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A serious error exists in the above paper. [ABSTRACT FROM AUTHOR]

The present comment concerns some doubtful results included in the above paper. [ABSTRACT FROM AUTHOR]

• The N/B co-doped porous carbon materials were obtained by direct pyrolysis of uniform eutectic liquid. • The sample materials process superior SSA. • The obtained NBPCs exhibited abundant pore structure. • The obtained NBPCs with rich B, N-doping level. • The NBPC-3 sample exhibit an excellent electrochemical performance as cathode materials for ZHSCs. N/B co-doped porous carbon materials (NBPCs) are regarded as an ideal cathode material for Zn-ion hybrid supercapacitors (ZHSCs). As a capacitive cathode material, the improvement of specific surface area (SSA) and pore structure can efficiently enhance the capacity and rate capability of NBPCs. However, the B atom doping progress will patch up the defect and pore of NBPCs, thereby impeding the further expansion of the SSA area and porous structure. This paper designs a new route for high-efficiency fabrication of NBPCs with high SSA and rich pore structure, employing biomass waste as the carbon source and a novel deep eutectic solvent (DES) as the activation agent. The obtained NBPCs process superior SSA (2270 m2 g–1) and abundant pore structure with rich B, N-doping level. Notably, an interesting occupied effect of doped B atoms on the N-doped carbon network can be identified, which optimizes the proportion of N-contained surface functional groups, leading to the enhancement of conductivity and capacity in NBPCs. Together with the large SSA, high B, N-doping level, an appropriate proportion of N-contained surface groups, and hierarchical porous structure, the NBPC-3 sample exhibits excellent electrochemical performance as cathode materials for ZHSCs, with an energy density of 139.46 W h kg–1. [ABSTRACT FROM AUTHOR]

The present paper focuses on the numerical modeling of groundwater flows in fractured porous media using the codimensional model description. Therefore, fractures are defined explicitly as a (d − 1) -dimensional geometric object immersed in a d -dimensional region and can act arbitrarily as a drain or a barrier. We numerically investigate a novel numerical strategy combining distinctive classes of conforming and nonconforming high-order Galerkin methods, both eligible for static condensation. This procedure is here particularly relevant, leading to a smaller and sparser final system with coupled degrees of freedom solely on the mesh skeleton. Precisely, we combine an inspired hybridizable interior penalty discontinuous Galerkin (HIP) formulation inside the bulk region and a standard continuous Galerkin (CG) approximation on the fracture network. The distinctive discretization of corresponding PDEs and the coupling strategy are rigorously exposed, and the local and global matrix assemblies are detailed. Extensive numerical experiments are then achieved to prove the model's performances for 2D/3D analytic and realistic benchmarks. Qualitative comparisons are also considered with other discretization methods and commercial software, such as comsol. • Combining of conforming and nonconforming methods for flow in fractured media. • The conceptual codimensional model description for the fracture network. • Distinctive discretization methods both eligible for static condensation. • Extensive numerical experiments based on 2D/3D analytic or realistic benchmarks. • Comparative analysis with commercial softwares and several discretization methods. [ABSTRACT FROM AUTHOR]

• Plate impact tests of AM AF9628 steel reported. • Implicit FE simulations of both launching and plate impact of AF9628. • FE predictions show initial porosity increase shock rise time. • Cazacu-Stewart porous model captures shock structure of wrought and AM AF9628. • Differences in the shock structure between AM and wrought AF9628 explained. Experiments have shown that for quasi-static and moderate strain-rates (of the order of 102–103/s) the mechanical response of additively manufactured (AM) and traditionally processed high-strength steels is similar whereas the impact behavior is markedly different. In this paper, we reveal that the main reason for this difference is the retained porosity in the AM material. Fully-implicit finite element calculations are presented in which we simulate both the launching of the impact plate and the impact between the two plates. The constitutive model used is the elastic/plastic model for porous ductile materials with matrix displaying tension-compression asymmetry and Johnson-Cook hardening law that accounts for both strain-rate effects and plastic history. It is shown that even a very small initial porosity changes the wave front, decreases the Hugoniot while increasing the shock rise time, when compared to a void free material. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 steel are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured. Additive manufacturing (AM) of metals is rapidly advancing as a robust method for production of geometrically complex parts. To enhance understanding of material performance and open up additional application opportunities, dynamic characterization of newly printed alloys is required to validate their effectiveness. In this paper, we present results from plate impact testing of AF9628 steel, a newly developed high-strength low alloy martensitic steel for structural applications which require resistance to high-rate deformation. We put into evidence differences in the shock structure between the AM and the traditionally processed material. To gain understanding, we conduct fully-implicit finite element (FE) calculations in which we model both the launching of the impact plate and the impact between the two plates, respectively. An elastic/plastic damage model that accounts for the effects of the tension-compression asymmetry in plastic deformation and its influence on porosity evolution is used. The FE results reveal that even a very small amount of initial porosity leads to an increase in the shock rise time, explaining the observed trends. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured. [ABSTRACT FROM AUTHOR]

This paper presents a novel fully implicit scheme for simulating three-dimensional (3D) oil-water two-phase flow with gravity and capillary forces using the meshless generalized finite difference method (GFDM). The approach combines an implicit Eulerian scheme in time with a GFDM discretization method in space to compute implicit solutions for the pressure and saturation in the flow control equations. The research introduces an L 2 norm error formula and conducts a sensitivity analysis on the impact of varying influence domain radii on computational accuracy within the Cartesian node collocation scheme. Findings suggest that larger influence domain radii correspond to reduced computational accuracy, providing a preliminary guideline for selecting the domain radius in 3D GFDM applications. Overall, this paper presents an effective and precise meshless method for addressing two-phase flow challenges in 3D porous media, highlighting the promising prospects of GFDM in numerical simulations. [ABSTRACT FROM AUTHOR]

Highlights: [•] Falkner–Skan flow along a wedge of a non-Newtonian, power-law fluid. [•] Darcy–Brinkman–Forchheimer porous medium. [•] Wrong Grashof number mixed convection. [Copyright &y& Elsevier]

