分形多孔介质中的奇异扩散

分形多孔介质和均质多孔介质相比具有许多特殊的性质,它在各个不同的尺度上有相互钳套的自相似结构.孔隙分形中的粒子扩散和经典的Fick扩散不同,其均方位移服从分形幂律关系.据此对孔隙分形中的粒子扩散利用随机过程的统计方法建立了奇异扩散的理论模型,讨论了奇异扩散的非马尔可夫性质和分形性质.     

双分散多孔介质圆形和圆环形通道内高速流动分析

基于双速度Brinkman-Darcy扩展流动模型,分析了高速流体在双分散多孔介质圆形和圆环形通道内的流动特征.双分散多孔介质裂纹相（f相）和多孔相（p相）流场相互耦合且本质上受四阶微分方程控制.采用正常模式降阶法将原控制方程化简为含两个中间变量的二阶解耦微分方程组,进而方便地推得f相和p相流场的速度分布解析解.不论圆形的还是圆环形的通道,两种结果均表明:两相流场的速度及其速度差随着Darcy数的提高而增大;但随着两相间动量传递程度的加强,两相流场呈现出相反的速度变化趋势,从而导致速度差变小.     

饱和多孔介质的超粘弹性本构理论研究

为了建立能考虑固体材料、多孔固体与流体可逆和不可逆变形的饱和多孔介质超粘弹性理论,以多孔固相为参考构型,以有效应力、材料真实应力和流相真实孔压作为状态变量,结合混合物均匀化响应原理获得各项均符合热力学功共轭特征的饱和多孔介质能量平衡方程,根据非平衡热力学熵分解理论求得熵流和熵产.结果表明,超弹塑性理论是该理论的一个特例;多孔固体的总变形可分为固相间隙和材料变形两部分,间隙应变与Terzaghi有效应力构成功共轭对,材料应变与材料真实应力构成功共轭对.饱和多孔介质的自由能可分为固相和流相两部分.当固相间隙和材料变形解耦时,固相所含的自由能又可分为间隙和材料两部分.证明了Skempton有效应力不是饱和多孔介质的基本应力状态变量.     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

不相混流体在多孔介质中置换不稳定现象的三维数值模拟

本文采用不连续势函数在待定界面上变化的方法模拟不相混流体在多孔介质中置换．描述流体在多孔介质中的流动的连续方程在三维直角坐标系下被转化为七点式代数方程．采用强隐式法（Stronglyimplictprocedure）求解，再确定变动的流体间界面．计算中只模拟从稳定向不稳定置换转化这一过程中界面的变动．计算中考虑了多孔介质的浸润特性、毛细管压力、及多孔介质渗透不均匀性．     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

饱和多孔介质中骨架的应变局部化萌生条件

应用饱和多孔介质控制方程和Liapunov稳定理论,导出了固相应力和有效应力描述的多孔介质骨架应变局部化的萌生条件．不同应力形式表达的多孔介质基体的控制方程,相应的应变局部化萌生条件的表达形式也不尽相同,其原因源于骨架本构中固液两相之间相互作用的不同描述．应用得出的Terzaghi有效应力描述的应变局部化萌生条件,可以理论解释多孔介质中固、液两相不同相对运动出现的破坏方式,如管涌、滑坡和泥石流．应用简单算例说明了应变局部化条件的具体实施方法．     

多介质大变形流动的MOF-MMALE数值模拟研究

多介质大变形流动数值模拟的关键和难点是在精确追踪物质界面的同时又能够处理好流体的大变形运动.将MOF(moment-of-fluid)界面重构算法与多介质任意Lagrange-Euler方法(MMALE)相耦合,形成MOF-MMALE方法,并应用于多介质大变形流动问题的数值模拟研究.MOF-MMALE方法在传统的ALE方法基础上,允许计算网格边界跨过物质界面,允许存在混合网格,即一个网格内可以存在两种或两种以上物质;在混合网格内,利用MOF界面重构算法来确定物质界面的位置和方向.数值算例表明,MOF-MMALE方法是模拟多介质大变形流动的有效手段,并且具有较好的数值精度和界面分辨率.     

