多孔介质中控制释放问题的Galerkin方法

多孔介质中的控制释放由边界积分 常微分方程描述，溶质迁移由带第三类边界条件的对流扩散（含机械弥散）方程描述，构造了这一非线性耦合问题的有限元半离散格式，利用先验估计理论进行了收敛性分析.     

裂隙介质溶质运移模型的数值模拟

考虑裂隙介质中溶质运移问题的数学模型,建立离散的广义差分格式,给出不同的裂隙介质阻滞系数下的数值算例,并将数值解与解析解进行比较;比较结果表明:利用所建广义差分格式求解裂隙介质中的溶质运移问题是可靠的,且该格式具有稳定性和可实用性,可以用来数值模拟更加复杂的裂隙介质中溶质运移的物理过程.     

变动区域非线性对流扩散问题的有限元格式

对具有活动边界的一维非线性对流扩散问题,给出全离散θ-格式和误差分析。     

求解二维扩散方程的一种高精度紧致差分格式

扩散方程通常用来描述扩散现象中的物质密度的变化或者与扩散相类似的现象,针对二维扩散方程提出了一种高精度紧致差分格式,该格式基于四次样条函数对空间变量进行离散,对时间导数采用(2,2)Padé逼近,从而得到了时间和空间均为四阶精度的紧致差分格式.然后证明了该格式是无条件稳定的.最后通过数值实验,验证方法的精确性和稳定性.     

底泥-上覆水界面污染物释放机制的数值模拟

当外源污染受到控制后, 河流与湖泊底泥中的污染物可能会引起上覆水的再次污染. 在上覆水流动不致底泥起动悬浮的条件下, 数值模拟了底泥中污染物在底泥-上覆水界面向上覆水释放的机制. 采用k-ε模型计算了上覆水的湍流流动, 并采用 Darcy 定律描述了多孔介质中的渗流, 这里底泥被看成是各向同性均匀多孔介质; 耦合计算了上覆水和底泥中孔隙水的定常流动, 并基于流场计算结果, 数值计算了非定常溶质迁移扩散过程; 数值研究了平整底泥-上覆水界面以及底泥-上覆水界面为周期性三角状时, 污染物由底泥向上覆水释放的规律. 研究结果表明, 底泥中孔隙水与上覆水的交换是决定底泥中污染物向上覆水释放量的重要因素.     

某渣场污染物在非饱和岩土介质中的迁移模拟研究

为研究某渣场污染物对周边地下水的污染状况,通过对渣场场地非饱和土壤弥散、渗流特性试验,并运用模拟地下水溶质迁移的软件Comsol Multiphysics建立渣场污染物在非饱和岩土介质中的迁移模拟计算模型.试验结果表明:土壤水扩散率D(θ)和非吸附性溶质C1-1的水动力弥散系数Dsh(θ)与土壤含水率θ成显著幂函数关系;同一吸力水头下,黏粒含量越高,储水能力越强,脱水速度越慢,即黏土②土样其持水性能远远高于熔炼渣①土样.100年内渣场污染物氟和锌的迁移污染对周边地下水污染浓度满足二类水标准;通过对渣场周边地下水试验结果表明:渣场现状下对周边地下水并未形成污染,这也验证了采用Comsol Multiphysics软件对渣场污染物迁移模拟分析的可靠性.     

时间分数阶变系数对流扩散方程的数值解法

对流扩散方程的研究大多在常系数或者整数阶的范围之内,为了更加精确地描述溶质的运动特征,将传统的整数阶对流扩散方程推广到分数阶变系数的情形。主要研究了变系数Caputo分数阶对流扩散方程的有限差分解法。引入半整数点,在空间网格上进行对偶剖分,再通过有限差分方法离散了空间导数。 理论分析可以说明,本文所提出的离散格式,其解是存在并且唯一的,收敛精度为ο(τ+h),一维数值算例验证出理论分析的准确性。     

非饱和含湿多孔介质传热传质的渗流模型研究

综述了非饱和含湿多孔介质传热传质模型研究的发展。从多相渗流和扩散迁移机制出发建立以温度、压力和饱和度为基本变量的实用化三参数模型。该模型由一组描述水－汽质量守恒、空气质量守恒和能量守恒的非线性偏微分方程组成。利用该模型对埋管的热过程、砂土物性测量、毛细滞后现象、回湿过程、突发高温作用下多孔介质内部的传热传质过程和冻融过程进行了研究。为了模型的进一步应用,仍需对束缚水饱和度以下毛细压力与饱和度的关系、导热系数的影响因素及其获取方法、非饱和多孔介质传热传质的边界效应和滞后效应的物理机理等方面深入研究。非饱和多孔介质中溶质的运移更是一个饶有意义的研究课题。     

时间分数阶对流-扩散方程的有限差分法

时间分数阶对流-扩散方程可以用来模拟由传统的对流-扩散方程演变而来的反常扩散方程.本文针对一类时间分数阶对流-扩散方程提出了一个新的隐式差分格式,时间分数阶导数采用直接离散,空间导数采用中心差分格式离散,讨论了差分解的存在唯一性,并利用能量范数证明了该格式的无条件稳定性、收敛性,分析了收敛阶.数值试验验证了该格式的有效性.     