This paper applies the meshless generalized finite difference method (GFDM) to analyze the subsurface flow problem in anisotropic formations for the first time, and develops the treatment methods of anisotropic permeability tensor in continuous function and discrete distribution expressions respectively. In particular, in case of the common discrete distribution expression of anisotropic permeability tensor in reservoir simulation, this paper suggests combining general difference operators and harmonic average scheme to simply and efficiently obtain the meshless discrete scheme of the anisotropic flow equation. Three numerical examples of steady and transient flow in the rectangular computational domain, transient flow with complex boundary, and steady flow with strongly discontinuous anisotropic permeability are used to verify the high accuracy and good convergence of GFDM to handle anisotropic flow problems. Compared with the traditional mesh-based reservoir numerical simulation method that replies on laborious gridding to discretize the reservoir domain and complicated multi-point flux approximation (MPFA) to handle discrete distribution anisotropic permeability tensor, the meshless GFDM can be more practically applied to the anisotropic flow problems in the reservoir domain with complex geometry and complex boundary conditions. Besides, it is found that the radius of the influence domain has little impact on the accuracy of steady flow. For the transient flow, it generally holds that the larger the radius of the influence domain, the lower the calculation accuracy in case of Cartesian collocation. In sum, this work provides an efficient and simple meshless solver to handle anisotropic flow problems in porous media under GFDM framework, which reveals the great application potential of GFDM in reservoir numerical simulation. [ABSTRACT FROM AUTHOR]

Gas-bearing sediments are widely distributed in marine and lacustrine areas. The engineering properties of gas-bearing sediments, containing enclosed bubbles, are significantly different with that of saturated and unsaturated sediments. This paper investigates the consolidation behaviors of gas-bearing sediments with modulus varying along depth subjected to horizontal load using an extended precise integration method (XPIM). The compressibility of enclosed bubble is introduced to a new derived seepage equation and a varying modulus along depth is considered in governing equations. With the aid of integral transformation and Taylor expansion, such problems are solved by XPIM, which is proved to be markedly efficient and precise for boundary value problems of porous media than traditional numerical methods. Detailed comparisons against analytical solutions are performed to confirm the accurateness of XPIM. Extensive parametric investigations are conducted to examine the influence of saturation degree, varying modulus along depth and type of external load on the consolidation behaviors of gas-bearing sediments. The present work is conveniently utilized to evaluate the behavior of gas-bearing sediments, and subsequently the response of foundations built in gas-bearing soil areas. [ABSTRACT FROM AUTHOR]

Fractional advection-diffusion equation, as a generalization of classical advection-diffusion equation, has been always mentioned to simulate anomalous diffusion in porous media. This work introduces a meshless generalized finite difference method (GFDM) to solve a class of three-dimensional variable-order time fractional advection-diffusion equation (TFADE) in finite domains. Three examples with known analytic solutions in different domains are given to demonstrate that the method is accurate and stable. To reduce computational and storage cost, we discretize the time derivative terms of TFADE by a fast finite difference method (FFDM) based on sum-of-exponentials (SOE) approximation. Meanwhile, discretizing space derivative terms, GFDM generates a linear equation set including function values of neighboring nodes with various weight coefficients. Then the partial derivatives of TFADE are indicated as the linear system above. Also, this paper investigates the irregular mesh in the finite spatial domain, which is more closely meets the description of practice problems. Numerical results indicate that models with irregular mesh can also be simulated by GFDM which maintains high accuracy. Furthermore, the method is stable and accurate in solving three-dimensional irregular domain problems, where the relative errors can be less than 0.01%. This paper shows that FFDM based on SOE approximation can improve computational efficiency, and GFDM can flexibly and efficiently solve three-dimensional variable-order and variable-coefficient TFADE. [ABSTRACT FROM AUTHOR]

A study of nonlinear axisymmetric Rayleigh-Bénard magnetoconvection in a cylindrical enclosure filled with a dilute concentration of carbon-based nanotubes in a weakly electrically conducting Newtonian liquid heated from below for various aspect ratios is carried out. Cylindrical geometry is the prototype for heat storage devices and thermal coolant systems with a controlled environment. There is an analogy between porous media and magnetohydrodynamic problems and hence Rayleigh-Bénard magnetoconvection problem is practically important. The solution of the velocity and the temperature is in terms of the Bessel functions of the first kind and hyperbolic functions that are further used to study the marginal stability curves, heat transport, and the dynamical system. Symmetric and asymmetric boundaries of the realistic-type are considered on the horizontal and vertical bounding surfaces. The results of these boundaries are compared with those of the idealistic-type which are symmetric. A unified analysis approach is adopted for all boundary combinations in deriving the Lorenz model and studying the nonlinear dynamics. The time-dependent Nusselt numbers incorporating the effect of the curvature of the cylinder accurately captures the enhanced heat transport situation in the regular convective regime. Further, the influence of various parameters on the indicators of chaos such as the r H -plots, Lorenz attractor, bifurcation diagram, and the time series plot is investigated. The r H -plots clearly point to the appearance of chaos and also assist in determining its intensity and periodicity. The trapping region of the solution of the Lorenz model having the shape like that of a rugby-ball is highlighted in the paper. The size of the ellipsoid shrinks with increase in the strength of the magnetic field and also depends on the boundary conditions. • Axisymmetric convection in shallow cylindrical enclosures is considered. • Investigation is made for symmetric and asymmetric boundary conditions. • Convective instability, heat transports and chaos are studied. • The rH-plots Lorenz attractor, bifurcation diagrams and times-series plots are used to explore the chaotic regime. • Trapping region in the form of a rugby-ball is highlighted in the paper. [ABSTRACT FROM AUTHOR]

Natural convection (NC) in high permeable porous media is usually investigated using the Darcy–Lapwood–Brinkman model (DLB). The problem of the porous squared cavity is widely used as a common benchmark case for NC in porous media. The solutions to this problem with the DLB model are limited to steady-state conditions. In this paper, we developed a time-dependent high accurate solution based on the Fourier–Galerkin method (FG). The solution is derived considering two configurations dealing with unsteady and transient modes. The governing equations are reformulated using the stream function. The Temperature and the stream functions are expended as unknowns in space using Fourier series which are appropriately substituted in the equations. The equations are then projected to the spectral space using Fourier trigonometric trial functions. The obtained developed equations form a nonlinear differential algebraic system of equations. An appropriate technique is used to integrate the spectral system in time and to ensure high accuracy. The results of the FG method are compared to a finite element solution for different Rayleigh and Darcy numbers values. The transient and unsteady solutions are obtained with a feasible and low computational cost. The paper provides high accurate time-dependent solutions useful for benchmarking numerical models dealing with NC in porous media. The results of the developed solutions are efficient to gain physical insight into the time-dependent NC processes. [ABSTRACT FROM AUTHOR]

