Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Journal of Earth system science

Abhishek Sanskrityayn1¹  Naveen Kumar1¹ 

[1] Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India.$$

关键词: Advection;    diffusion;    heterogeneity;    non-degenerate form;    Green’s function method;   

DOI  :  

学科分类：天文学(综合)

来源: Indian Academy of Sciences

【 摘 要 】

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.

【 授权许可】

Unknown