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This study deals with the analytical investigation of oscillatory squeeze film flow through a Brinkman viscoelastic Oldroyd-B fluid-saturated porous layer subject to two vertically harmonically oscillatory disks. The validity of the present proposed analytical solutions is first demonstrated for the Newtonian fluids when both Λ1 and Λ2 tend to zero by comparison with the previous literature. Results demonstrate that an increase in the elasticity parameter Λ1 correlates with a rise in axial velocities, indicating that the relaxation time Λ1 facilitates enhanced squeeze flow. In the case of squeeze film flow in porous layers, low oscillating frequencies exert minimal effects on axial velocities, independent of variations in the viscoelasticity parameter Λ1. However, at higher oscillating frequencies, axial velocities escalate with increasing the viscoelasticity parameter Λ1. Furthermore, the retardation time Λ2 of the viscoelastic fluid shows no significant effect on the axial velocity, regardless of oscillating frequency changes in both pure fluids and porous layers. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology. [ABSTRACT FROM AUTHOR]

In this short paper, some analytical results found in "Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term" by F. Capone, R. De Luca, M. Vitiello, Ricerche Mat. 68, 581–595 (2019), are recalled in order to better explore the dynamic of thermosolutal convection in a horizontal porous layer with the influence of Vadasz and Soret terms. [ABSTRACT FROM AUTHOR]

This study provides a theoretical analysis of how time-dependent injection strategies affect the development of viscous fingering in a miscible finite slice. We are specifically examining a sinusoidal injection, which is characterized by its amplitude (Γ ) and periodicity (T). This study presents two case studies: injection-extraction ( Γ > 0 ) and extraction-injection ( Γ < 0 ), which have been examined for different values of T. The extraction-injection process demonstrates that diffusion plays a prominent role, leading to a notable delay in the interaction between stable and unstable interfaces. In the injection-extraction case, the onset of fingers does not change with an increase in T, whereas the onset gets delayed in the case of extraction-injection in a nearly linear fashion as the time period increases. Additionally, by quantifying the impact of convective forces on the time-dependent injection strategy, we can gain a deeper understanding of the underlying physical mechanism responsible for the observed delay in onset at higher T values. The delayed onset of instability will have a positive impact on the separation of chemicals in chromatographic applications. [ABSTRACT FROM AUTHOR]

We present a foam displacement model with a separate balance equation for the surfactant concentration in the aqueous phase. We consider the gas mobility that depends on the surfactant concentration and the dynamic behavior of foam as Newtonian. We study traveling wave solutions for the proposed model considering a high initial water saturation (drainage scenario) and varying the injected water saturation. The traveling wave solutions are studied using phase portrait analysis and validated with direct numerical simulations. For surfactant concentration at the injection and initial conditions above the Critical Micelle Concentration (CMC), we only found traveling wave solutions in the case when these concentrations are equal. For surfactant concentration at the injection and initial conditions below the CMC, we found traveling wave solutions whenever surfactant concentration at the injection is greater or equal to that at the initial condition. [ABSTRACT FROM AUTHOR]

In this paper we present numerical solutions for thermal boundary layers that are developed during forced convection in a porous medium located above a flat plate. The basic feature of such layers is that they are nonsimilar. In our study we consider thermal nonequilibrium between the two phases. Accordingly, each phase is endowed with its own energy equation. The boundary-layer equations are solved with the local nonsimilarity method. We examine convection of air and liquid water, while the solid matrix is supposed to be made of cast iron. According to our computations, there are significant differences between the temperature distributions of the two phases, especially at short and moderate distances from the edge of the flat plate. Also, due to the high conductivity of the solid matrix, the thermal boundary layers are much thicker than the hydrodynamic one. The profile of the local Nusselt number is quite sensitive on the Prandtl number and only far downstream it scales with the square root of the distance. Finally, the validity of the local thermal equilibrium assumption is assessed via a comparative study. According to it, this assumption leads to significant inaccuracies in the temperature profiles but yields reasonable estimates for the thickness of the thermal boundary layer of the fluid. [ABSTRACT FROM AUTHOR]

This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows capturing the contact of media of different types, such as free-flow and porous media flow. We apply Chorin's projection method to decouple the system. The splitting of the system yields a momentum conservation equation and an anisotropic pressure correction equation. We propose a combination of collocated finite-volume methods to solve the problem. [ABSTRACT FROM AUTHOR]