• Second law aspects of hybrid nanofluid in a MCHS whit porous fins are examined. • The water based silver/graphene hybrid nanofluid is used as coolant. • Frictional entropy generation augments by boosting the nanoparticle concentration. • By rising the flow rate, thermal entropy generation declines. • Artificial neural network is employed to obtain a model for the entropy generation. This paper evaluates the characteristic of second law of thermodynamic, including Bejan number and entropy generation for hybrid nanofluid containing graphene-silver nanofluid through a MCHS whit porous fins. Finite-volume technique is utilized to solve the governing equations. To simulate the problem, different porous medium thicknesses, nanoparticle concentrations, and inlet mass flow rates are used while the heat flux remains constant. The minimum values of the frictional and thermal entropy generation are 5 × 10−4 and 6.25 × 10−2, while the maximum values are 3.2 × 10−4 and 9.75 × 10−2. With increasing nanoparticle concentration up to 0.06% wt at constant porous thickness t p =200 µm, frictional entropy generation rises up by 3 × 10−5 and heat transfer rate go up while, thermal entropy generation decreases by 1.5 × 10−2. In addition, by doubling the input mass flow rate and reaching 0.02% at constant nanoparticle concentration (0.06%), thermal entropy generation decreases by 2 × 10−2 while the frictional entropy generation increases by 2.4 × 10−4. The minimum magnitude of Bejan number is 0.994. This show that the irreversibility is derived significantly from thermal entropy generation rate. Finally, an artificial neural network is employed to obtain a model for entropy generation. [ABSTRACT FROM AUTHOR]

The application of flow simulations on porous media, reconstructed through Computerized Tomography (CT) scans, has emerged as a prevalent methodology for the computation of rock permeability. However, constructing a proper 3D model of a rock sample is a real challenge, mainly due to the lack of a unified procedure. Indeed, to ensure precise outcomes, specific prerequisites must be fulfilled. This paper proposes a methodology to assess the convergence and accuracy of computed solutions from CT data to pore-scale simulations. Starting from 3D volume data obtained by X-ray CT, we develop a workflow to investigate the effects of the reconstructed shape on the permeability of a granular porous medium composed of glass beads. Indeed, the choices of CT scan resolution and digital rock discretization can compromise the quality and computational cost of numerical results. Especially in configurations of porous media with high solid volume fractions and very narrow porous spaces, as observed in solid/solid contact zones, which can be either under or over-resolved depending on the numerical tools used. Highly resolved Direct Numerical Simulations (DNS) are conducted to solve incompressible Navier–Stokes equations through porous media. Body-fitted meshes are employed to resolve irregular shapes accurately, ensuring precise results even with coarser meshes. The methodology is validated with challenging simulations of flows through simple cubic close packing of particles, incorporating various geometric surface modeling techniques. A convergence of the results with respect to grid resolution is obtained for low- to moderate-Reynolds-number flows. The numerical results indicate that permeability calculation strongly depends on surface processing. Finally, we apply these recommendations to construct accurate digital replica models generated from CT data of our assembly of randomly arranged glass beads in a tube. The study of the pressure drop convergence demonstrates an excellent agreement with the empirical correlation. • Methodology to assess digital replica accuracy from CT data to 3D pore-scale simulations. • Highly resolved Direct Numerical Simulations have been performed for porous media. • 2nd-order convergence for low porosity and low- to moderate-Reynolds-number flows. • Permeability calculation strongly depends on the surface geometric modeling of solids. • Particle surfaces are obtained from a Medical-CT scan in STL format. [ABSTRACT FROM AUTHOR]

• A fully coupled u-p format hydraulic fracturing model is developed using the numerical manifold method (NMM). • Fluid loss along fractures is incorporated by imposing flow boundary conditions, eliminating the need for filtration coefficients. • Space and time are discretized using NMM and Newmark implicit algorithm. • The model is validated through KGD hydraulic fracturing, pre-cracked specimens, and multi-fracture interference simulations. Accurate and efficient simulation of dynamic hydraulic fracturing of the saturated porous media has always been a pivotal topic in the oil and gas extraction. Leveraging the Numerical Manifold Method (NMM) and its inherent cutting technique, this paper proposes a fully coupled hydraulic fracturing model based on the u - p format, which incorporates the overall momentum balance and continuity conditions in both porous media and fractures. NMM approximations and the Newmark implicit algorithm are employed respectively to discretize the spatial and time domains, and the resulting system is solved based on the Newton-Raphson method. By imposing flow boundary conditions on the fracture surfaces, the present model accounts for fluid loss without introducing extra filtration coefficients. Using the Mohr-Coulomb-based LT criterion and the maximum circumferential stress criterion to determine whether crack propagation has occurred and crack propagation direction respectively, the present model is capable of simulating initiation and development of multiple cracks under hydraulic stimulations. Through modeling the KGD hydraulic fracturing, hydraulic fracturing of a pre-cracked cubic specimen and fracture interference phenomena during expansion of multiple fracture ports of a single injection well, accuracy and effectiveness of the model are validated. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a deep neural network approach for solving the stationary compositional two-phase equilibrium problems in porous media. A recent approach is the unified formulation advocated by Lauser et al. (2011) which contains the complementarity conditions. The advantage of this formulation lies in its potential to handle the appearance and disappearance of phases automatically. To solve numerically the system of equations, a new strategy called NPIPM (NonParametric Interior-Point Method) is proposed by Vu et al. (2021). However, the method still has some disadvantages preventing the convergence to a solution. Taking inspiration from the work of Raissi et al. (2019) for the study of nonlinear partial differential equations using Physics-Informed Neural Networks (PINN), we realize that we can apply a deep neural network to obtain the solution of the stationary compositional model containing gas and liquid. We design a deep neural network structure and define a new loss function for the problem. The effectiveness of the proposed method is validated through numerical results obtained from a series of systems with increasing components. This machine learning approach provides a promising idea to solve the curse of dimensionality issue in the sense of the increasing number of components in stationary problems. • Existing methods for solving the multiphase equilibrium problems may diverge. • Using PINN approach to solve for the two-phase equilibrium states. • Using synthetic data of different regimes to train the neural network. • Producing high-accuracy solutions even in cases other than training data sets. [ABSTRACT FROM AUTHOR]

This paper applies GFDM to analyze coupled two-phase flow and geomechanics for the first time, to our knowledge, is also the first meshless solver for two-phase fluid-solid coupling problems in porous media. Firstly, the implicit GFDM-based discrete schemes of the hyperbolic two-phase flow equation and elliptic stress equilibrium equation coupled by Biot's poroelastic theory are derived. Then the nonlinear solver based on Newton's method is used to solve the fluid pressure, water saturation, and displacement at each node simultaneously. Two technical details are found critical to the implementation of this method. The one is using different radii of the node influence domain to discretize the flow equation and the stress equilibrium equation respectively, and the other one is the selection criterion of the two radii of the node influence domain, which improves the implementation flexibility of the multi-physics coupling calculation, reduces the dissipation error of the calculation results of the convection-dominated water saturation distribution, and ensure a low computational cost. Several numerical test cases are implemented to analyze the computational efficiency and accuracy, and illustrate that GFDM can achieve good computational performance in case of regular domains, irregular domains, and different point clouds. Overall, this work may provide an important reference for building a GFDM-based general-purpose numerical simulator for multi-physics flow problems in porous media. [ABSTRACT FROM AUTHOR]

