A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source
A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source
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源头为第一类边界条件的有界介质中流体动力色散的广义二维解析解
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Vedat Batu
中科院分区：
文献类型：
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作者：
Vedat Batu
本文提出了一种广义二维解析解，用于求解具有第一类边界条件的单向有界表面和地下介质流场中的水动力弥散问题。纵向和横向色散，放射性衰变，和线性吸附被认为是。在数学分析中，同时采用了拉普拉斯变换和傅里叶分析技术，得到了非稳态浓度分布的无穷级数形式的一般方程。作为一般解的特例，得到了单条形源的解。对流-色散通量分量的方程也被导出。Bruch和Street [1967]对对称分布的条形源的解是该解的一个特例。浓度分布和对流-弥散通量分量的稳态溶质运移的情况下的表达式也被提出。结果与两种不同的有限元程序进行了比较，具有良好的一致性。该模型的结果可用于单向多孔介质流场中的溶质运移，也可用于河流和运河中的溶质运移。该解也可用于数值模型验证。
A generalized two-dimensional analytical solution is developed for hydrodynamic dispersion in a unidirectional-bounded surface and subsurface media flow field from time- and space-dependent sources with the first-type boundary condition at the source. Longitudinal and transverse dispersion, radioactive decay, and linear adsorption are considered. In the mathematical analysis, Laplace transform and Fourier analysis techniques are used simultaneously, and a general equation, in infinite series form, for the unsteady state concentration distribution has been obtained. Solution for a single-strip source is obtained as a special case from the general solution. The equations for convective-dispersive flux components are also derived. The solution of Bruch and Street [1967] for a symmetrically located strip source is shown to be a special case of the solution. Expressions for concentration distribution and convective-dispersive flux components for the steady state solute transport case are also presented. The results are compared with two different finite element codes with a good agreement. The results of this model may be used for solute transport in a unidirectional porous media flow field as well as in rivers and canals with some additional assumptions. The solutions can also be used for numerical model validation.