采,是不会导致海水入侵问题。
The studies of the interaction between the surface water and groundwater are the key and hot problems, which is also the important physical process in the interaction of the land and water. International Association of Hydrological Sciences (IAHS) in 1986 and International Association of Hydro geologists (IAH) in 1994 submited this topic into the congress, and then it came to the hot problems of the water resource in hydrology and hydrogeology. However, due to the limitation of the computer and other matters, the modeling of the interaction between the surface water and groundwater, always trended to either surface water modeling or groundwater modeling, and the surface water movement is described by the 1-D flow or 2-D flow. In fact, the sea water movement is 3-D. With the development of the economy and the computer, the accuracy of numerical simulation should be higher and higher. Therefore,3-D groundwater and 3-D surface water were coupled to simulate the spatial distribution of water quality and quantity with time in this paper.
The first part of this thesis is on numerical simulation of the interaction between the groundwater and surface water as boundary condition of the aquifer, that is the movement of the surface water is ignored in the stress period. Firstly, the traditional finite difference scheme and semi finite difference scheme are established under the condition that the difference of density between the fresh water and salt water is ignored. The influences of the initial condition, time step and spatial step to the results of finite difference method are discussed, and the relations and difference among semi finite difference method, traditional finite difference method and analytical solution were studied. Secondly, the finite difference scheme was established if the density of salt water was considered. By comparing the numerical results from semi finite difference method, traditional finite difference method and analytical solution, the limitations and demerits of these models were obtained by numerical simulations. The results shows
(1) The semi-analytical numerical solution of the groundwater level, which is numerical for the spatial variables and analytical for the time variable. The results from numerical experiments show that the dimension of spatial step does affect the numerical results very much, by comparing the traditional finite difference method, semi finite difference method and analytical method. In contrary, the time step dimension is an important factor to the accuracy of the numerical simulations.
(2) If the tidal amplitude is small in relevant to the aquifer's thickness in the unconfined aquifer, the error caused by the linearization for the nonlinear model can be ignored, or the error is large.
(3) The groundwater flow in coastal aquifer is simulated by the traditional finite difference method, the initial condition is necessary for the unsteady flow. The semi finite difference method and analytical method do not need it, due to the tidal period. By comparing the simulations among traditional finite difference method, semi finite difference method and analytical method, the results show the average sea level is better as the initial head for the unsteady flow.
(4) The storage coefficient is a very sensitive factor for the groundwater level movement caused by the sea intrusion. If it is small, the error, caused by neglecting the difference between the fresh water and salt water, can not be ignored. However, as for the unconfined aquifer where the storage is small, the error exists in the area not far from sea water, and is small for the area far form sea water.
(5) The sea water moves to the inland with time. Due to the fluctuant of sea water, it moves fast at the beginning, but slowly later.
The second part corresponding to the chapter three is about the interaction between the groundwater and surface water whose movement has been considered by the 3-D Navier-Stokes equations. Firstly, the upstream weighted semi implicit finite difference scheme was established, based on the Katerina's numerical method. Secondly, the character of this finite difference scheme was analyzed, and then the improved finite difference method was presented——weighted factor predicting method, and the fomula of the weighted factor was derived. Lastly, the rationality of the improved method was verified by two numerical simulations, at the same time, the influence of the aquifer property to the water quality and quantity distribution spatially was simulated.The results show
(1) The computation of Katerina's numerical method is small to simulate the surface water and groundwater interaction, but the convergent condition is difficult to be satisfied. If it can not be met, mass in region can not be balanced and the water level is fluctuant, more than the maximum or smaller than the minimum. Therefore, the improved numerical method was presented, and the numerical simulations show it is more reasonable.
(2) If the permeability of the aquifer is low, and storage is high, the interaction between the surface water and groundwater is strong, in the contrary, it is not strong and the surface water level fluctuant decrease drastically.
The third part corresponding to the chapter four is about the contaminant transport numerical simulation under the flow field of the groundwater-surface water. Firstly, the finite difference scheme of the solute transport governing equation was established, and then its law in the surface water and groundwater coupling flow field is simulated by the numerical experiments. Results show:the velocity of the surface water flow is very fast, comparing with groundwater flow velocity, so the contaminant moves faster in the surface water than in the groundwater. If some region was polluted, the contaminant should be limited in small zone by some measures, such as impermeable wall, and some biochemistry solvents could be injected into the aquifer, simultaneously, in order to purify the groundwater.
The fourth part is about the practical application. Using the numerical method, the special distributions of the water quality and water quantity were simulated under the interaction of surface water and groundwater in Lei Zhou Peninsula. Firstly, the hydraulic background in this area should be made clear through arranging and analyzing the data from the field investigation. Secondly, hydrageological conceptual model was generalized, and the corresponding mathematic model and numerical model were built. Lastly, the special distribution of the water quality and water quantity was simulated by computer programs written by myself. The results show hydraulic head in aquifer in 100m from sea changes with the fluctuant of surface water, and it is almost not affected by the sea water tidal movement in the aquifer more than 100m from sea. As for the sea water intrusion, salt water moves into the aquifer in the beginning, but the interface of the salt water and fresh water does not move later. In Leizhou Peninsula, if the exploitation is not strong, the sea water does not move into the aquifer.
引文
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