The paper covers a porous particle drying problem, which can be divided into two or three stages. The first stage is drying of surface moisture, the second stage is drying inside the particle, and the third, one which is relevant only to hygroscopic material, represents the change of particle moisture due to the change of environmental moisture. The second stage is the most relevant for the porous materials, and is, therefore, covered in more detail in this paper, with the main focus on the heat transfer inside the particle which affects the drying kinetics. The heat transfer problem inside the spherical particle has been solved using BEM, by transforming a 3D problem into a quasi 1D case by assuming uniform boundary conditions all around the particle, resulting in the solution depending only on the radial direction. The solution of the heat transfer needs to be calculated accurately as it directly affects the evaporation rate of the liquid on the interface between the dry crust and the wet core, which dictates the drying speed and affects the drying time. An in-depth analysis of space and time discretisation was performed on a typical spray drying example, where it is shown that a choice of a correct time step is cruicial for achieving good computational accuracy of the drying kinetics. The proposed numerical approach has also been tested on various drying conditions, with changing the particle size and the temperature of the drying gas, which have a largest effect on the drying kinetics. Finally, an analysis of the computed drying times is made as this is the most important parameter from the practical point of view, especially when designing the drying chambers. [ABSTRACT FROM AUTHOR]

Abstract Based on mimetic Green element method (GEM), which synthesizes some typical advantages of boundary element method (BEM), finite element method (FEM) and mimetic finite difference method (mimetic FDM), This paper study the application of mimetic GEM in the system of partial differential equations (PDEs) of oil-water two-phase flow in porous media. It is the first time to apply GEM to solve numerically the system of PDEs, which is one of novelties in this paper. For numerical simulation of oil-water two-phase flow in porous media, this paper provides a novel numerical method based on mimetic GEM, which is the other novelty of this work. [ABSTRACT FROM AUTHOR]

Pasting porous material on the inner surface of a tire is an effective means to mitigate the tire cavity resonance noise. However, its performance is highly related to the material properties and geometry. This paper proposes an eigenvalue analysis approach based on the multi-domain boundary element method (MBEM) to evaluate this performance and further help determine the optimal parameters of the porous material lining in a tire. In this approach, the porous material is equivalent to a fluid, and the MBEM is used to model the sound fields in the air and equivalent fluid domains inside the tire cavity, based on which the eigenvalue analysis is conducted and the associated nonlinear eigenproblem is solved by using a contour integral method. The accuracy and validity of the proposed method are first verified by using a two-dimensional tire model with analytical solution, and then testified by comparing with the experimental results of a real tire lined with porous materials with different flow resistivities, thicknesses and widths. Furthermore, the effects of porous materials with different parameters are investigated based on the proposed method and the optimal parameters are suggested for a typical three-dimensional tire model. [ABSTRACT FROM AUTHOR]

In this paper, the space-time generalized finite difference scheme is proposed to effectively solve the unsteady double-diffusive natural convection problem in the fluid-saturated porous media. In such a case, it is mathematically described by nonlinear time-dependent partial differential equations based on Darcy's law. In this work, the space-time approach is applied using a combination of the generalized finite difference, Newton-Raphson, and time-marching methods. In the space-time generalized finite difference scheme, the spatial and temporal derivatives can be performed using the technique for spatial discretization. Thus, the stability of the proposed numerical scheme is determined by the generalized finite difference method. Due to the property of this numerical method, which is based on the Taylor series expansion and the moving-least square method, the resultant matrix system is a sparse matrix. Then, the Newton-Raphson method is used to solve the nonlinear system efficiently. Furthermore, the time-marching method is utilized to proceed along the time axis after a numerical process in one space-time domain. By using this method, the proposed numerical scheme can efficiently simulate the problems which have an unpredictable end time. In this study, three benchmark examples are tested to verify the capability of the proposed meshless scheme. [ABSTRACT FROM AUTHOR]

This research paper examines the chaos control in porous media convection by imposing an external excitation on the system. The excitation is under the form of a quasi-periodic gravitational modulation with two incommensurate frequencies σ 1 and σ 2. This will be accomplished by taking into consideration a two-dimensional rectangular porous layer that is saturated with fluid, heated from below, and subjected to a quasi-periodic vertical gravitational modulation. The model consists of a nonlinear heat equation coupled with a system of equations representing motion under the Darcy–Brinkman law. Utilizing a spectral approach, the problem is simplified into a set of four ordinary differential equations. Three equilibria of the system are given, namely the motionless convection steady state and convection steady states. The local and global stability for the motionless convection steady state were performed. Additionally, the local stability of the other equilibria is fulfilled. The fourth-order Runge–Kutta method is used to solve the system numerically. Numerical simulations have shown that the quasi-periodic gravitational modulation plays an essential role on the fluid dynamics behavior. We find chaotic and oscillating convection regimes depending on the ratio of gravitational modulation frequencies. It was demonstrated that by properly adjusting the frequencies ratio η = σ 2 / σ 1 , transition from oscillating regime to chaos is observed and vice versa. Those transitions were checked by Poincaré section, Lyapunov exponent or phase diagram. It was concluded that controlling the dynamical behavior of the fluid in porous media may be achieved by implementing an appropriate quasi-periodic gravitational modulation. • A Darcy–Brinkman model is suggested and studied. • Spectral analysis was applied to reduce our problem to a system of three ODEs. • The local and global stability analysis of the equilibrium points were carried out. • Numerical simulations are carried out supporting the theoretical findings. • Oscillating regimes and transition to chaos are observed. [ABSTRACT FROM AUTHOR]

This paper presents an analytic approach to solving the classical problem of free boundary porous media flow. The solution is found by constructing an operator, derived from a conformal map, which is then reduced to a matrix and inverted. This matrix is then used to solve a system of linear equations with all terms in the matrix calculated exactly. To confirm the solution, we made a comparison with an iterative boundary element solution, which shows good agreement. Visual representations of the flow are also provided. • Free boundary flow in porous media solved using a conformal map. • The analytical, up to matrix inversion, solution is found. • The solution is validated by an iterative boundary element method. • Solution provides hydraulic head and streamlines through out the domain. [ABSTRACT FROM AUTHOR]

