CAJ | 학술논문

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。
침대현유해석방법적국한성，인입동륜분석법구해토개질중오염물천이문제。통과선취보조선성산자화비선성산자，구조령계형변방정，편제료계산정서。응용동륜분석법구해료구유일반초시조건적항원농도하고필오염물강해작용적대류확산모형，획득적해답여정학해문합량호，증명료해방법적정학성。연후장동륜분석법추엄도구해고필원농도수시간안지수쇠감적일유오염물천이모형，극복료상규방법난이직접구해적결함，획득료오염물농도수시간화공간변화적이론해답。실례계산표명，동륜분석법가이구해구유경일반초시조건적복잡적오염물천이모형，병차수학개념청초、계산간편，시연구오염물천이문제적일충유효방법。
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 computa-tion solution is in good agreement with the exact solution,which proves the correctness of the pro-posed 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 diffi-culty in direct solution of the general methods,and the theoretical solutions of the contaminant con-centration 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.