改进的有限体积法扩散项离散格式

分析了传统的有限体积法求解扩散问题中,当扩散系数在有限控制体界面两侧差异较大时,扩散通量在界面附近出现的数值振荡现象.根据界面两侧扩散通量相等和有限控制体内变量线性变化假设,推导了改进的有限体积法扩散项离散格式.数值算例表明：由2种扩散项离散格式计算得到的变量及其梯度分布很接近,而改进的扩散项离散格式消除了扩散通量的振荡问题,计算结果更加准确,能应用于扩散系数剧烈变化时的扩散问题求解.     

Combinatorial model of solute transport in porous media

Modeling of solute transport is a key issue in the area of soil physics and hydrogeology. The most common approach (the convection-dispersion equation) considers an average convection flow rate and Fickian-like dispersion. Here,we propose a solute transport model in porous media of continuously expanding scale, according to the combinatorics principle. The model supposed actual porous media as a combinative body of many basic segments. First, we studied the solute transport process in each basic segment body, and then deduced the distribution of pore velocity in each basic segment body by difference approximation, finally assembled the solute transport process of each basic segment body into one of the combinative body. The simulation result coincided with the solute transport process observed in test. The model provides useful insight into the solute transport process of the non-Fickian dispersion in continuously expanding scale.     

Simulation of the diffusion process in composite porous media by random walks

A new random-walk interpolation scheme was developed to simulate solute transport through composite porous media with different porosities as well as different diffusivities. The significant influences of the abrupt variations of porosity and diffusivity on solute transport were simulated by tracking random walkers through a linear interpolation domain across the heterogeneity interface. The displacements of the random walkers within the interpolation region were obtained explicitly by establishing the equivalence between the Fokker-Planck equation and the advection-dispersion equation. Applications indicate that the random-walk interpolation method can simulate one- and two-dimensional, 2nd-order diffusion processes in composite media without local mass conservation errors. In addition, both the theoretical derivations and the numerical simulations show that the drift and dispersion of particles depend on the type of Markov process selected to reflect the dynamics of random walkers. If the nonlinear Langevin equation is used, the gradient of porosity and the gradient of diffusivity strongly affect the drift displacement of particles. Therefore, random-walking particles driven by the gradient of porosity, the gradient of diffusivity, and the random diffusion, can imitate the transport of solute under only pure diffusion in composite porous media containing abrupt variations of porosity and diffusivity.     

纤维表面Zeta电位对多孔纤维材料透湿性能的影响

考虑双电层效应对多孔纤维材料热湿传递的影响,根据双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程建立模拟多孔纤维材料热湿传递过程的数学模型,并给定初始条件和边界条件,数值计算了多孔纤维材料热湿传递过程中温度和电解液体积百分比的分布。和实验结果的对比表明该数学模型能很好的反映多孔纤维材料热湿传递过程,也显示出双电层效应对多孔纤维材料热湿传递过程存在影响。     

一类带溶质吸附的混溶驱动问题的粘性分离方法

针对一类带溶质吸附的混溶驱动问题,给出其粘性分离格式并对这种分离格式进行误差估计。     

高浓卤水在多孔介质中的运移

与淡水溶液不同，高浓卤水在多孔介质中的运移是一个受多因素影响的、复杂的物理、化学作用过程。本文在系统分析卤水运移基本特征的基础上，综述了高浓卤水在多孔介质中运移所遵循的基本规律及其相应的数值模拟方法。     

Experimental study on moving boundaries of fluid flow in porous media

Researches on the boundary shape of fluid flow in porous media play an important role in engineering practices, such as petroleum exploitation, nuclear waste disposal and groundwater contamination. In this paper, six types of artificial porous samples （emery jade） with different porosities are manufactured. With the background of slow flow in porous media, laboratory experiments are carried out by observing the movement of five types of fluids with different dynamic viscosities in various types of porous media. A digital video recorder is employed to record the complete process of the fluid flow in the porous media. Based on the digital photos of the moving boundaries of fluid flow in porous media, the average displacement and fractal dimension of the moving boundary are estimated for different combinations of porosity and dynamic viscosity. Moreover, the evolution behavior of the average velocity and fractal dimension of the moving boundary with time is known. The statistical relations of the average velocity, the fractal dimension of the moving boundary and the porosity of porous media and the dynamic viscosity of fluids are proposed in this paper. It is shown that the front shape of the moving boundary of fluid flow in porous media is an integrated result of the porosity of porous media and the dynamic viscosity of fluids.     

一类多孔介质抛物型方程组解的渐近性态

为了描述物理学中多孔介质力学、流体力学、气体流量等问题3种介质的反应扩散问题,研究了一类具有3个变量耦合且同时具有加权非局部边界和非线性内部源的多孔介质抛物型方程组解的渐近性态,打破常用的第一特征值等构造上下解的方法,而采用常微分方程方法构造了该方程组的上、下解,引用比较定理,证明得到了由幂函数和指数函数完全耦合的一类抛物型方程组解的存在及爆破问题,在推广了已有的结果的基础上,为多孔介质及流体力学等问题提供理论支持.     

多孔介质中非饱和流第二边值问题点源函数的渐进分析

在多孔介质中的非饱和流扩散过程,可描述为变系数抛物型方程带流量边界条件的定解问题.我们不可能期望获得此类问题的精确解,而在应用中人们感兴趣的只是这一问题解在较短时间内的特性.为此本文对问题的点源函数,在短时间内作了渐近分析,并给出误差.     

Lower Bound of Blow-Up Time for Solutions of a Class of Cross Coupled Porous Media Equations

In this paper, blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied. The differential inequality techniques are used to obtain the lower bounds on the blow up time of the equation set under two different boundary conditions.