污染物对流-扩散逆过程源项反演的伴随方法

Adjoint method for source term inversion in reverse process of pollutant convection-diffusion

针对突发污染事故中确定污染源时反向时间积分求解对流-扩散方程易导致计算发散的问题,通过建立目标泛函,利用伴随方法同时求解伴随方程和原方程,逐次迭代得到目标泛函的极值,以实现污染源的反演。为验证该方法的有效性,分别利用污染物空间分布和时间序列对污染源进行反演,其中污染源包括单污染源和双污染源。结果显示,计算值与解析解之平均相对误差小于15%,满足工程应用的精度要求。

Determination of pollution source in sudden pollution accidents can be solved through convectiondiffusion equation by reverse time integral.However,such method may result in divergence of numerical calculations.In this study,an objective function is established to solve the adjoint equation and the original equation by using the method of adjoint.Then,the extremums of the objective function are obtained by the successive iteration calculation method.In the end,the pollution source inversion can be realized.In order to verify the effectiveness of the method,pollution source was inverted by using the spatial and temporal distribution of the pollutant concentration,in which both single and double pollution source were included.The results show that the average relative errors between calculated values and analytical solutions are less than 15%,which can be accepted in engineering applications.