Advances in analytical solutions for time-dependent solute transport model
Document Type
Article
Publication Date
6-1-2022
Abstract
Abstract: This study adopts generalized dispersion theory in one-dimensional advection–dispersion equation (ADE), where time-dependent dispersion and velocity are considered. The generalized dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity with power n, where n is any real number. Homotopy analysis method (HAM) that uses a simple algorithm is adopted to handle the non-linearity that occurred in the ADE under the generalized dispersion. A point source is introduced to the entry boundary and a line source is introduced to the entire model domain. Three time-dependent point sources in the form of (i) exponentially decreasing function, (ii) linear function and (iii) sinusoidal function, at the entry boundary are considered. Two-line sources are considered in the form of (i) linear space-dependent function and (ii) nonlinear space-time-dependent function. Using the HAM, semi-analytical solutions for any power n are derived and semi-analytical solutions for n = 1 and n = 1.5 are discussed in particular. Comparison with the analytical solution is discussed and found good agreement for 6th order of solution obtained by HAM. Research Highlights: 1.Generalized dispersion theory in 1-D ADE2.Generalized semi-analytical solution using HAM3.Compared with analytical solution4.Good agreement for 6th order of semi-analytical solution
Publication Source (Journal or Book title)
Journal of Earth System Science
Recommended Citation
Kumar, R., Chatterjee, A., Singh, M., & Tsai, F. (2022). Advances in analytical solutions for time-dependent solute transport model. Journal of Earth System Science, 131 (2) https://doi.org/10.1007/s12040-022-01858-5