基于三维CFD-DEM的多孔介质流场数值模拟

将多孔介质局部细观流动与基于Darcy定律的宏观物理模型相结合，应用三维CFD-DEM对多孔介质流场进行局部细观数值模拟，得到多孔介质的惯性阻力系数和粘性阻力系数.并将其作为参数提供给基于Darcy定律的CFD多孔介质模型，从而可用于更大规模的多孔介质流场计算.应用Voronoi多面体作为网格单元，解决了CFD DEM中网格孔隙率精确计算的困难.文中发展的多尺度结合应用的研究方法，在计算精度和计算效率的矛盾中找到了较好的平衡，对于工程应用而言，有节约实验成本、提高计算结果可靠性的功效.     

多孔介质瞬态分析中非分裂PML及时域有限元实现

在波场的数值模拟中,完全匹配层(perfectly matched layer,PML)已经被证明是一种十分有效的吸收技术,并得到了广泛的应用.为了解决具有无限域的多孔介质中2阶弹性波动方程数值模拟中的吸收边界问题,提出了一种非分裂格式的PML(non-splitting perfectly matched layer,NPML).首先,基于Biot多孔介质波动理论,建立了以固相和流相位移表示的2阶动力控制方程,其中考虑了固体颗粒和孔隙流体的可压缩性、惯性以及孔隙流体的粘性.其次,根据复伸展坐标变换的定义,通过Laplace变换获得了非分裂格式PML的频域表达式.然后,借助辅助函数将该方程变换到时间域内,得到了一种有效的非分裂PML.最后,基于Galerkin近似方法,给出了其时域有限元计算格式.通过数值算例分析了该非分裂格式的PML在饱和介质动力响应分析中的有效性.     

A biphasic transverse isotropic FEM model for cartilage

Articular cartilage is a viscoelastic, two-phase and fiber-strengthen tissue; it consists of a solid and a fluid phase. We describe this tissue using the Theory of Porous Media (TPM). Some simulation results are shown. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of wave propagation in the fluid-saturated porous media

In the present work, a so-called hybrid two-phase model composed of a materially incompressible solid and a compressible pore fluid is studied. The mechanical behavior is described by the thermodynamically consistent Theory of Porous Media (TPM). Numerical experiments were performed with the space-time coupled discontinuous galerkin (DGT)-method. The existence of two compressional waves (P-waves) and one shear wave (S-wave) was confirmed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic analysis of porous materials: Numerical modeling with a space-time FEM

In the current work, we investigate the dynamic analysis of a two-phase porous material using the space-time discontinuous Galerkin method. The physical model is based on the Theory of Porous Media (TPM). The finite element approximation consists of continuous approximations in space but discontinuous ones in time. The continuity condition between the adjacent time intervals is weakly enforced by the upwind flux treatment. No artificial penalty function is involved. Moreover, the Embedded Velocity Integration technique is applied to reduce the second-order equation in time into a first order one without introducing an additional constraint. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Improved Gagliardo-Nirenberg-Sobolev inequalities on manifolds with positive curvature

We apply the method of [J. Demange, From porous media equation to generalized Sobolev inequalities on a Riemannian manifold, preprint, http://www.lsp.ups-tlse.fr/Fp/Demange/, 2004] and [J. Demange, Porous Media equation and Sobolev inequalities under negative curvature, preprint, http://www.lsp.ups-tlse.fr/Fp/Demange/, 2004], based on the curvature-dimension criterion and the study of Porous Media equation, to the case of a manifold M with strictly positive Ricci curvature. This gives a new way to prove classical Sobolev inequalities on M. Moreover, this enables to improve non-critical Sobolev inequalities as well. As an application, we study the rate of convergence of the solutions of the Porous Media equation to the equilibrium.     

A three-phase FE-model for the simulation of partially saturated soils

While for many numerical simulations in geotechnics use of a two-phase model is sufficient, separate consideration of all three phases is mandatory for numerical simulations of partially saturated soils subjected to compressed air. This is a common technique frequently applied for temporary ground support in tunnelling. For the numerical simulation of tunnelling using compressed air, a multiphase model for soft soils is developed, in which the individual constituents of the soil – the soil skeleton, the fluid and the gaseous phase – and their interactions are considered. The three phase model is formulated within the framework of the Theory of Porous Media (TPM), based upon balance equations and constitutive relations for the soil constituents and their mixture. Water is modelled as an incompressible and air as a compressible phase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Enriched Biphasic Model for Solute Driven Degradation

Transport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks on the method of modulus of continuity and the modified dissipative Porous Media Equation

We employ Besov space techniques and the method of modulus of continuity to obtain the global well-posedness of the modified Porous Media Equation.