A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen–Loève expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.     

A moving grid finite element method applied to a model biological pattern generator

Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis.     

多孔介质中盐指现象的数值模拟

运用基于杂交网格的高精度数值方法研究了多孔介质中的盐指现象.该算法将基于边界拟合坐标下的高精度有限差分法和高精度的泊松方程快速求解器有效地结合在一起,从而达到提高整体的计算精度、计算效率和稳定性的目的.通过比较不同孔隙率的多孔介质对盐指对流的传热传质效应的影响,发现在标准孔隙率较低的多孔介质中,盐度扩散的速度明显比热扩散的速度快,盐指很快触及上下壁面,使得上下层的盐度梯度迅速减小,这是与非多孔介质具有明显差异之处. 关键词： 多孔介质 双扩散对流 盐指     

Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89–101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.     

A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load

This paper is concerned with the analysis of dynamic deflection and acceleration of a concrete bridge which is subjected to a moving vehicle load. The bridge, to be constructed across the River Brahmaputra in India, consists of 20 main spans, and each main span is assumed to be double cantilever type with a small suspended span. The moving vehicle is modeled as one degree of freedom. The deflections and accelerations at specific locations on the bridge when the vehicle moves at constant speed are analyzed by using the finite element method.     

Discrete models of liquid-vapour phase change phenomena in porous media

This survey presents recent developments in the modelling of liquid-vapor phase change phenomena in porous media within the framework of the discrete approach. The pore network (or discrete) approach is first illustrated through the example of the evaporation at low capillary number of a pure liquid from a capillary porous medium. In particular, it is shown that invasion percolation patterns characterise the phase distribution. Then first results concerning the vaporisation of a liquid within the porous wick of a capillary evaporator are presented. These results show that capillary fingering patterns can be expected within the wick.     

A finite element approach for scattering from inhomogeneous media with a rough interface

Electromagnetic scattering from an inhomogeneous medium with a one-dimensional rough interface is analysed. The proposed procedure combines the finite element method (FEM), to model the electromagnetic field in the inhomogeneous region, with a perturbative technique to account for the contributions due to the rough interface. Backscattering and bistatic scattering coefficients are computed and plotted for both plane wave and Gaussian beam incident fields in the case of TM_z polarization.     

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

Waves and energy in random elastic guided media through the stochastic wave finite element method

Energy propagation in random viscoelastic media is considered in this Letter. The forced response of uncertain waveguide subject to time harmonic loading is treated. This energy model is based on a spectral approach called the “Stochastic Wave Finite Element” (SWFE) method which is detailed in this Letter. Assuming that the random properties are spatially homogeneous in the media, the SWFE is a hybridization of the deterministic wave finite element and a parametric probabilistic approach. The proposed model is applicable in a wide frequency band with reduced time consumption. Numerical examples show the effectiveness of the proposed approach to predict the statistics of kinematic and quadratic variables of guided wave propagation. The results are compared to Monte Carlo simulations.     

Stochastic reaction-diffusion phenomena in porous media with nonlinear kinetics: effects of quenched porosity fluctuations

We study the effects of quenched porosity fluctuations in the presence of nonlinear kinetics in a reaction-diffusion porous system. Adopting a weak-noise approximation and a mean-field assumption, a renormalized equation of motion for the average concentration of a chemical species is obtained. It is characterized by a smaller effective diffusion coefficient and by the presence of supplementary nonlinear reactive terms. Explicit results are given for a Gaussian porosity distribution and for a long-ranged one. Comparisons with simulations in one dimension are presented.     

A finite element model for rigid porous absorbing materials

An eight node isoparametric finite element is used to represent a rigid porous absorbing material. Tests on an assembly of these elements for a one dimensional model gave good agreement with an exact solution for the input impedance. Results from a two dimensional model show the effects of transverse propagating modes on the input impedance and indicate that for an absorbent with finite dimensions extended reaction is important.     

Multifield coupled finite element analysis for sound transmission in otitis media with effusion

In this paper, a newly constructed three-dimensional finite element (FE) model of the human ear based on histological sections of a left ear temporal bone is reported. The otitis media with effusion was simulated in the model with variable fluid levels in the middle ear. The interfaces among the air, structure, and fluid in the ear canal and middle ear cavity were identified and the acoustic-structure-fluid coupled FE analysis was conducted when the middle ear fluid level was varied from zero to full fill of the cavity. The results show how the displacements of the tympanic membrane and stapes footplate or the middle ear transfer function is affected by fluid in the cavity across the auditory frequencies. Comparison of model results with measured data in temporal bones indicates that this model has the capability to extend FE analysis into pathological ears such as otitis media with visualized fluid-air interfaces inside the middle ear structures.     

Calculating the forced response of two-dimensional homogeneous media using the wave and finite element method

The forced response of two-dimensional, infinite, homogenous media subjected to time harmonic loading is treated. The approach starts with the wave and the finite element (WFE) method where a small segment of a homogeneous medium is modelled using commercial or in-house finite element (FE) packages. The approach is equally applicable to periodic structures with a periodic cell being modelled. This relatively small model is then used, along with periodicity conditions, to formulate an eigenvalue problem whose solution yields the wave characteristics of the whole medium. The eigenvalue problem involves the excitation frequency and the wavenumbers (or propagation constants) in the two directions. The wave characteristics of the medium are then used to obtain the response of the medium to a convected harmonic pressure (CHP). Since the Fourier transform of a general two-dimensional excitation is a linear combination of CHPs, the response to a general excitation is a linear combination of the responses to CHPs. Thus, the response of a two-dimensional medium to a general excitation can be obtained by evaluating an inverse Fourier transform. This is a double integral, one of which is evaluated analytically using contour integration and the residue theorem. The other integral can be evaluated numerically. Hence, the approach presented herein enables the response of an infinite two-dimensional or periodic medium to an arbitrary load to be computed via (a) modelling a small segment of the medium using standard FE methods and post-processing its model to obtain the wave characteristics, (b) formulating the Fourier transform of the response to a general loading, and (c) computing the inverse of the Fourier transform semi-analytically via contour integration and the residue theorem, followed by a numerical integration to find the response at any point in the medium. Numerical examples are presented to illustrate the approach.     

Acoustic technique to monitor the kinetics of porous development phenomena in viscoelastic media

In this paper, the potential of a low frequency acoustic technique for the study and characterisation of viscoelastic porous media is investigated. This work was based on the limits of ultrasonic applications in highly absorbent porous media. In this context, fermenting dough was used as a model propagation medium. This type of product has a very complex matrix in terms of texture, openings and moisture. The basic theory of sound in such matter is recalled, especially the effects of the scattering of sound energy in matrices like that of the product under investigation. Depending on the properties of the openings, acoustic velocity and intensity of sound were chosen to represent the state of evolution of the matter. A tap-test acoustic technique was employed and allowed a quality indicator to be obtained. The results of the validation step using various technological parameters indicate that a high degree of sensitivity can be reached with non-destructive acoustic techniques.     

Critical phenomena with convergent series expansions in a finite volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish first- from second-order transitions within a finite-size scaling analysis. The criterion applies also to other methods for investigating the phase structure, such as Monte Carlo simulations. Our computational tools are illustrated with the example of scalar (O(N) models with four- and six-point couplings forN=1 andN=4 in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.     

Quasiisotropic asymptotic method for electromagnetic waves in moving media

Radiophysics and Quantum Electronics -