Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

作者：Bharati Vinod Kumar; Singh Vijay P^*; Sanskrityayn Abhishek; Kumar Naveen

来源：Journal of Engineering Mechanics, 2017, 143(11): 04017126.

DOI：10.1061/(ASCE)EM.1943-7889.0001346

• Dispersivity
• Generalized integral transform technique (GITT)
• Sturm-Liouville problem (SLP)
• Orthonormal function
• Heterogeneity

In the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the nth power of groundwater velocity, where n varies from 1 to 2. The present study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport for any permissible value of n. For a nonhomogeneous medium, groundwater velocity is considered as a linear function of space and analytical solutions are obtained for n = 1, 1.5, and 2.0. For n = 1, the dispersivity (ratio of dispersion coefficient and velocity) remains uniform, representing a homogeneous medium, while it varies with position in the finite domain (aquifer) for any other permissible value of n representing the heterogeneity of the medium. From a hydrological point of view, the derived solutions are of significant interest and are of value in the validation of numerical codes. A generalized integral transform technique (GITT) with a new regular Sturm-Liouville problem (SLP) is used to derive analytical solutions in a finite domain. The analytical solutions elucidate the important features of solute transport with Dirichlet-type nonhomogeneous and homogeneous conditions assumed at the origin and at the far end of the finite domain, respectively. The first condition expresses a uniform continuous source of the dispersing mass. The analytical solutions are also compared with numerical solutions and are found to be in perfect agreement. The effect of a Peclet number on the solute concentration pattern is also investigated.

• 出版日期2017-11