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Abstract
The numerical simulation of the contaminant transport in subsurface porous media have been a hotspot for years. It is always considered to be tough to deal with the problems regarding the numerical dispersion and the oscillation around sharp front area of contaminants. This paper presents a new method which can reduce the numerical dispersion in the numerical modeling of the contaminant transport in groundwater. The core of the new method is adding a new numerical dispersion estimation term to the hydrodynamic dispersion coefficient and obtaining a modified hydrodynamic dispersion coefficient (MHDC). We use MHDC instead of the traditional hydrodynamic dispersion coefficient and put forward a new parameter of numerical dispersion factor (μNDF). The research area can be divided into different μNDF areas, and their values can be adjusted according to our needs. In this way, we can control the numerical oscillation and diminishing the numerical dispersion. The Simulated results of several examples from one-dimension problems to two-dimension problem indicate that the new method can considerably reduce the numerical dispersion on the basis of diminishing the numerical oscillation and obtain more precise simulation results. Hence, the new method is simple in theory, convenient in application and worth popularizing.
... It can be seen that the leaching process of the three pillars was convection dominated. The two examples in the study by Mei et al. [33] were used to verify the rationality of the method proposed in this paper. The parameters in Example 1 are L = 120 m, u = 2 m/d, and D = 0.04 m 2 /d, the ions are non-reactive ions, and the concentration of injected agent was always 1.00 g/L. ...
Ion-adsorption-type rare-earth ores (IATREOs) that have experienced granite weathering have good permeability, and their leaching process involves the solute transport problem, which is dominated by convection. Because of the oscillation and dispersion errors of existing numerical methods for solving the convective-dominated solute transport equation, the results have low precision in the twin leaching process. In this paper, the convection–dispersion equation is decoupled into the dispersion equation, the convection equation, and the source-sink equation; the Crank–Nicolson and implicit difference methods are used to solve the dispersion equation and the source-sink equation, respectively. The solution of the convection equation is achieved on the basis of its physical interpretation. Therefore, a decoupling method for the convective-dominated solute transport equation is established. In comparison to the two examples with analytical solutions, the calculation errors of the method established in this paper are less than 2.00%, and it can solve the oscillation and dispersion problems. The rationality of the method is further demonstrated through the column leaching experiment of IATREOs. In comparison to the test results, the coefficients of determination of the breakthrough curves of rare-earth ions and ammonium ions calculated by the proposed method are all greater than 0.850, and the peak concentration error of rare-earth ions is less than 7.00%. This indicates that the proposed method can simulate the leaching process well. Furthermore, by combining the multiple/half method and the dichotomy method, an optimization method for determining the leaching agent amount was established to analyze the relationship between the leaching agent and the ratio of dispersion to pillar length. The results can provide a solution that can be used to mine IATREOs from experience to theory.
... For example, XUE Yu-qun established such model of groundwater pollution in leaky aquifer systems (XUE Yu-qun et al. 1997). WU Ji-chun adopted modified dispersion coefficient for more accurate numerical simulation of groundwater solute transport and two-dimensional solute transport problem for calculation and verification (MEI Yi and WU Ji-chun, 2009). Another scholar, XIAO Chang-lai, used analytical method and numerical simulation to predict transport process and incidence of hexavalent chromium along with both consistency (LIU Ting et al. 2015). ...
The construction and hydrogeological area in the low hill, which is northwest of Laixi City and in the east of Shandong Province more precisely, is one of Dagu River's groundwater source. Regarding COD as the typical pollutant according to general situation of groundwater pollution in aforementioned area, a three-dimensional advection-dispersion model was established to simulate the transport of organic pollutants under two accident conditions. In addition, the effect of corresponding dispersity was analyzed. The results show that COD transport is mainly in accordance with the direction of groundwater flow, pollutant concentration and its gradient as well as the rule of narrower pollution range in deeper stratum. Moreover, COD is mainly transported and diffused in groundwater of sandy soil in the first and second layers. However, under accident condition II, the pollutant concentration begins to decay gradually after its transport and diffusion tends to be stable. Besides, in terms of dominance, dispersion is to transverse transport of pollutants what advection is to longitudinal transport. If considering random dispersion, the final results see higher peak concentration of COD and longer transverse distance from pollution center compared to transport route. What's more, the pollution plume changes and concentration isocline becomes slightly irregular.
Ensemble Kalman Filter (EnKF) has been introduced to estimate groundwater parameters and examined by some numerical experiments in literature. However, it suffers from spurious correlations resulting from sampling noises when approximating covariances from a small-size ensemble. It is important to deal with such inaccuracy in order to maintain filter process robust and effective. Covariance localization is one of suggested methods to modify EnKF using a small ensemble, and used to rectify spurious correlations. Covariance localization is implemented by adding distance-related weight to covariance in the way of Schur product. A two-dimensional synthetic example is constructed to demonstrate the effect of covariance localization. It is found that EnKF with localization can capture reliable both a mean and a variance of hydraulic conductivity field with obviously improved efficiency, as well as avoiding filter divergence to a large extent. Considering vulnerability to errors, hydrogeological parameters of relatively small correlation length e.g. lnK need localization more badly.
In a brief but fundamental review of the evolution of the conventional numerical techniques used in the solution of convection-dominated transport problems, we explore the difficulties that have been remedied to various degrees by various workers. In the course of this review we obtain the performance characteristic of the Crank-Nicolson Galerkin finite element method in the form of a curve in Peclet number and Courant number space. We show that the performance can be altered through a new upwind parameter that can easily be incorporated into many of the existing numerical solution methods. By providing an insight into the limitations of some of these methods we demonstrate, by means of numerical experiments, that the proposed upwinding procedure ensures acceptable solutions throughout the Pe-Cr space at a reasonable cost of the smearing effect.
Petrov–Galerkin finite element models (PGFEMs) appear to be the preferred choice for simulating advective–dispersive transport of chemicals in the natural environment for their ability to provide oscillation-free results. The PGFEM, however, provides oscillation-free results at the expense of introducing significant artificial dispersion. Introduction of artificial dispersion may lead to erroneous prediction of faster movement of the chemical and underestimation of the peak concentration. The objective of this paper is to develop an optimized PGFEM (OPGFEM). The OPGFEM developed is found to predict advective–dispersive transport of chemicals more accurately than the PGFEM.
Oscillation and numerical dispersion limit the reliability of numerical solutions of the convection-dispersion equation when finite difference methods are used. To eliminate oscillation and reduce the numerical dispersion, an optimal upstream weighting with finite differences is proposed. The optimal values of upstream weighting coefficients numerically obtained are a function of the mesh Peclet number used. The accuracy of the proposed numerical method is tested against two classical problems for which analytical solutions exist. The comparison of the numerical results obtained with different numerical schemes and those obtained by the analytical solutions demonstrates the possibility of a real gain in precision using the proposed optimal weighting method. This gain in precision is verified by interpreting a tracer experiment performed in a laboratory column.