The injection and in situ generation of foam in porous media successfully control gas mobility and improve the fluids' sweep efficiency inside porous media. Mathematical models describing this problem use two phases, foamed gas, and fluid, and usually have a term for foam generation and destruction. Moreover, the non-Newtonian foam behavior is frequently modeled using Hirasaki and Lawson's formula for foamed gas viscosity. In this paper, we detail how the traveling wave analysis can be used to estimate the propagation profiles and velocity for a range of non-Newtonian foam models in porous media at constant total superficial flow velocity. We reformulate Hirasaki and Lawson's formula in an explicit form allowing us to find traveling wave solutions for a foam model with non-Newtonian gas viscosity and a foam generation linearly dependent on the foam texture. Comparing the solution with the one for the Newtonian version allows us to analyze qualitatively and quantitatively the rheology of the foam flow in porous media. [ABSTRACT FROM AUTHOR]

This paper is concerned with the structure and properties of boundary-layer flow in a porous domain above a flat plate. The flow is generated by an incoming uniform stream at the vertical boundary of the porous domain and is maintained by an external pressure forcing. Herein we provide the parametrization of the interphasial drag in terms of a Darcy–Forchheimer law, derive the momentum boundary-layer equation and elaborate on the profile of the free-stream velocity. The boundary-layer equation is then solved numerically via the local similarity method and via two local nonsimilarity methods at different levels of truncation. The accuracy of these methods is compared via a series of numerical tests. For the problem in hand, the free-stream velocity decreases monotonically to a terminal far-field value. Once this value is reached, the velocity profile no longer evolves in the streamwise direction. The computations further reveal that, for sufficiently small external forcing, the boundary-layer thickness initially increases, reaches a peak and then decreases towards its terminal value. This unusual overshoot is attributed to the large variation of the rate of decrease of the free-stream velocity. On the other hand, our computations predict that the wall stress always decreases monotonically in the streamwise direction. [ABSTRACT FROM AUTHOR]

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor β which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter β ^ proportional to the compressibility factor β , proving that β ^ enhances the onset of convective motions. Article Highlights: The onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect. The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis. The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor. [ABSTRACT FROM AUTHOR]

This paper studies a model for flow in a fractured porous medium with intersecting fractures. The fractures are treated as lower-dimensional manifolds and then physical transmission conditions express the pressure jump and the continuity of the flux across the fractures. Specific attention is borne to the conditions when several fractures intersect. The resulting system is discretized with mixed finite element, and the well-posedness of both the continuous and the discrete problems are proved. Then a domain decomposition method is formulated, so that the problem is reduced to the set of fractures, and a simple preconditioner is proposed. Numerical results exemplify the performance of the method. [ABSTRACT FROM AUTHOR]

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data. [ABSTRACT FROM AUTHOR]

A spectral method is developed to study the steady and unsteady flow of fluid into a line sink from a horizontally confined aquifer, and the results are compared to solutions obtained implementing the finite element package COMSOLTM. The aquifer or drain is considered to be confined below so that the solutions are fundamentally unsteady. Comparison is made between the two methods in determining the drawdown of the surface. [ABSTRACT FROM AUTHOR]

In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞{L}^{\infty } stability under appropriate CFL conditions and BV{\rm{BV}} estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1{L}^{1}. Results of numerical experiments are presented to validate the theoretical analysis.

A primal C0-conforming virtual element discretization for the approximation of the bidimensional two-phase flow of immiscible fluids in porous media using general polygonal meshes is discussed. This work investigates the potentialities of the Virtual Element Method (VEM) in solving this specific problem of immiscible fluids in porous media involving a time-dependent coupled system of non-linear partial differential equations. The performance of the fully discrete scheme is thoroughly analysed testing it on general meshes considering both a regular problem and more realistic benchmark problems that are of interest for physical and engineering applications. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in horizontal porous layers filled by an electrically conducting fluid embedded in a magnetic field, is investigated on taking into account of Soret phenomenon. Sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained. Conditions guaranteeing that Hopf convection in the absence of Soret phenomenon, turns into steady convection by the Soret parameter, have been found. [ABSTRACT FROM AUTHOR]

We study a regularised version of the magnetohydrodynamics (MHD) equations, the tamed MHD (TMHD) equations. They are a model for the flow of electrically conducting fluids through porous media. We prove existence and uniqueness of TMHD on the whole space R 3 , that smooth data give rise to smooth solutions and show that solutions to TMHD converge to a suitable weak solution of the MHD equations as the taming parameter N tends to infinity. Furthermore, we adapt a regularity result for the Navier–Stokes equations to the MHD case. [ABSTRACT FROM AUTHOR]

