Stochastic Numerical Model For Unsaturated Flow

Randomness is ubiquitous in nature. Diverse application fields of great materials, structure, turbulence, contaminant transport in geological media, hydrological circulation and so are related to the randomness, these physical phenomena occurring at spatial scale and time scale with uncertainty in both. Uncertainty invariably exists in simulation processes as incomplete knowledge about media material properties, boundary conditions, initial conditions, and governing physical model equations, numerical methods, errors, etc. Hydraulic properties of the natural porous medium soil, such as hydraulic conductivity as input parameters of water flow models, exhibit a high degree of spatial variability, considerably impact saturated-unsaturated flow movement, and limiting saturated unsaturated flow movement for accurate description. Stochastic theory has been important tools of exploring water flow and solute transport in porous media. The objective of this work is exploring the saturated-unsaturated flow movement in porous media with parameters randomly distributed based on stochastic collocation method. The key issues of stochastic collocation model are theoretical analysis and numerical experiments. The main content of the dissertation are listed as follows.Firstly, this dissertation disscusses the background and improtance of stochastic numerical methods for saturated-unsaturated flow movement in porous media. A brief review about the development of stochastic theories in the world is given. We analyze the sources and theretical baisses of uncertainties. Some related concepts and methods which will be used in this work are introduced. Moreover, the simulation method for flow movement in porous media based on the random field is analysed and the Monte Carlo method as reference is also introduced.Secondly, the theory of sparse grid collocation method is derived and the numerical model base on this theory is developed. The outputs are represented by Lagrange polynomial expansion. The stochastic partial differential equation is reduced into a series of independent deterministic equaions in grid points applying the numerical integral. Comparision about the simulation way of random field and random variable is given. The pre-processing and post-processing programs which are independent of the deterministic model are programed.Thirdly, numerical examples based on sparse grid collocation method with Gaussian or log-gaussian distributed parameters are verified. Comparation and verification from single-layered single parameter unsaturated flow model to a multi-layered unsaturated flow model with Monte Carlo simulation are given. The model under the condition of parameter correlation is built, and the effection of correlated parameters are analysed.Fourthly, the theories of sparse grid collocation method with Beta distribution and uniform distribution are derived. The hydraulic conductivity of the measured data with the Borden aquifers in Canadian are tested goodness of fitting. The simulation results of different distribution are compared to the simulation results of measured values. The numerical examples based on sparse grid collocation method with Beta distributed parameters are verified, and applicability of this method is analyzed.Lastly, the main research results are summarized, and the issues that need further investigations are outlined. We provide our views to the future development.