The paper shows that the quasi-static process of filling a nanoporous medium with a non-wetting liquid is a process of self-organized criticality. In the system, there are distributed stepwise noncorrelated avalanches, separated both in space and time. In addition, it is shown that in the vicinity of the critical point (the threshold pressure of the filling) and above it the "avalanche" clusters of all possible sizes arise. The revealed mechanism allows to pass further to consideration of anomalously slow relaxation as the SOC process and to understanding of uniform internal mechanisms underlying the observed phenomena in such systems. • The process of filling porous medium is a process of self-organized criticality. • The nonlinear interaction between clusters propagate avalanches. • The key role in avalanche formation is played by available pores. [ABSTRACT FROM AUTHOR]

• Time-fractional generalized Navier-Stokes equations are proposed for porous flows. • An LB model is developed to solve time-fractional generalized Navier-Stokes equations. • The influence of time-fractional effects on flows in porous media is investigated. • The non-equilibrium processes of porous flows at the REV scale are studied. Anomalous transport has been commonly observed in the fluid flow through a complex porous medium, where the evolution exhibits a complex memory-like behavior. Classical integer-order models fail to depict anomalous transport phenomena, while fractional calculus has been proved effective in describing such behavior due to its ability to characterize long memory processes. In this paper, the time-fractional generalized Navier-Stokes (N-S) equations are formulated to model anomalous transport in porous media at the representative elementary volume (REV) scale by incorporating the Caputo fractional derivative of time into the widely employed generalized N-S equations. An innovative lattice Boltzmann (LB) model is presented for solving the time-fractional generalized N-S equations. We validate the proposed LB model by conducting a numerical example with analytical solutions, and observe a good agreement between the LB results and the analytical solutions. The proposed LB model is utilized for simulating Poiseuille flow, Couette flow, and cavity flow in porous media. Unlike the previous studies, which focus on the steady state of these flows, the present work focuses on the unsteady process from the initial state to the final steady state. It is found that time-fractional effects play a significant role in the unsteady processes of these flows. As the fractional order decreases, the flows undergo a slower evolution process and the impact of Darcy number on the unsteady process becomes increasingly noticeable. The Reynolds number has a significant impact on the velocity profile in the steady state, but it has relatively little effect on the duration of the unsteady process. [ABSTRACT FROM AUTHOR]

This paper presents a 3D discrete mixed seepage model that considers the effect of fracture on pore seepage. We unify the 3D fracture-pore mixed seepage model and finite-discrete element method (FDEM) to build a coupled hydro-mechanical model to simulate the fluid-driven deformation and fracturing, which can also consider the influence of fracture propagation on fracture seepage and pore seepage. The model has been implemented in a GPU parallel multiphysics finite-discrete element software MultiFracS. For the continuum seepage problem, we conduct a parameter sensitivity analysis for the fluid exchange coefficient and propose the criterion for selecting the coefficient. Then, we verify the model to deal with 3D pore seepage in a continuum media, fracture-pore seepage in discontinuous media with a single fracture, and fracture-pore seepage in discontinuous media with multi-fractures. Finally, the coupled hydro-mechanical model is employed to study a one-dimensional consolidation and a hydraulic fracturing problem. The research shows that the simulation results are in good agreement with the analytical solutions and the experimental results, which verifies the effectiveness of the method for solving the 3D fracture-pore mixed seepage and the coupled hydro-mechanical model for dealing with seepage problems in fractured porous media and fluid-driven fracturing. [ABSTRACT FROM AUTHOR]

The paper discusses from first principles all aspects relevant to the plasticity of porous materials. Emphasis is laid on unhomogeneous yielding, defined as the process of yielding and plastic flow under gradient-free macroscopically nonuniform deformation. The nonuniformity is represented by strain localization in one or more bands of finite thickness. A universal feature of all intrinsic yield criteria is their dependence upon the normal and shear tractions resolved on the band. When specialized to isotropy, a Mohr–Coulomb criterion and a Rankine–Tresca criterion emerge as two extremes. The latter is an ideal that typifies the yield behavior of porous materials under arbitrary loadings. The general theory stands for a finite number of bands or yield systems. Its overall structure bears some features of crystal plasticity, but with dependence upon the resolved normal stress. The evolution of microstructural parameters can be given in general terms, being solely based on the kinematic constraints of unhomogeneous yielding and matrix incompressibility. Throughout the paper, the competition with homogeneous yielding, heretofore taken for granted, is analyzed with or without strain and strain-rate hardening effects. We close by discussing the thermodynamic consistency of this new class of constitutive relations and a link to strain-gradient theories. [ABSTRACT FROM AUTHOR]

The paper presents the radially and spherically symmetric problems associated with the inflation of poro-hyperelastic regions. The theory of poro-hyperelasticity is a convenient framework for modelling the mechanical behaviour of highly deformable materials in which the pore space is saturated with fluids. Including the coupled mechanical responses of both the hyperelastic porous skeleton and the fluid is regarded as an important consideration for the application of the results, particularly to soft tissues encountered in biomechanical applications. The analytical solutions for radially and spherically symmetric problems involving annular domains are used to benchmark the accuracy of a standard computational approach. The paper also generates results applicable to the hyperelastic solutions when coupling is eliminated through the presence of a highly permeable pore structure. [ABSTRACT FROM AUTHOR]

In this paper, we have developed and demonstrated a novel high-velocity impact experiment to study dynamic fragmentation of additively-manufactured metals. The experiment consists of a light-gas gun that fires a conical nosed cylindrical projectile, that impacts axially on a thin-walled cylindrical tube fabricated by 3 D printing. The diameter of the cylindrical part of the projectile is approximately twice greater than the inner diameter of the cylindrical target, which is expanded as the projectile moves forward, and eventually breaks into fragments. The experiments have been performed for impact velocities ranging from ≈ 180 m / s to ≈ 390 m / s , leading to strain rates in the cylindrical target that vary between ≈ 9000 s-1 and ≈ 23500 s − 1 . The cylindrical samples tested are printed by Selective Laser Melting out of aluminum alloy AlSi10Mg, using two printing qualities, with two different outer diameters, 12 mm and 14 mm, and two different wall thicknesses, 1 mm and 2 mm. A salient feature of this work is that we have characterized by X-ray tomography the porous microstructure of selected specimens before testing. Three-dimensional analysis of the tomograms has shown that the initial void volume fraction of the printed cylinders varies between 1.9% and 6.1%, and the maximum equivalent diameter of the 10 largest pores ranges from 143 μ m to 216 μ m , for the two different printing conditions. Two high-speed cameras have been used to film the experiments and thus to obtain time-resolved information on the mechanics of formation and propagation of fractures. Moreover, fragments ejected from the samples have been recovered, sized, weighted and analyzed using X-ray tomography, so that we have obtained indications on the effect of porous microstructure, specimen dimensions and loading velocity on the number and distribution of fragment sizes. To the authors' knowledge, this is the first paper (i) providing a systematic experimental study (34 impact tests) on the fragmentation behavior of printed specimens, and (ii) including 3 D reconstructions of dynamic cracks in porous additively-manufactured materials. • A novel high-velocity impact experiment to study dynamic fragmentation. • 3D-printed AlSi10Mg cylindrical tubes have been impacted up to 400 m/s. • Comparison of pre- and post-mortem X-ray analysis of specimens and fragments. • Different printing qualities, specimen diameters and thicknesses. • Characterization of the effect of porosity on dynamic fragmentation. [ABSTRACT FROM AUTHOR]

