土介质中污染物迁移模型的同伦分析解

Homotopy analysis solutions of contaminant transport model in soil medium

针对现有解析方法的局限性,引入同伦分析法求解土介质中污染物迁移问题.通过选取辅助线性算子和非线性算子,构造零阶形变方程,编制了计算程序.应用同伦分析法求解了具有一般初始条件的恒源浓度下考虑污染物降解作用的对流-扩散模型,获得的解答与精确解吻合良好,证明了该方法的正确性.然后将同伦分析法推广到求解考虑源浓度随时间按指数衰减的一维污染物迁移模型,克服了常规方法难以直接求解的缺陷,获得了污染物浓度随时间和空间变化的理论解答.实例计算表明,同伦分析法可以求解具有更一般初始条件的复杂的污染物迁移模型,并且数学概念清楚、计算简便,是研究污染物迁移问题的一种有效方法.

Due to the limitations of the existing analytical methods, the homotopy analysis method （HAM） is implemented to solve the contaminant transport model in soil medium. With the auxiliary linear operator and the nonlinear operator, the zero order deformation equation is proposed and the computation program is compiled. By using the HAM, the advection-diffusion model considering decay is solved at a fixed contaminant concentration under general initial conditions. The computation solution is in good agreement with the exact solution, which proves the correctness of the proposed method. Then, the HAM is applied to solve the one-dimensional contaminant transport model considering the exponential decay of the source concentration with time, which overcomes the difficulty in direct solution of the general methods, and the theoretical solutions of the contaminant concentration changing with time and space are obtained. Case study results show that the HAM, with clear concept and simple computation, can be used for contaminant transport models under general and complex initial conditions and owes, which is one of the most effective methods for research in the contaminant transport issue.