基于小波变换的随机地下水模拟的非平稳谱方法研究

The groundwater simulation has become the most effective method and measurement to evaluate the influences of the human activities on the water quality and quantity and to develop and protect the groundwater. However, the difficulties due to the spatial variability and nonstationary property of aquifer highly restrict the application on the real problem of the current groundwater models. The wavelet transform method which has inherent advantages in dealing with non-stationary random process will be adopted to replace the classical non-stationary stochastic groundwater model (NSM) which is based on the Fourier transform and a non-stationary stochastic groundwater model based on wavelet transform is expected to be established for the first time to overcome the defect of classical one which assumes the fluctuation of the input parameters is stationary. In addition, the simple form of the governing equations with good parallel performance probably avoid the convergence problem due to the coupling iteration between the virtual and real parts of the governing equations based on Fourier transform. Another merit of the new model is its good multi-resolution capability in both frequency and time domains which can resolve the problem that NSM cannot deal with the intermediate frequency band efficiently. Finally, a parallel stochastic groundwater numerical program will be developed based on finite volume method in unstructured grid system independently and a systematic comparative analysis of computational accuracy and efficiency of the new method will be conducted by means of experimental and field data and Monte Carlo simulation. The research is an important improvement to the existing non-stationary stochastic groundwater theory, which may provide a new effective method to solve the real large scale complex stochastic groundwater problem.

地下水模拟已成为评价人类活动对地下水水质及水量的影响、合理开发利用地下水以及预测地下水污染发展趋势的最主要的方法和手段。然而，由于空间变异性和非平稳性等带来的难题至今仍制约着现有地下水模型在实际问题中的应用。本项目首次将小波变换方法引进到非平稳随机地下水模型研究中来，旨在克服传统的基于傅立叶变换的非平稳随机地下水模型（NSM）的缺点，解除输入参数脉动项满足平稳假定的限制，避免傅氏变换带来的虚、实部耦合迭代的收敛难题，利用小波分析在时、频域内均具有多分辨特性，可望有效解决NSM不能很好地处理中间频率段的问题；最后，将通过自主研发基于非结构化网格和有限体积法的串并行随机地下水数值计算程序，通过资料、现场数据和MonteCarlo模拟等手段对新方法的计算精度和效率进行系统的对比分析。预期研究成果是对现有随机地下水理论的完善和重要改进，为解决更复杂的区域地下水问题提供了新的理论方法和技术支持。

本项目对基于谱方法的随机地下水模型进行了详细的推导，从确定性模型到平稳谱方法再到非平稳谱方法，最后首次将小波变换方法引进到非平稳随机地下水模型研究中来，旨在克服传统的基于傅立叶变换的非平稳随机地下水模型的缺点，解除输入参数脉动项满足平稳假定的限制，避免傅氏变换带来的虚、实部耦合迭代的收敛难题，利用小波分析在时、频域内均具有多分辨特性；通过编制的程序对一些算例进行了模拟，与已有研究成果对比，本研究采用的方法具有较好的优势，小波变换技术在非平稳地下水模拟中有广阔的应用空间，提出的模型是对现有随机地下水理论的完善和重要改进，为解决更复杂的区域地下水问题提供了新的理论方法和技术支持。