The determinative objective of this research is to theoretically examine MHD steady flow of the non-Newtonian Maxwell fluid due to a stretching sheet that is embedded in a porous medium with the case of convective boundary condition. The current detailed examination separately highlights the internal heat generation, viscous dissipation, variable conductivity and variable viscosity processes and their effects on evaluating the temperature distribution. Attention was especially concentrated on how to introduce similar solution for our problem which was achieved via our paper. Utilizing an efficient shooting method, the numerical solution for the coupled highly nonlinear ordinary differential equations describing the velocity and temperature is introduced. Accordingly, the important influence of all controlling parameters such as magnetic parameter, Maxwell parameter, Eckert number, the surface-convection parameter and viscosity parameter on the fluid flow becomes evident through diagrams. Further, to explain the present problem more comprehensively and clearly, both the local skin-friction coefficient and the local Nusselt number are discussed. Additionally, there is a noticeable good degree of internal consistency for the numerical results with early published data. [ABSTRACT FROM AUTHOR]

This paper deals with the comparison between two methods to treat immersed boundary conditions: on the one hand, the Brinkman penalization method (BPM); on the other hand, the direct-forcing method (DFM). The penalty method treats the solid as a porous medium with a very low permeability. It provides a simple and efficient approach for solving the Navier–Stokes equations in complex geometries with fixed boundaries or in the presence of moving objects. A new approach for the penalty-operator integration is proposed, based on a Strang splitting between the penalization terms and the convection-diffusion terms. Doing so, the penalization term can be computed exactly. The momentum term can then be computed first and then introduced into the continuity equation in an implicit manner. The direct-forcing method however uses ghost-cells to reconstruct the values inside the solid boundaries by projection of the image points from the interface. This method is comparatively hard to implement in 3D cases and for moving boundaries. In the present paper, the performance of both methods is assessed through a variety of test problems. The application concerns the unsteady transonic and supersonic fluid flows. Examples include a normal shock reflection off a solid wall, transonic shock/boundary layer in a viscous shock tube, supersonic shock/cylinder interaction, and supersonic turbulent channel flow. The obtained results are validated against either analytical or reference solutions. The numerical comparison shows that, with sufficient mesh resolution, the BPM and the DFM methods yield qualitatively similar results. In all considered cases, the BPM is found to be a suitable and a possibly competitive method for viscous-IBM in terms of predictive performance, accuracy and computational cost. However, despite its simplicity, the method suffers from a lack of regularity in the very near-wall pressure fluctuations, especially for the turbulent case. This is attributed to the fact that the method requires no specific pressure condition at the fluid/solid interface. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation. [ABSTRACT FROM AUTHOR]

Intermetallic compounds have the characteristics of long-range ordered structure and combination of metallic and covalent bonds, showing intrinsic brittleness and outstanding performance stability. The synthesis mechanism, pore structure characterization and material properties of powder metallurgy porous intermetallics are reviewed in this paper. Compared with traditional porous materials, porous intermetallics have good thermal impact resistance, machinability, thermal and electrical conductivity similar to metals, as well as good chemical corrosion resistance, rigidity and high-temperature property similar to ceramics. The mechanisms of preparation and pore formation of porous intermetallics mainly include four aspects: (1) the physical process based on the interstitial space between the initial particles and its evolution in the subsequent procedures; (2) the chemical combustion process based on the violent reaction between the initial powder components; (3) the reaction kinetics process based on the difference between the diffusion rates of elements; (4) the phase transition process based on the difference between the phase densities. The characterization parameters to the pore structure description for porous intermetallics include mainly overall porosity, open porosity, permeability, maximum pore size, pore size distribution and tortuosity factor. In terms of microstructure characterization of porous intermetallics, three-dimensional pore morphology scanning technology has the potential to reveal the internal characteristics of pore structures. The research on material properties of porous intermetallics mainly focuses on electrochemical catalytic activity, generalized oxidation resistivity at high temperature, resistance against chemical corrosion and mechanical properties, which have obvious advantages over traditional porous materials. In the field of the development of porous intermetallics, it is expected to expand their applications by further reducing the pore size to the nanoscale level to improve the filtration accuracy or increase the specific surface area, as well as introducing the high entropy design on the composition to improve the brittleness and enhance their material performance. [ABSTRACT FROM AUTHOR]

Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high solution gradients and short wavelength excitations. Despite such advantages, no public software using hybrid-Trefftz finite elements to model wave propagation through solid and porous media exists to date. This paper covers the formulation and implementation of hybrid-Trefftz finite elements for single-phase, biphasic and triphasic media, subjected to dynamic loads. The formulation is cast in a unified framework, valid for the three types of materials alike, and independent of the nature (harmonic, periodic or transient) of the applied load. Displacement, traction, elastic and absorbing boundary conditions are accommodated. The implementation is made in three novel, open-source and user-friendly computational modules which are freely distributed online. [ABSTRACT FROM AUTHOR]

A new solver, via the enthalpy multiple-relaxation lattice Boltzmann method, is developed to simulate the Ga melting (considering Ga as a phase change material) for different settings. At first, the phase change simulation of a simple bar is performed, this case is implemented to validate the heat transfer in our model via the analytical solution. Second, the solid–liquid phase change simulation with convection driven by gravity of Ga immersed in a 2D non-Darcy heterogeneous porous media, obtained from an image, is provided. Here, we present a novel process where Kozeny law is used globally for the homogeneous porosity and locally for the heterogeneous porosity. The second case is validated by experimental data already published in the literature. The fact that our solver is enforced in a single Nvidia GPU device with CUDA technology in Phyton 3.8 is a new feature introduced in this paper. Our results are given as a different approach to phase transitions embedded in porous media within an acceptable error margin from analytical and experimental results. [ABSTRACT FROM AUTHOR]

