一维污染物非恒定扩散逆过程反问题的变分伴随方法

On Variational Adjoint Method for Inverse Problem in Reverse Process of Unstable Diffusion of One Dimensional River Pollutants

在环境水力学领域中,解决水污染问题是一项非常艰巨而且重要的任务,本文讨论了一维污染物非恒定紊动扩散逆过程反问题的变分伴随方法,根据正则化思想改造最小二乘方法构造目标泛函表达式,依据变分伴随思想构造迭代算法,迭代过程中,首次搜索方向采用泛函下降最快的负梯度方向,第二次及以后搜索方向采用共轭梯度法确定,数值模拟试验验证了理论算法的可靠性.

In the field of environmental hydraulics, it is a very difficult and important task to solve the water pollution problem. In this paper, an inverse problem in reverse process of unstable turbulent diffusion of river poilutants is discussed by the variational adjoint method. The least squared method is modified by means of the regularization and a new iteration algorithm is derived by using the variational adjoint method. The negative gradient direction is selected as the first search direction, and the conjugate gradient method is applied to determine the second search direction and later iteration direction. The validity and efficiency of algorithm is finally proved through the numerical simulation experiments.