Chunhong Xie

A Three-Dimensional Miscible Transport Model For Seawater Intrusion in China

A three-dimensional miscible transport model for seawater intrusion in a phreatic aquifer with a transition zone is presented. This model considers many important factors, such as the effect of variable density on fluid flow, the effect of precipitation infiltration and phreatic surface fluctuation on the process of seawater intrusion, the existence of great discharge pumping wells, etc. The difficulty in solving this problem can be tackled by the presented numerical method and iteration technique. This model is used to describe seawater intrusion in Huangheying, Longkou, Peoples Republic of China. The simulated values agree very well with the field data (e.g., the total mean values of the absolute error of Cl− concentration are 46.13 mg/L and 55.67 mg/L, respectively, and those of the water head are 0.24 m and 0.08 m, respectively).

Modified Multiscale Finite-Element Method for Solving Groundwater Flow Problem in Heterogeneous Porous Media

AbstractThe purpose of this paper is to modify the multiscale finite-element method (MSFEM) to solve groundwater flow problems in heterogeneous porous media, such as large-scale problems, long-term prediction problems, and nonlinear problems. The MSFEM has been developed to deal with flows in heterogeneous porous media. Many practical works and numerical simulations have been done to show its accuracy. However, for the large-scale or long-term prediction problems, the MSFEM needs a great amount of computational cost in constructing base functions, which is not efficiency. The primary feature of our modified MSFEM (MMSFEM) is to use a new coarse element subdivision to reduce the number of the interior nodes, thus to decrease the unknowns in the reduced elliptic problems to save much computational cost while ensuring computational accuracy. Some numerical experiments in this paper indicate that the MMSFEM can reduce more than 90% of CPU time of the MSFEM.

Cubic-Spline Multiscale Finite Element Method for Solving Nodal Darcian Velocities in Porous Media

AbstractThis paper presents a cubic-spline multiscale finite element method (CMSFEM) for solving groundwater flow problems in porous media. The main idea of this method is using the multiscale finite element method (MSFEM) to efficiently solve the hydraulic heads and nodal Darcian velocities. CMSFEM employs the cubic-spline technique to obtain continuous nodal head derivatives, which ensures the continuity of velocities. Furthermore, CMSFEM can not only solve velocities at coarse-scale grid nodes but also solve those at the fine-scale nodes in each coarse element grid. Instead of solving the full study region problem, the computation of the fine-scale velocities is decoupled from coarse element to coarse element, which can be implemented in parallel. Therefore, CMSFEM saves much computational costs in solving heads and velocities, which is important for high computation problems. The applications in this paper demonstrate that the CMSFEM has high accuracy and efficiency in solving velocities and heads.

A Characteristic Alternating Direction Implicit Scheme for the Advection-Dispersion Equation

Publisher Summary This chapter describes a numerical scheme based on combining the utility of a fixed grid in Eulerian coordinates with the computational power of the Lagrangian method. This is followed by a detailed comparison of the simulated concentrations with the analytical solutions. An analytical solution of the three-dimensional advection–dispersion equation is developed in this connection. A new method for the numerical solution of the convection–diffusion equation in one, two, and three dimensions is presented. The method is employed to obtain the numerical solution of some solute transfer and heat-transfer problems. The numerical results presented demonstrate that the method is capable of solving advection–dispersion problems without generating significant numerical diffusion when Peclet number is not too large, and oscillations. Numerical diffusion is mainly caused by the interpolation between nodes. Also, due to the increasing of interpolation and computation, the results of two- and three-dimensional problems are not as good as one-dimensional one.

