三维非均匀不稳定渗流方程的自适应网格粗化算法

将渗透率自适应网格技术应用于三维非均匀不稳定渗流方程的网格粗化算法中,在渗透率或孔隙度变化异常区域自动采用精细网格,用直接解法求解渗透率或孔隙度变化异常区域的压强分布,在其它区域采用不均匀网格粗化的方法计算,即在流体流速大的区域采用精细网格.用该方法计算了三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的三维非均匀自适应网格粗化算法的解在渗透率或孔隙度异常区的压强分布规律与采用精细网格的解非常逼近,在其它区域压强分布规律与粗化算法的解非常逼近,计算速度比采用精细网格提高100多倍.     

Method of dimensionality reduction in contact mechanics and tribology. Heterogeneous media

The method of dimensionality reduction in contact mechanics is based on the mapping of three-dimensional contact problems onto one-dimensional systems. The method was developed and verified for homogeneous media. The present paper discusses the possibilities of generalizing the method to heterogeneous media with an illustration of basic ideas on the example of an elastic medium with a coating. The proposed method is easy to extend to media with lateral heterogeneity or to arbitrary heterogeneous media; this is illustrated by considering linear non-dissipative media. The proposed method can be used for calculation of contact and frictional interactions and for interpretation of experiments on indentation of heterogeneous media.     

A hierarchical fracture model for the iterative multiscale finite volume method

An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.     

Dispersion and thermal resistivity in silicon nanofilms by molecular dynamics

On nanoscale, thermal conduction is affected by system size. The reasons are increased phonon scattering and changes in phonon group velocity. In this paper, the in-plane thermal resistivity of nanoscale silicon thin films is analyzed by molecular dynamics (MD) techniques. Modifications to the dispersion relation are calculated directly with MD methods at high temperature. The results indicate that the dispersion relation starts to change for very thin films, at around two nanometers. The reasons are band folding and phonon confinement. Thermal resistivity is analyzed by the direct non-equilibrium method, and the results are compared to kinetic theory with modified dispersion relations. Thermal resistivity is affected by both surface scattering and dispersion. Moreover, in thin films, the characteristic vibrational frequency decreases, which in standard anharmonic scattering models indicates a longer relaxation time and affects the resistivity. The results indicate that in very thin films, the resistivity becomes highly anisotropic due to differences in surface scattering. In two cases, surface scattering was found to be the most important mechanism for increasing thermal resistivity, while in one case, phonon confinement was found to increase resistivity more than surface scattering.     

Disorder resistivity of solid neutron-star matter

Lower limits are found for the disorder electrical resistivity of solid neutron-star matter in the neutron-drip region which is amorphous and heterogeneous in nuclear charge. This temperature-independent resistivity, large compared with that produced by phonon scattering, has direct consequences for theories of neutron-star magnetic field generation and evolution.     

Computation of effective propagation parameters in the optical domain with a finite difference time domain method

The study of optical scattering by heterogeneous media is a complex topic where homogenization is very helpful and rigorous methods are useful. Finite difference time domain (FDTD) method coupled with Monte Carlo process is used to compute the effective parameters of heterogeneous media. Effective parameters based on the coherent field propagation of a beam in the medium are determined in bidimensional geometry and for both polarizations. It is applied to media composed of small particles embedded in an host medium, for relevant ranges of particle sizes and optical constants for both binder and particles. The results are compared to the Maxwell–Garnett and Bruggeman mixing laws and the Foldy–Twersky and Keller perturbative approximations, leading to the assessment of their validity domain.     

Effect of humidity on the parameters of mechanoelectrical transformations in concretes

An increase in the humidity of a cement solution from 0 to 8% is found to result in an exponential decrease in the principal spectral maximum of its electric response to an impact excitation according to the change in the electrical resistivity. A physical model is proposed for the mechanoelectrical transformations occurring in a wet heterogeneous material, and this model agrees well with the experimental data.     

