饱和-非饱和土壤中污染物运移过程的数值模拟

本文提出了一个模拟饱和 非饱和土壤中溶和污染物运移过程的数值模型．模拟的控制污染物运移的物理 化学现象包括：对流，机械逸散，分子弥散，吸附，蜕变，不动水效应．发展了一个修正的特征线Ｇａｌｅｒｋｉｎ方法以离散污染物运移过程的控制方程并导出了一个用于有限元方程求解的显式算法．数值例题结果表明所提出模型和算法的功能

NUMERICAL MODELLING OF POLLUTANT TRANSPORT IN UNSATURATED/SATURATED SOILS 1)

A numerical model to simulate miscible pollutant transport through unsaturated/satu-rated soils is presented. The model is composed of the two coupled phases: the hydromechanical analysis of the two immiscible fluids through the deforming porous medium to determine the velocity fields of the porous water and air flows and the saturation degrees; the pollutant transport analysis through the porous medium. The emphasis of the present paper for the numerical modelling is specially given to the second phase. The main governing phenomena of the miscible pollutant transport modelled in the present numerical simulation include: convection; mechanical dispersion and molecular diffusion. In addition, three other phenomena responsible for temporary pollutant storage (or release) and inducing retardation effects, that is adsorption, degradation and immobile water effect, are also integrated into the model. Solute transport in porous media is governed by transient advection-diffusion equations with primary unknowns c w m , where c w m is the pollutant volumetric concentration in porous mobile water, in a generalized sense as certain retardation terms appear is theequations due to such phenomena as adsorption, degradation and immobile water effect integrated into the model. It is remarked that the pollutant concentration in the immobile water and the solid particles are treated as state variables at the element integration points. The difficulties in numerical solution of the advection-diffusion equations have long been recognized. It is noted that the seeping flow in porous media is usually dominat by diffusion terms, while production of porous fluids can yield dominant advective transport. Hence, the proper numerical methods should be utilized to deal with the problem with different balances of advection and diffusion terms within the same applications. To take into account the retardation effects in the model, a modified version of the characteristic Galerkin method for discretization of equations governing the pollutant transport is developed. One of the main merits of the method is that it justifies the use of the Galerkin spatial discretization in contrast with the Taylor-Galerkin process and the streamline upwind Petrov-Galerkin process, in addition, the balancing diffusion term is introduced as the `upwinding' in a rational form to avoid using arbitrary mesh-dependent upwind coefficients. The success of the method in solving the advection-diffusion equations is achieved by a suitable operator splitting procedure. A fully explicit algorithm is derived for the numerical solution of the transient advection-diffusion equation. The advantage of the algorithm is that it is very efficient to compute, very easy to implement and gives accurate results. The numerical examples validate and demonstrate the performance and the capability of the presented numerical model and algorithms. In addition, numerical results quantitatively illustrate the effects of various phenomena in the pollutant transport.