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Application of the homotopy analysis method to multispecies reactive transport equations with general initial conditions

Yu, Chuang, Zhou, Min, Ma, Jianjun, Cai, Xiaoqing, Fang, Dongfang
Hydrogeology journal 2019 v.27 no.5 pp. 1779-1790
chemical reactions, convection, deformation, equations, hydrogeology, models, soil, solutes
Multispecies solute transport through soils is characterized by the dynamic processes of convection, diffusion, decay and a series of chemical reactions, posing difficulties when seeking to derive analytical solutions related to subsurface hydrology. At present, most analytical solutions for multiple-species contaminant transport problems are based on the Laplace transform or Fourier transform technique, a decomposition strategy such as ingenious transform format and matrix diagonalization procedure, classical integral methods, the generalized integral transform technique, etc. These methods have been limited to some cases with simple initial conditions, identical retardation coefficients for all species, and complicated mathematical procedures, which restrict their use for cases under complex initial conditions. To cope with these limitations, the homotopy analysis method (HAM) is implemented to solve multispecies reactive transport models with more general, smooth initial conditions. Applying an auxiliary linear and nonlinear operator, a zero-order deformation equation is derived to obtain an approximate solution with high accuracy (different cases with various initial and boundary conditions). The semi-analytical solutions are compared with exact analytical solutions from the literature; good agreement between the resulting simulation and analytical solutions has been achieved. This illustrates that HAM is one of the most effective methods for solving the multispecies reactive transport models with more general and smooth initial conditions.