The paper discusses the numerical algorithm constructing a three-dimensional model for a flow of two-phase incompressible fluid caused by the mass force of gravity in a porous medium. The algorithm is based on a combination of a hybrid upwind method with an explicit scheme for determination of the saturation. The hybrid upwinding allows us to take into account flows of fluid of various nature (in this case, viscous and gravitational flows) separately, which is extremely important in the case of gravitational flow with opposite directions of phase flows. The explicit scheme being extremely simple in implementation provides a small dispersion of solutions on discontinuities. The proposed algorithm is illustrated by the results of numerical experiments demonstrating the monotonicity of the method considered in this paper. [ABSTRACT FROM AUTHOR]

Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. A common way to describe the foam displacement is by using population balance models, which consider the foam texture as part of the gas phase. Numerical simulation of such equations presents serious difficulties connected to the high non-linearity in the fractional flow. The linear kinetic model is studied mathematically for large initial reservoir water saturation and all possibilities of injection saturation. It was observed that the model contains some structural instabilities, i.e., a small variation in some parameters leads to qualitatively different solutions. One of these solutions presented localized decay in relative gas mobility, indicating that this behavior is due to the equations' mathematical properties. [ABSTRACT FROM AUTHOR]

This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal metrics with power law scaling transform which, respectively, connect the temporal and spatial complexity during transport. The Hausdorff derivative model can be transformed to an advection-dispersion equation with time- and space-dependent dispersion and convection coefficients. This model is a fractal partial differential equation (PDE) defined on a fractal space and differs from the fractional PDE which is derived for non-local transport of particles on a non-fractal Euclidean space. As an example of applications of this model, an explicit solution with a constant diffusion coefficient and flow velocity subject to an instantaneous source is derived and fitted to the breakthrough curves of tritium as a tracer in porous media. These results are compared with those of a scale-dependent dispersion model and a time-scale dependent dispersion model. Overall, it is found that the fractal PDE based on the Hausdorff derivatives better captures the early arrival and heavy tail in the scaled breakthrough curves for variable transport distances. The estimated parameters in the fractal Hausrdorff model represent clear mechanisms such as linear relationships between the orders of Hausdorff derivatives and the transport distance. The mathematical formulation is applicable to both solute transport and water flow in porous media. [ABSTRACT FROM AUTHOR]

The numerical modelling of flows in geologic porous media, accounting for plastic behaviour of rocks at high temperatures and hydrofracturing at high fluid pressures, is required for a better understanding of hydrothermal and volcanic systems. The investigation of these systems is limited given the lack of reliable and available reservoir simulation software that accounts for complicated rock behaviour at elevated temperatures. In this paper, we present such software as an extension of the MUFITS reservoir simulator. We describe the mathematical model utilised for modelling the permeability changes of elastic and plastic rocks and input data formats to the simulator. We present several application examples related to the modelling of brittle–ductile transition in hydrothermal systems, in particular perturbed with the emplaced degassing magma body, and provide the corresponding simulator input data to facilitate and ease its further usage. [ABSTRACT FROM AUTHOR]

We describe and analyze a streamline-upwinded, Petrov–Galerkin (SUPG) method for numerical simulation of transport models with adsorption kinetics. Specifically, we rewrite the adsorption term to pose the problem using a single mass accumulation term for the liquid phase concentration. The rate of adsorption is used in the nonlinear coefficient for the mass accumulation. We use streamline upwinding to stabilize the advection-dominated applications we consider. We provide a priori error analysis verified by numerical results, and we provide additional numerical results demonstrating the usefulness of our scheme. We consider a variety of adsorption model parameters and describe the performance of our algorithm in these cases. [ABSTRACT FROM AUTHOR]

This article unveils the combined impact of heat generation/absorption and Joule heating on MHD flow of Ag-H2O nanofluid into a porous stretching/shrinking divergent/convergent channel with viscous dissipation and solid volume fraction. The mathematical modeling is presented for the existing equations of continuity, momentum, and energy fraction. The reduced boundary value problem is solved numerically employing Runge-Kutta-Fehlberg (RKF) method via shooting scheme and then the outcomes are sketched and interpreted. The results explore that the thermal boundary layer thickness of the stretching divergent and the shrinking divergent channels enhance by increasing the value of the Eckert number, while the opposite tendency is scrutinized on the momentum boundary layer thickness by increasing the value of the porosity parameter for the stretching divergent and the shrinking convergent channels. [ABSTRACT FROM AUTHOR]

Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field). Recently, closer to the spirit of PDF models for turbulent flows, some approaches have used this statistical viewpoint also in pore-scale transport processes (fully resolved porous media models). When a concentration field is transported, by advection and diffusion, in a heterogeneous medium, in fact, spatial PDFs can be defined to characterise local fluctuations and improve or better understand the closures performed by classical upscaling methods. In the study of hydrodynamical dispersion, for example, PDE-based PDF approach can replace expensive and noisy Lagrangian simulations (e.g., trajectories of drift-diffusion stochastic processes). In this work we derive a joint position-velocity Fokker–Planck equation to model the motion of particles undergoing advection and diffusion in in deterministic or stochastic heterogeneous velocity fields. After appropriate closure assumptions, this description can help deriving rigorously stochastic models for the statistics of Lagrangian velocities. This is very important to be able to characterise the dispersion properties and can, for example, inform velocity evolution processes in continuous time random walk dispersion models. The closure problem that arises when averaging the Fokker–Planck equation shows also interesting similarities with the mixing problem and can be used to propose alternative closures for anomalous dispersion. [ABSTRACT FROM AUTHOR]

An explicit computational algorithm is developed to simulate complex flow of multiphase multicomponent slightly compressible fluid through porous media in view of heat sources. The proposed algorithm is based on the original model of porous media flow constructed by the analogy with the quasigasdynamic system of equations including the total energy conservation equation and modified to change the continuity equation type from parabolic to hyperbolic. It is approximated by a three-level explicit difference scheme having the second order of approximation in time and in space with a rather mild stability condition. The model takes into account gravitational and capillary forces, includes strongly nonlinear functions of the relative phase permeability. For the description of mass and energy transfer between the phases the model is generalized to account for multicomponent fluid structure. Conservation laws are formulated now for the components in terms of mass concentrations of components in the phases. The dependence of phase density and dynamic viscosity on pressure, temperature and multicomponent composition should be noted. Constants of the phase equilibrium close the system of equations. The created approach has been verified by test predictions of two- and three-phase fluid flows. Physically correct results were obtained, a good agreement with results by other authors was observed. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained. [ABSTRACT FROM AUTHOR]

A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem, we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment. [ABSTRACT FROM AUTHOR]

A model for thermal convection of a fluid saturating an inclined layer of porous medium with a Brinkman law and stress-free boundary conditions is studied. When the Darcy number D~a is zero, this problem has been studied by Rees and Bassom (Acta Mech 144(1-2):103-118, 2000). When the Brinkman term is present in the model (D~a≠0) the basic motion is a combination of hyperbolic and polynomial functions. With the Chebyshev collocation method we study the linear instability of the basic motion for three-dimensional perturbations. We also give nonlinear stability conditions and, for longitudinal perturbations, we prove the coincidence of linear and nonlinear critical Rayleigh numbers. [ABSTRACT FROM AUTHOR]

In this work we are interested in single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than other characteristic sizes, can allow one part of the domain to slide past to the other. We propose a mathematical scheme where a reduced model for the fault flows is employed yielding a problem of co-dimension one. The hybrid finite volume method is used to obtain the discretized problem, which uses two different meshes on each side of the fault. These two meshes can move with the corresponding domain, resulting in non-matching grids between the two parts of the fault. In an earlier paper a mathematical scheme was proposed where the numerical discretization considers the hybrid finite volume method. In this paper we focus on the well-posedness of the continuous problem, the convergence of the discretized problem, and we support the theoretical findings with several numerical tests. [ABSTRACT FROM AUTHOR]

Two-phase flow through a porous medium with hysteresis effects is considered. The model consists of a system of two coupled nonlinear equations: a transport equation for the water saturation and an evolution equation for the hysteresis variable. The latter is not in conservation form and contains discontinuous functions of the two unknown variables as coefficients. Some qualitative properties of piecewise smooth solutions of the system are proved. In particular, the hysteresis variable is shown to satisfy a maximum principle, and that its total variation is bounded by the total variation of its initial value. The traveling waves are investigated under the assumption that the convective term is convex. Riemann solvers for the inviscid system are constructed. Non-uniqueness due to hysteresis loops is finally discussed; several solutions are discarded by the maximum principle for the hysteresis variable. [ABSTRACT FROM AUTHOR]

