扩散系数反演及其差分格式研究

INVERSION OF DIFFUSION COEFFICIENTS AND EFFECT OF RELATED DIFFERENCE SCHEMES

空气污染预报属于正问题 ,而从污染物浓度来求解扩散系数则属于反问题。正问题和反问题有着本质的不同 ,在解的定义和求解方法上也有很大的区别。从最优控制的角度定义了大气边界层中垂直扩散系数反演问题的解 ,用伴随模式方法得到目标函数的梯度并求解反问题。研究中发现 ,反演的结果与模式差分格式的选取有关 ,与测试源的设置也有直接的关系。在经过多次数值试验后 ,对于误差的来源进行了理论分析 ,发现了反演结果与差分格式及测试源之间的联系 ,得到了满意的反演结果 ,并为实验测定扩散系数提供了依据。

Air pollution prediction is a direct problem, and deriving diffusion coefficients from the concentration of pollutants is an inverse problem. A direct problem is different from an inverse problem in essence, and their definitions and methods of resolution are quite different. A sort of solution of the inversion of the vertical diffusion coefficients in the atmospheric boundary layer is defined based on the theory of optimum control. The adjoint model method is introduced to calculate the gradient of the objective function, and then the inverse problem is solved. It turns out that the result of the inverse problem is sensitive to the choice of difference algorithms, and is directly affected by the settlement of the sources used in the measurement. The causes of errors are analyzed both in theory and in numerical experiments. The relationships between the inverse result and the difference algorithms and sources are summarized, and then satisfactory results are shown in the resolutions. The above studies are of help to the practical experiments to measure diffusion coefficients.