污染物二维非恒定输运初值反问题研究

Inverse problem for 2D unsteady pollutant transport

采用时空全域MQ径向基函数配点法建立了恒定水流中的污染物二维非恒定输运初值反问题模型,可利用含有测量误差的观测数据反演污染物浓度的初始分布,并结合交叉验证法估计模型最优参数。通过纯扩散和对流-扩散算例,模拟了误差水平0.05和0.1的观测数据在不同边界条件下污染物初始分布。结果表明,各算例的误差分别为0.0361、0.0357、0.0419、0.0453和0.0712、0.0695、0.0507、0.0703,均小于相应的测量误差水平,反演模型能准确模拟污染物的初始浓度分布。

A global space-time MQ collocation method is used to solve an inverse problem of 2D unsteady pollutant transport in steady flow, and the initial distribution of pollutant concentration is reconstructed from observation data with a certain level of noise. A cross-validation technique is used for estimation of optimal model parameters. Application of this method in case studies of diffusion and advection-diffusion under different boundary conditions show that in different scenarios the initial concentration distribution can be accurately estimated and that for input noise levels 0.5 and 1.0 the calculation errors are 0.0361, 0.0357, 0.0419, 0.0453 and 0.0712, 0.0695, 0.0503, 0.0703 respectively, all lower than the corresponding input noise level.