Efficient Triple-Grid Multiscale Finite Element Method for Solving Groundwater Flow Problems in Heterogeneous Porous Media

This paper proposes an efficient triple-grid multiscale finite element method (ETMSFEM) for the simulation of groundwater flow in heterogeneous porous media. The main goal of this method is to improve the efficiency of constructing basis functions. It is accomplished by introducing an intermediate grid between the coarse grid and the fine grid. Instead of solving a local problem in a full coarse element, the ETMSFEM breaks the basis function construction problem down to subproblems in the elements of the intermediate grid. Hence, the computational cost can significantly be reduced and the accuracy can be ensured. For this reason, the ETMSFEM can save much computational cost in solving groundwater flow problems, especially for large-scale problems, long-term prediction problems, transient flow problems and nonlinear problems. Some numerical examples in this paper indicate that the ETMSFEM achieves almost the same accuracy as the MSFEM, while saving a large amount of CPU time.

Combination of Multiscale Finite-Element Method and Yeh’s Finite-Element Model for Solving Nodal Darcian Velocities and Fluxes in Porous Media

AbstractBased on the multiscale finite-element method (MSFEM) and Yeh’s finite-element model, this paper proposes a MSFEM–Yeh model (MSFEM-Y) for solving nodal Darcian velocities in porous media. The main idea of this method is to solve Darcy’s law directly by MSFEM so as to obtain continuous coarse-scale velocities with high efficiency, while ensuring the mass conservation is satisfied to an acceptable degree. The MSFEM features allow this method to obtain fine-scale velocities directly by an interpolation equation, which only consists of coarse-scale velocities and base functions. Because the base functions have been constructed in head computation, the computation of fine-scale velocities does not need much cost. Furthermore, MSFEM-Y also ensures the continuity of fluxes, so that the MSFEM-Y fluxes are more accurate than those obtained by the original MSFEM. Numerical experiments indicate that the MSFEM-Y can achieve more accurate heads, velocities, and fluxes with high efficiency.

A Thermal Energy Storage Model for a Confined Aquifer

Publisher Summary This chapter discusses a thermal energy storage model for a confined aquifer. The chapter proposes a three-dimensional convection-heat dispersion model, which is used for describing a series of seasonal aquifer thermal energy storage experiments in China. The simulated results are compatible with the field data. The governing equation used in this sort of problem generally had convection and conduction items without having heat dispersion item. But in practice, one discovers that like the mechanical dispersion phenomena in mass transfer problems, heat mechanical dispersion cannot be neglected. The simulated temperatures agree very well with the field data. The parameters obtained from the multiwell experiment can be extended to simulate the data obtained from the double well experiment at the same location. All of this shows that the model is reasonable and dependable. It is necessary to consider the heat-dispersion term in the governing equation, and it is inadequate to consider only the convection and conduction terms.

Logarithmic Interpolation for Groundwater Flow near Wells

A new logarithmic finite element interpolation has been developed to model groundwater flow near wells in two or three dimensional confined flows. An important feature of the new method is its ability to represent the curved outline of the well and to model the logarithmic head distribution in its vicinity. The logarithmic elements are compatible with linear elements and thus, both can be used in the same grid.

Application of the multiscale finite element method to groundwater flow in heterogeneous porous media

The multiscale finite element method is applied to flow in heterogeneous porous media with different change in coefficients in the paper. The method can efficiently capture the large scale behavior of the solution without resolving all the small scale features by constructing the multiscale finite element basis functions that are adaptive to the local property of the differential operator, which offers significant savings in CPU time and computer memory. The potential and flow rate of the two dimensional ground water flow problems with continuous change in coefficients, with gradual change in coefficients and with abrupt change in coefficients are analyzed by the multiscale finite element method and the conventional finite element method, respectively. The solutions based on the former method are much more accurate than those based on the later one with the same mesh size. The applications demonstrate the main advantages of the multiscale finite element method, i.e., significantly reducing computational effort and improving the accuracy of the solutions.

Study On The Motion Equation For HighTemperature Variation And Applying It To TheAXES Experiment In Shangai

An equation of motion is presented in this paper, in which the variation of temperature is considered. Based on that, a new mathematical model of Aquifer Thermal Energy Storage (ATES) is then presented. The model is applied to simulate a multi-well ATES experiment which was performed in the second confined aquifer in Shanghai. The results show a better correspondence between the simulated and observed temperatures than that of our early work. This demonstrates that the presented motion equation is necessary and important in theory and practice.