The problem of reconstruction and quantitative characterization of the microstructure of random composites, as a fundamental problem of material sciences, has been a subject of a considerable amount of literature. Thus far, previous studies used for the reconstruction either statistical microstructure descriptors or the overall property of real material. This paper makes a major contribution to research on reconstruction by formulating a procedure to recover the microstructure that produces the same effective thermal conductivity as the real composite material. In particular, our goal is to find a binary representation of 'replacement' microstructure that, being a two-phase statistically isotropic medium, produces minimal disagreement with the experimental data. Such a binary microstructure is invariant with respect to the conductivity of fluid occupying the porous space. Thus, in some sense, the paper is an extension of the concept proposed by Łydżba et al. (2018) , who showed, in the framework of analytical homogenization, that any isotropic microstructure can be represented by randomly oriented spheroids of certain distribution over the aspect ratios. The efficiency of our methodology was illustrated by examples including Wiener and Hashin-Shtrikman bounds as well as the microstructure created by the system of non-overlapping disks. Finally, we use our algorithm to construct the 'replacement' microstructure for the real porous medium, i.e., medium sand. The main advantage of the digital representation of 'replacement' microstructure over the analytical one, is that it can be further used in computational modeling as well as in 3D printing applications. [ABSTRACT FROM AUTHOR]

A fully coupled dynamic model is presented in this paper by considering the effect of matric suction, varying parameters in connection with saturation, stratification and transverse isotropy. This model can describe separate flows of two immiscible fluids in layered transversely isotropic unsaturated poroelastic media subjected to harmonically dynamic loads. The ordinary differential matrix equations of this model are derived based on Hankel integral transform and a series of algebraic manipulations. Then the final solution is obtained by conducting the extended precise integration method, and further verified against the existing solution. Numerical examples are carried out to demonstrate the effects of saturation, transversely isotropic parameters, angular frequency and soil thickness on dynamic behavior of unsaturated porous media. [ABSTRACT FROM AUTHOR]

In this paper, we will observe the wave profile that comes to a harbor of various geometries shapes with porous media at the edge of it. The governing equation is linear shallow water equation with modification by adding a friction term in the momentum equation. The analytical solution is derived to get the value of natural resonant period of the basin for various geometric. The equation will be solved numerically using finite volume method on a staggered grid. For validation, we compare our numerical results with the analytical solution. Effect of the friction term as the existence of porous media for wave's resonance will be analyzed numerically. [ABSTRACT FROM AUTHOR]

The present paper is concerned with a study of wave propagation due to incidence of an obliquely incident wave on a thin porous vertical barrier with variable porosity. Two different configurations of the barrier are considered: 1. partially immersed barrier 2. bottom standing barrier in water of finite depth. The problem is formulated in terms of a Fredholm integral equation of the second kind, where the unknown function represents the difference of potentials across the barrier. The integral equation is then solved using two methods: the boundary element method and the collocation method. Using the solution of the integral equation, the reflection coefficient and amount of energy dissipated are determined and depicted graphically. It is observed that a barrier with variable porosity induces more reflection than a barrier with constant porosity. Also the energy dissipation for barrier with variable porosity is in general less than a barrier with constant porosity. However for partially immersed long barrier, energy dissipation of waves with certain wavelength is more for barrier with variable porosity than a barrier with constant porosity. For both configurations of the barrier, a long barrier induces more reflection and dissipation of wave energy. The inertial force coefficient of the porous material of the barrier reduces the reflection and dissipation of wave energy. Also, for an obliquely incident wave, the presence of porous barrier reduces reflection and dissipation of energy as compared to a normally incident wave. • Wave scattering • Non uniformly porous barrier • Integral equation formulation • Reflection Coefficient • Energy Dissipation [ABSTRACT FROM AUTHOR]

This paper proposes a method to identify the static, fully relaxed elastic Hooke’s matrix of a porous open-cell material. The moduli are estimated through an inverse estimation method, by performing a fit of a numerical model on the measured displacements on the faces of the porous material. These displacements are obtained from a static compression along each of the three coordinate axes. The material is modelled as an orthotropic equivalent solid, of which the principal directions are not necessarily aligned with the orthonormal coordinate system in which the experiments are conducted. The angles of relative orientation accounting for the misalignment are among the properties to be estimated. The focus in this paper is on the methodology itself, and its validity is verified by applying the method to four artificial materials with different levels of anisotropy. In addition, the robustness of the method to perturbations on the input data is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we propose and verify a numerical approach to simulate fluid flow in deformable porous media without requiring the discretization to conform to the geometry of the sealed fractures (possibly intersecting). This approach is based on a fully coupled hydro-mechanical analysis and an extended finite element method (XFEM) to represent discrete fractures. Convergence tests indicate that the proposed scheme is both consistent and stable. The contributions of this paper include: (1) a new junction enrichment to describe intersecting fractures in deformable porous media; (2) the treatment of sealed fractures. We employ the resulting discretization scheme to perform numerical experiments, to illustrate that the inclination angles of the fractures and the penetration ratio of the sealed fractures are two key parameters governing the flow within the fractured porous medium. [ABSTRACT FROM AUTHOR]

Averaged effective models for inhomogeneous media with constituents of very different properties, in particular, composites, mixtures, and porous materials are considered in this paper. It is known that effective properties of composites and mixtures may differ from their components properties not only quantitatively but also qualitatively. The paper aims to demonstrate examples of appearance of qualitatively new models as a result of homogenization procedure. Media consisting of qualitatively similar components are considered. The following effective models are described: models with higher derivatives that describe dispersion of waves in composites consisting of elastic components while there is no dispersion of waves in individual components; models of compressive media for incompressible elastic materials with pores; models with long-range memory or with additional internal parameters for mixtures of viscous fluids as well as for composites consisting of elastoplastic components; models for sound propagation in mixtures of fluids that are different depending on relations between the inhomogeneity length scale and parameters linked with fluids viscosity and heat conductivity. The paper is a brief review of the results obtained by N.S. Bakhvalov and the author. [ABSTRACT FROM AUTHOR]