Acoustical characterization of perforated facings

An experimental method to estimate the acoustical parameters of perforated facings used for noise control applications is proposed. These perforating facings (also called screens) can be woven or non-woven fabrics or even micro-perforated plates (MPP). Following the work by Atalla and Sgard [J. Sound Vib. 303, 195-208 (2007)], the perforated facings are modeled as porous media composed with identical cylindrical perforations of circular cross-section. The acoustical parameters characterized with the proposed method are the radius of the perforations and the perforation rate (also named the open-porosity). These parameters are obtained from analytical expressions and a single measurement of the normal acoustic surface impedance of the perforated facing backed by an air cavity in a standing wave tube. The value of the static air flow resistivity can also be recovered with no additional assumption or measurement. In the case of a facing that contains perforations of an arbitrary shape, the radius parameter should be understood as a characteristic length of the visco-inertial dissipative effects. Results for two characterization examples (a low porosity screen and a high porosity one) are presented and discussed. Values of the estimated static air flow resistivity are compared with the results from direct measurements. Values of the predicted sound absorption coefficients are compared to the measured ones.     

Direct measurement of porous media local hydrodynamical permeability using gas MRI.

The concept of hydraulic permeability is at the core of modeling single phase or multi-phase flow in heterogeneous porous media, as it is the spatial distribution of the permeability that primarily governs the behavior of fluid flow in the medium. To date, the modeling of fluid flow in porous media has been hampered by poor estimates of local permeability. Magnetic Resonance Imaging is well known for its ability to measure non-invasively the local density and flow rate of different fluids saturating porous media [1,2]. In this paper we demonstrate the first non-invasive method for the direct measurement of a single projection of the local permeability tensor of a porous medium using gas-phase MRI. The potential for three-dimensional imaging of the medium permeability is also discussed. The limitations of the method are listed and results are presented in a model porous medium as well as in a real oil reservoir rock.     

Dielectric dispersion of three-and four-component matrix media

The dielectric dispersion of heterogeneous matrices containing dissimilar cylindrical inclusions is studied. Conditions for the dispersion in multicomponent media are found and explained from the physical standpoint. It is shown that the effective loss factor may have several maxima with their number depending on the number of dissimilar inclusions in the composite. Effective permittivity diagrams in the complex plane are constructed. For media with a low inclusion concentration, an approximate method for finding the frequency of the maxima is suggested.     

Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.     

Hybrid cellular automata method. Application to research on mechanical response of contrast media

In the work, a hybrid cellular automata method was developed to study behavioral peculiarities of heterogeneous materials and contrast media. The method is a combination of two approaches: classical and movable cellular automata methods. The method was verified through comparing simulation data on sorption of carbon dioxide in lignite and corresponding experimental data provided by researchers from Velenje Lignite Mine (Slovenia). The obtained estimates of model parameters were used in numerical simulation of the gas phase on the strength and fracture of lignite samples. It is shown that the presence of the gaseous atmosphere even of pressure 0.1 MPa changes the effective strength of the lignite sample and the character of their fracture. The developed method can be used to study behavioral peculiarities of complex multicomponent media such as coal beds in mine zones.     

温度对AZO薄膜红外辐射性能的影响

随着全球资源的减少和环境的恶化,节能减排已成为人们关注的焦点,具有保温隔热功能的低辐射玻璃成为研究的热点。提高玻璃保温隔热性能最有效的方法就是在其表面涂覆低辐射率层。原材料丰富、导电性能好、可见光透过率高等优势使得Al掺杂ZnO (AZO)薄膜成为最具潜力的低辐射率层。系统研究了温度对AZO薄膜红外辐射性能的影响,分析了变化机理。首先研究了在一定的温度下持续一段时间后,AZO薄膜的红外比辐射率的变化情况。然后研究了在变温环境中红外比辐射率的变化情况。采用直流磁控溅射法在室温下玻璃基片上沉积500 nm厚的AZO薄膜,将薄膜放到马弗炉中进行热处理,在100～400 ℃空气气氛下保温1 h,随炉冷却。采用X射线衍射仪对AZO薄膜进行物相分析,采用扫描电子显微镜观察薄膜表面形貌变化。利用四探针测试法测量AZO薄膜的电阻率,采用红外比辐射率测试仪测试薄膜红外比辐射率, 可见分光光度计测量可见光谱。测试的结果表明,薄膜热处理前后均为六角纤锌矿结构,(002)择优取向。300 ℃及以下热处理1 h后,(002)衍射峰增强,半高宽变窄,晶粒尺寸长大。随着热处理温度的升高,薄膜的电阻率先减小后增大,200 ℃热处理后的薄膜具有最小的电阻率(0.9×10-3 Ω·cm)。热处理温度升高,晶粒长大使得薄膜电阻率降低。热处理温度过高,薄膜会从空气中吸收氧,电阻率下降。薄膜的红外比辐射率变化趋势和电阻率的一致,在200 ℃热处理后获得最小值(0.48)。自由电子对红外光子有较强的反射作用,当电阻率低,自由电子浓度高的时候,更多的红外光子被反射,红外辐射作用弱,红外比辐射率小。薄膜的可见光透过率随着热处理温度的升高先减小后增大,200 ℃热处理后的薄膜的可见光透过率最小,但仍高达82%。这种变化是由于自由电子浓度变化引起的,自由电子对可见光有很强的反射作用。选取未热处理和200 ℃热处理后的样品进行变温红外比辐射率的测量,将样品放在可加热的样品台上,位置固定,在室温到350 ℃的升温和降温过程中每隔25 ℃测量一次红外比辐射率,结果表明,在室温到350 ℃的温度范围内,AZO薄膜的红外比辐射率在升温过程中随着温度的上升而增大,在降温过程中减小,经过整个升、降温过程后,薄膜的红外比辐射率增大。     

耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术.首先引入电场的矢势和标势,将电场分解为无散场和无旋场之和,Maxwell方程转换为关于矢势与标势的混合Helmholtz方程,克服低感应数问题.在此基础上,借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式,建立混合Helmholtz方程的离散方程.并采用直接法求解器PARDISO求解离散方程,有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解.此外,在数值模拟中利用差异场技术,克服源的奇异性问题,尽可能提高近场的计算精度.与解析解的对比证明了该算法的有效性.数值模拟结果表明,海洋可控源电磁法沿测线方向的电场,对油气藏的纵向电阻率敏感,对横向电阻率不敏感;对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.     

Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube

This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.     

Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.     

Numerical upscaling for the eddy-current model with stochastic magnetic materials

This paper deals with the upscaling of the time-harmonic Maxwell equations for heterogeneous media. We analyze the eddy-current approximation of Maxwell’s equations to describe the electric field for heterogeneous, isotropic magnetic materials. The magnetic permeability of the materials is assumed to have random heterogeneities described by a Gaussian random field. We apply the so-called Coarse Graining method to develop a numerical upscaling of the eddy-current model. The upscaling uses filtering and averaging procedures in Fourier space which results in a formulation of the eddy-current model on coarser resolution scales where the influence of sub-scale fluctuations is modeled by effective scale- and space-dependent reluctivity tensors. The effective reluctivity tensors can be obtained by solving local partial differential equations which contain a Laplacian as well as a curl–curl operator. We present a computational method how the equation of the combined operators can be discretized and solved numerically using an extended variational formulation compared to standard discretizations. We compare the results of the numerical upscaling of the eddy-current model with theoretical results of Eberhard [J.P. Eberhard, Upscaling for the time-harmonic Maxwell equations with heterogeneous magnetic materials, Physical Review E 72 (3), (2005)] and obtain a very good agreement.     

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

The effective absorption cross-section of thermal neutrons in a medium containing strongly or weakly absorbing centres

The structure of a heterogeneous system influences diffusion of thermal neutrons. The thermal-neutron absorption in grained media is considered in the paper. A simple theory is presented for a two-component medium treated as grains embedded in the matrix or as a system built of two types of grains (of strongly differing absorption cross-sections). A grain parameter is defined as the ratio of the effective macroscopic absorption cross-section of the heterogeneous medium to the absorption cross-section of the corresponding homogeneous medium (consisting of the same components in the same proportions). The grain parameter depends on the ratio of the absorption cross-sections and contributions of the components and on the size of grains. The theoretical approach has been verified in experiments on prepared dedicated models which have kept required geometrical and physical conditions (silver grains distributed regularly in Plexiglas). The effective absorption cross-sections have been measured and compared with the results of calculations. A very good agreement has been observed. In certain cases the differences between the absorption in the heterogeneous and homogeneous media are very significant. A validity of an extension of the theoretical model on natural, two-component, heterogeneous mixtures has been tested experimentally. Aqueous solutions of boric acid have been used as the strongly absorbing component. Fine- and coarse-grained pure silicon has been used as the second component with well-defined thermal-neutron parameters. Small and large grains of diabase have been used as the second natural component. The theoretical predictions have been confirmed in these experiments.