A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the...A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the seepage region is particularly divided into several virtual layers along the z direction and vertical 1-D columns covering x-y 2-D area according to stratum properties. The numerical algorithm is replacing the full 3-D water and mass balance analysis as the 2-D Galerkin finite element method in x- and y-directions and 1-D finite differential approach in the z direction. The reasonable method of giving minimum thickness is successfully used to handle transient change of water table, drying cells and problem of rewetting. The solution of the simplified model is preconditioned conjugate gradient and ORTHOMIN method. The validity of the developed 3-D groundwater model is tested with the typical pumping and backwater scenarios. Results of water balance of the computed example reveal the model computation reliability. Based on a representative 3-D pollution case, the solute transport module is tested against computing results using the MT3DMS. The capability and high efficiency to predict non-stationary situations of free groundwater surface and solute plume in regional scale problem is quantitatively investigated. It is shown that the proposed model is computationally effective.展开更多
The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve （KL） expansion is employed to decompose the log transformed hydraulic conductivity. The head, veloci...The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve （KL） expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation （collocation） points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.展开更多
A numerical model physically based on a formulation of water, vapor, and heat transport in saturated- unsaturated soils coupled with a lower atmosphere boundary layer modelling is presented. The inputs required for t...A numerical model physically based on a formulation of water, vapor, and heat transport in saturated- unsaturated soils coupled with a lower atmosphere boundary layer modelling is presented. The inputs required for the computer simulation are weather data, soil thermal and hydraulic properties. The coupled numerical model is tested separately with the experimental result and analytical solution because of the scarcity of suitable analytical solution for the coupled problem. The agreements of the numerical model with the experimental data and the analytiCal solution are excellent. Numerical experiments are performed to analyse the effects of weather conditions, soil water conductivity K, thermal vapor diffusivity DTV, and isothermal vapor conductivity DHV on the evaporation rate from the soil surface. When the soil is wet, the evaporation rate is more sensitive to the input atmospheric conditions. This is the situation for high ground water table and just after rainfall. The accuracy of the measurement of air humidity has stronger effect on evaporation rate than the roughness length. When the soil is dry enough,the soil water conductivity dominates evaporation rate. Neglecting thermal vapor diffusivity and isothermal vapor conductivity introduces an error less than 2. 5% in evaporation rate.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars(Grant No.40701071)
文摘A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the seepage region is particularly divided into several virtual layers along the z direction and vertical 1-D columns covering x-y 2-D area according to stratum properties. The numerical algorithm is replacing the full 3-D water and mass balance analysis as the 2-D Galerkin finite element method in x- and y-directions and 1-D finite differential approach in the z direction. The reasonable method of giving minimum thickness is successfully used to handle transient change of water table, drying cells and problem of rewetting. The solution of the simplified model is preconditioned conjugate gradient and ORTHOMIN method. The validity of the developed 3-D groundwater model is tested with the typical pumping and backwater scenarios. Results of water balance of the computed example reveal the model computation reliability. Based on a representative 3-D pollution case, the solute transport module is tested against computing results using the MT3DMS. The capability and high efficiency to predict non-stationary situations of free groundwater surface and solute plume in regional scale problem is quantitatively investigated. It is shown that the proposed model is computationally effective.
基金supported by the National Basic Research Program of China (973 Program,Grant No.2006CB403406)the National Natural Science Foundation of China (Grant Nos.50688901,40701071)
文摘The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve （KL） expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation （collocation） points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.
文摘A numerical model physically based on a formulation of water, vapor, and heat transport in saturated- unsaturated soils coupled with a lower atmosphere boundary layer modelling is presented. The inputs required for the computer simulation are weather data, soil thermal and hydraulic properties. The coupled numerical model is tested separately with the experimental result and analytical solution because of the scarcity of suitable analytical solution for the coupled problem. The agreements of the numerical model with the experimental data and the analytiCal solution are excellent. Numerical experiments are performed to analyse the effects of weather conditions, soil water conductivity K, thermal vapor diffusivity DTV, and isothermal vapor conductivity DHV on the evaporation rate from the soil surface. When the soil is wet, the evaporation rate is more sensitive to the input atmospheric conditions. This is the situation for high ground water table and just after rainfall. The accuracy of the measurement of air humidity has stronger effect on evaporation rate than the roughness length. When the soil is dry enough,the soil water conductivity dominates evaporation rate. Neglecting thermal vapor diffusivity and isothermal vapor conductivity introduces an error less than 2. 5% in evaporation rate.