Purpose The paper aims to find an accurate analytic solution (series solution) for MHD stagnation point flow in porous medium for different values of Prandtl number and suction/injection parameter. Design/methodology/approach In this paper, the homotopy analysis method (HAM) with unknown convergence-control parameter has been used to derive accurate analytic solution for MHD stagnation point flow in porous medium. Findings Main findings are; the skin-friction coefficient decreases with Prandtl number, and with the increasing values of M the Nusselt number significantly increases with low Prandtl number. Practical implications The HAM with unknown convergence-control parameter can be used to obtain analytic solutions for many problems in sciences and engineering. Originality/value This paper fulfils an identified need to evaluate the accurate analytic solution (series solution) of practical problem. Some deduced results can be obtained in a limiting sense. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a general set of equations of motion and duality conditions to be imposed at macroscopic surfaces of discontinuity in partially saturated, solid-second gradient porous media are derived by means of the Least Action Principle. The need of using a second gradient (of solid displacement) theory is shown to be necessary to include in the model effects related to gradients of porosity. The proposed governing equations include, in addition to balance of linear momentum for a second gradient porous continuum and to balance of water and air chemical potentials, the equations describing the evolution of solid and fluid volume fractions as supplementary independent kinematical fields. The presented equations are general in the sense that they are all written in terms of a macroscopic potential which depends on the introduced kinematical fields and on their space and time derivatives. These equations are suitable to describe the motion of a partially saturated, second gradient porous medium in the elastic and hyper-elastic regime. In the second part of the paper an additive decomposition for the potential is proposed which allows for describing some particular constitutive behaviors of the considered medium. While the potential associated to the solid matrix deformation is chosen in the form proposed by Cowin and Nunziato (1981) and Nunziato and Cowin (1979) and the potentials associated to water and air compressibility are chosen to assume a simple quadratic form, the macroscopic potentials associated to capillarity phenomena between water and air have to be derived with some additional considerations. In particular, two simple examples of microscopic distributions of water and air are considered: that of spherical bubbles and that of coalesced tubes of bubbles. Both these cases are suitable to describe capillarity phenomena in porous media which are close to the saturation state. Finally, an example of a simple microscopic distribution of water and air giving rise to a macroscopic capillary potential depending on the second gradient of fluid displacement is presented, showing the need of a further generalization of the proposed theoretical framework accounting for fluid second gradient effects. [Copyright &y& Elsevier]

Abstract: The paper deals with a model of the homogenized fluid saturated porous material which recently was obtained by the authors using the asymptotic analysis of the Biot type medium characterized by the double porosity. The homogenized macroscopic model is featured by the fading memory effects arising from the microflow in the dual porosity. We derive the steady state formulations and discuss several topics related to the numerical implementation of the model, namely the solution procedure of the discretized microscopic problems, evaluation of the homogenized coefficients and an approximation of the convolution integrals of the macroscopic model, so that the fading memory effects are computationally tractable. Numerical examples are presented to illustrate the approximation schemes discussed in the paper. All computations were performed using the in-house developed finite element code SfePy allowing the multiscale simulations. Besides various potential engineering applications, the present model is intended for simulations of compact bone poroelasticity. [Copyright &y& Elsevier]

Single phase flow and reactive transport modelling involve solving a highly nonlinear coupled system of partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. In this paper, we propose a fully implicit finite volume method using a direct substitution approach to improve the efficiency and the accuracy of numerical computations for such systems. The approach has been developed and implemented in the framework of the parallel open-source platform DuMu X. The object oriented code allows solving reactive transport problems considering different coupling approaches. A number of 2D and 3D numerical tests were performed for verifying and demonstrating the capability of the coupled fully implicit approach for single phase flow and reactive transport in porous media. Numerical results for the reactive transport benchmark of MoMaS and long-term fate of injected CO 2 for geological storage including a comparison between the direct substitution approach and the sequential iterative approach are presented. Parallel scalability is investigated for simulations with different grid resolutions. [ABSTRACT FROM AUTHOR]

Many porous media such as natural rocks have mesoscale inhomogeneities. The characteristic sizes of such inhomogeneities are much larger than the pore sizes but much less than the characteristic scale of the problem, such as the length of the sample on which the measurements taken. In this paper, we have solved the one-particle problem for depolarization of an ellipsoidal particle located in a porous medium with electrokinetic effect. To calculate the effective physical properties of a porous medium with many interacted ellipsoidal inclusions we have applied the homogenization scheme named differential effective medium method. This method leads to some system of differential equations for the effective constant determination. General theory is illustrated by calculations of these constants for media containing spherical and ellipsoidal inclusions. [ABSTRACT FROM AUTHOR]

The main aim of this work is to derive equations describing quasi-static and quasi-stationary processes of capillary transport of liquid and gas in unsaturated porous materials. Considerations are based on the new macroscopic model of the capillary transport in porous media, proposed in the paper (Cieszko, 2016). This model has been formulated in the spirit of the theory of interacting continua and shows that the capillary processes of transport in porous materials take place in five-dimensional pressure-time-space. This means that the equations for quasi-static and quasi-stationary processes are not a simple consequence of reduction of the general system of equations. An extended definition of quasi-static processes is proposed, allowing such processes to be analysed as a special case of the general description. A nonlinear first-order evolution equation is obtained for pore saturation with mobile liquid in quasi-static processes; it simultaneously describes the non-stationary processes of saturation evolution taking place in the pressure-space continuum. A new class of processes of capillary transport in unsaturated porous materials is proposed, called quasi-stationary, and a system of strongly coupled nonlinear equations describing these processes is derived. It is shown that even the geometrically very simple boundary value problem of non-wetting liquid flow through an unsaturated porous layer is described by a system of three nonlinear coupled equations for the saturation, pressure and velocity of the liquid. [ABSTRACT FROM AUTHOR]

In this paper, we study the influence of the presence of phototactic microorganisms on thermal bioconvection in horizontal porous annulus. To this end, an additional equation describing the concentration of the microorganism cells will be added to the classical ones of heat and hydrodynamics. The Boussinesq and Darcy approximations will be under consideration due to the incompressibility of the fluid in the porous medium. The derived problem with the stream function will be descritized numerically using the alternate direction implicit finite difference method and solved via Thomas algorithm. Numerical simulations have shown that the presence of the microorganisms enhances the heat transfer and has a destabilizing effect on the natural convection. [ABSTRACT FROM AUTHOR]

In this paper, a meshfree Radial Point Collocation method (RPCM) for modelling of reactive transport involving first-order decay and adsorption is presented. Unlike conventional grid-based methods such as Finite Element (FEM) and Finite Difference Methods (FDM), it does not require nodal connectivity information for domain representation. The proposed method does not necessitate operator splitting for accommodating reactions as it is done in FEM and FDM. The model domain is divided into intersecting circular shaped local support domains. This technique solves the ill-conditioning problem associated with globally supported system and allows use of more number of nodes which increases the accuracy of models. The multi-quadrics radial basis function (MQ-RBF) is used for the approximation/interpolation of solute concentration values in the local support domain. 1D and 2D models are developed and verified against benchmark analytical solutions. Sensitivity analyses are performed for shape parameters of the MQ-RBF, support domain size and nodal density. Two case studies are presented with regular and irregular shaped domains and results are compared with FEM. The results demonstrate advantages of the proposed model over grid-based methods while handling adsorption and first-order decay reactions. This study shows that the proposed model is effective for simulating reactive transport problems in porous media. [ABSTRACT FROM AUTHOR]