随机非均质多孔介质中水流与溶质运移问题的随机降维多尺度数值方法研究

项目名称： 随机非均质多孔介质中水流与溶质运移问题的随机降维多尺度数值方法研究

项目编号： No.41472238

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 地质学

项目作者： 贺新光

作者单位： 湖南师范大学

项目金额： 68万元

中文摘要： 地下多孔介质水力特性的空间多尺度非均质性和不确定性，使得有效模拟预测其中的水流与溶质运移过程极具挑战性。高维随机模型分解、多尺度数值模拟及不确定性量化三者的协同作用可为有效处理这类挑战性问题提供一类新的模型和技巧。本项目诣在设计高维随机模型自适应降维技巧和发展有效的随机多尺度数值方法。应用灵敏度分析筛选最活跃的随机参数，然后，将高维随机模型分解成仅包含这些活跃参数的重要低维子问题和若干一维问题，并在低维空间执行随机多尺度模拟，而达到高效捕捉介质特性非均质影响与不确定性信息的目的。重要研究内容：1.设计有效的高维随机模型自适应降维方法，并自动捕捉不确定性信息和评估对解的影响。2.构造能有效传送和过滤水流速度场细尺度不确定性的多尺度基函数。3.设计适应于非饱和水力参数场随时间非线性变化的自适应随机降维多尺度方法。4.构造能有效捕捉溶质运移方程中弥散系数和水流速度场细尺度不确定性的多尺度基函数。

中文关键词： 高维随机模型；随机降维；不确定性量化；地下水流；溶质运移

英文摘要： The spatial multiscale heterogeneity and uncertainty of hydraulic properties of subsurface porous media lead to significant challenges for the effective simulation and prediction of ground water flow and solute transport processes. The synergy of stochastic high-dimensional model decompositon, multiscale numerical simulation and uncertainty quantification can provide a new model and approach for efficiently solving these challenging problems. This proposal aims at designing adaptive dimension reduction techniques for high-dimensional stochastic models and developing effective stochastic multiscale numerical methods. To this end, the most active stochastic parameters are screened by the sensitivity analysis, then the high-dimensional stochastic model is represented into an important low-dimension model which only include these active parameters and a few one-dimension models, and stochastic multiscale simulation is applied to each of low-dimension stochastic models to reduce computational complexity and efficiently capture the heterogeneities. The importances of proposed project are as follows: (1) design effective dimension reduction methods for high-dimensional stochastic model, and automatically capture uncertainty information and assess impacts on solutions; (2) construct multiscale basis functions which are capable of efficiently transmitting and filtering fine-scale uncertainties of water flow velocity field; (3) design adaptive stochastic dimension reduction multiscale methods that are adapted to the nonlinear change of the unsaturated hydraulic parameter fields with time; and (4) construct multiscale basis functions, which are capable of efficiently capturing the fine-scale uncertainty information of diffusion coefficiency and water flow velocity fields in the solute transport equations.

英文关键词： High-dimensional stochastic models;Stochastic dimension reduction;Uncertainty quantification;Groundwater flow;Solute transport