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The aim of this study is to numerically simulate the density-driven convection in heterogeneous porous media associated with anisotropic permeability field, which is important to the safe and stable long term CO₂ storage in laminar saline aquifers.

The study uses compact finite difference and the pseudospectral method to solve Darcy’s law.

The presence of heterogeneous anisotropy may result in non-monotonic trend of the breakthrough time and quantity of CO₂ dissolved in the porous medium, which are important to the CO₂ underground storage.

The manuscript numerically study the convective phenomena of mixture contained CO₂ and brine. The phenomena are important to the process of CO₂ enhanced oil recovery. Interesting qualitative patterns and quantitative trends are revealed in the manuscript.

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.

The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.

Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.

This paper aims to analyze the influence of rotated anisotropy on the stability of slope, the random finite element method is used in this study.

The random field is generated by the discrete cosine transform (DCT) method, which can generate random field with different rotated angles conveniently.

Two idealized slopes are analyzed; it is observed that the rotated angle significantly affects the slope failure risk. The two examples support the conclusion that when the orientation of the layers is nearly perpendicular to the slip surface, the slope is in a relative stable condition. The results of heterogeneous slope with two clay layers demonstrate that the rotated angle of lower layer mainly controls the failure mechanism of the slope, and the rotated angle of upper layer exhibits a significant influence on the probability of slope failure.

The method for rotated anisotropy random field generation based on the DCT has a simple expression with few parameters and is convenient for implementation and practical application. The proposed method and the results obtained are useful for analyzing the stability of the heterogeneous slopes in engineering projects.

The purpose of this paper is to investigate the effect of corrugation, wave number, initial stress and the heterogeneity of the media on the phase velocity of the Love-type wave. Moreover, the paper aims to have a comparative study of the presence and absence of anisotropy, heterogeneity, corrugation and initial stress in the half-space, which serve as a focal theme of the study.

The present paper modelled the propagation of the Love-type wave in a corrugated heterogeneous monoclinic layer lying over an initially stressed heterogeneous transversely isotropic half-space. The method of separation of variables is used to procure the dispersion relation.

The closed form of dispersion relation is obtained and found to be in well agreement to the classical Love wave equation. Neglecting the corrugation at either of the boundary surfaces, expressions of the phase velocity of the Love-type wave are deduced in closed form as special cases of the problem. It is established through the numerical computation of the obtained relation that the concerned affecting parameters have significant impact on the phase velocity of the Love-type wave. Also, a comparative study shows that the anisotropic case favours more to the phase velocity as comparison to the isotropic case.

Although many attempts have been made to study the effect of corrugated boundaries on reflection and refraction of seismic waves, but the effect of corrugated boundaries on the dispersion of surface wave (which are dispersive in nature) propagating through mediums pertaining various incredible features still needs to be investigated.

Microstructure-sensitive design (MSD), for optimal performance of engineering components that are sensitive to material anisotropy, has largely been confined to the realm of theory. The purpose of this paper is to insert the MSD framework into a finite element environment in order to arrive at a practical tool for improved selection and design of materials for critical engineering situations.

This study applies the recently developed Hybrid Bishop-Hill (HBH) model to map the yield surface of anisotropic oxygen free electronic copper. Combining this information with the detailed local stresses determined via finite element analysis (FEA), a “configurational yield stress” is determined for the entire component. By varying the material choice/processing conditions and selecting the directionality of anisotropy, an optimal configuration is found.

The paper provides a new FEA-based framework for MSD for yield-limited situations. The approach identified optimal directionality and processing configurations for three engineering situations that are particularly sensitive to material anisotropy.

The microstructure design space for this study is limited to a selection of eight copper materials produced by a range of processing methods, but is generalizable to many materials that exhibit anisotropic behavior.

The introduction of MSD methodology into a finite element environment is a first step toward a comprehensive designer toolkit for exploiting the anisotropy of general materials (such as metals) in a way that is routinely undertaken in the world of fiber-based composite materials. While the gains are not as sizeable (due to the less-extreme anisotropy), in many applications they may be extremely important.

The purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely.

Techniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed.

Complex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model.

To the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space.

The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave.

Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

We propose a simplified method to simulate damage evolution in heterogeneous media from geodesic propagation calculations. The method introduced for the case of porous media (polycrystalline graphite), was generalized to multiphase media, and then to a continuous variation of local fracture energy. It is based on a minimization of the fracture energy criterion, ignoring the local variations of the stored strain energy. With this simplification, the microcracking process is simulated by very efficient algorithms, involving a low calculation cost, to extract minimal paths on graphs with edges valued according to the local fracture energy. From the simulations, made on micrographs in materials or on random microstructure simulations, we get images of the possible microcracks paths, to be compared with real cracking of materials, and an estimation of the effective toughness of heterogeneous materials. Our approach is illustrated from two‐dimensional simulations corresponding to various types of microstructure involving the following micro‐geometrical distributions of the local fracture energy: isotropic and anisotropic two‐phase media, polycrystal with cleavage and intergranular fracture, material with a continuous distribution of surface energy.

Thermal conduction anisotropy, which is defined by the dependency of thermal conductivity on direction, is an important parameter in many engineering and research studies such as the design of nuclear waste depositional sites. In this context, the authors aim to investigate the effect of grain shape in thermal conduction anisotropy using pore scale modeling that utilizes real shapes of grains, pores and throats to characterize petrophysical properties of a porous medium.

The authors generalize the swelling circle approach to generate porous media composed of randomly arranged but regularly oriented elliptical grains at various grain ratios and porosities. Unlike previous studies that use fitting parameters to capture the effect of grain–grain thermal contact resistance, the authors apply roughness to grains’ surface. The authors utilize Lattice Boltzmann method to solve steady state heat conduction through medium.

Based on the results, when the temperature field is not parallel to either major or minor axes of grains, the overall heat flux vector makes a “deviation angle” with the temperature field. Deviation angle increases by augmenting the ratio of thermal conductivities of solid to fluid and the aspect ratios of grains. In addition, the authors show that porosity and surface roughness can considerably change the anisotropic properties of a porous medium whose grains are elliptical in shape.

The authors developed an algorithm for generation of non-circular-based porous medium with a novel approach to include grain surface roughness. In previous studies, the effect of grain contacts has been simulated using fitting parameters, whereas in this work, the authors impose the roughness based on the its fractal geometry.

This paper aims to describe and investigate the mathematical models and numerical modeling of how a cell membrane is affected by a transient ice freezing front combined with the influence of thermal fluctuations and anisotropy.

The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics and how it influences the freezing process of a single red blood cell. The numerical calculation has been modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing.

The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.