Application Of The Homotopy Analysis Method In Contaminant Transport With Variable Coefficient

The homotopy analysis method(HAM)proposed by Shijun Liao is based on the concept of the homotophy,a fundamental concept in topology.It's a powerful analytic technique for nonlinear problems.By constructing the zero-order deformation equations,the initial solution enolves to the exact solution as the embeding parameter increases from 0to 1.It should be emphasized that we have freedom to choose the initial approximation and the auxiliary linear operator.By means of the rule of solution expression,rule of solution existence,and rule of coefficient ergodicity can be uniquely determinaned.The method does not depend on any parameters.The auxiliary parameters provide us a convenient method to control and adjust convergence region and rate of approximation solutions.This method is manageable and reliable.Assuming that diffusion coefficient and convection coefficient are time-dependent.The HAM is used to find series solutions of the one-dimensional contaminant diffusion models.The results withconstant coefficient model agree well with the results from the literature,which proves the validity and reliability of HAM.Compared to other numerical methods,the HAM is easily to be used due to the freedom of choosing the initial approximations and nonlinear operator.The approximate solutions can be derived by algebra software conveniently.The sensitivities for the relevant parameters in the model are analyzed and discussed.Based on HAM,the two-dimensional contaminant transport models without decay,and with decay are solved.In the present analysis,exponential and sinusoidal forms of velocity expressions are considered.The dispersion coefficient varies approximately in direct proportion to the convection.The HAM is used to find series solutions of the two-dimensional contaminant diffusion models.It is noted that the HAM is readily adeptable.Based on the series solutions,the effects of relevant parameters are discussed.It is indicated that the flow resistance coefficient can greatly reduce the concentration of contaminant.In summary,it is found that HAM has a broad scope of application in solving contaminant transport with variable coefficient.