The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by correction terms to respect the local pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D models corresponding to the portal and hepatic veins are coupled with the 3D model through point sources, or sinks. The contrast fluid saturation is governed by transport equations adapted for the 1D and 3D flow models. The complex perfusion model has been implemented using the finite element and finite volume methods. We report numerical examples computed for anatomically relevant geometries of the liver organ and of the principal vascular trees. The simulated tissue density corresponding to the CT examination output reflects a pathology modeled as a localized permeability deficiency. [ABSTRACT FROM AUTHOR]

A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem generalizes two distinct approaches that are being used with success in the applications to model different flows through porous media. The novelty of the problem relies on the consideration of the classical Navier-Stokes equations with a feedback forces field, whose presence in the momentum equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. By assuming suitable growth conditions on the feedback forces field and on the function that describes the rate of dissipation of the TKE, as well as on the production term, we will prove the existence of the velocity field and of the TKE. The proof of their uniqueness is made by assuming monotonicity conditions on the feedback forces field and on the turbulent dissipation function, together with a condition of Lipschitz continuity on the production term. The existence of a unique pressure, will follow by the application of a standard version of de Rham’s lemma. [ABSTRACT FROM AUTHOR]

In the upscaling from pore to continuum (Darcy) scale, reaction and deposition phenomena at the solid–liquid interface of a porous medium have to be represented by macroscopic reaction source terms. The effective rates can be computed, in the case of periodic media, from three-dimensional microscopic simulations of the periodic cell. Several computational and semi-analytical models have been studied in the field of colloid filtration to describe this problem. They typically rely on effective deposition rates defined by complex fitting procedures, neglecting the advection-diffusion interplay, the pore-scale flow complexity, and assuming slow reactions (or large Péclet numbers). Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to several conceptual inconsistencies and significant errors. To study more accurately the dependence of deposition on the flow parameters, in this work we advocate a clear distinction between the surface processes (that altogether defines the so-called attachment efficiency), and the pore-scale processes. With this approach, valid when colloidal particles are small enough, we study Brownian and gravity-driven deposition on a face-centred cubic (FCC) arrangement of spherical grains, and define a robust upscaling based on a linear effective reaction rate. The case of partial deposition, defined by an attachment probability, is studied and the limit of perfect sink is retrieved as a particular case. We introduce a novel upscaling approach and a particularly convenient computational setup that allows the direct computation of the asymptotic stationary value of effective rates. This allows to drastically reduce the computational domain down to the scale of the single repeating periodic unit. The savings are ever more noticeable in the case of higher Péclet numbers, when larger physical times are needed to reach the asymptotic regime and thus, equivalently, much larger computational domain and simulation time would be needed in a traditional setup. We show how this new definition of deposition rate is more robust and extendable to the whole range of Péclet numbers; it also is consistent with the classical heat and mass transfer literature. [ABSTRACT FROM AUTHOR]

We model random locations of spatial interfaces of heterogeneities in porous media by means of the hybrid stochastic Galerkin (HSG) approach. This approach extends the concept of the generalized polynomial chaos (PC) expansion for a multi-element decomposition of the multidimensional stochastic space. In this way, the physically two-dimensional hyperbolic-elliptic fractional flow formulation for two-phase flow in heterogeneous porous media is transformed from a random partial differential equation into a deterministic system for the coefficients of the PC expansion of the primary unknown saturation, total velocity, and global pressure. The hyperbolic part is discretized based on a central-upwind finite volume scheme along with a mixed finite element method for the elliptic part. The latter partly uses the tensor product structure of the saddle point system together with appropriate preconditioning to speed up the computations. Since we use the sequential implicit pressure explicit saturation (IMPES) approach, the elliptic part is solved in every time step. The proposed method is particularly well-suited for parallel computations and allows for the consideration of a huge variety of complex flow problems. We illustrate the power of the method by means of several striking numerical examples of different complexities including their numerical convergence analysis. [ABSTRACT FROM AUTHOR]

We prove time decay of solutions to the Muskat equation in 2D and in 3D. In the previous work, the following norms were utilized to prove global existence of solutions to the Muskat problem: In this paper, for the 3D Muskat problem, given initial datafor somel≥3 such thatfor a constantk0≈1∕5, we prove uniform in time bounds of ∥f∥s(t) for −2

In this paper we present a framework for computational homogenization of the fluid–solid interaction that pertains to the coupled deformation and flow of pore fluid in a fluid-saturated porous material. Large deformations are considered and the resulting problem is established in the material setting. In order to ensure a proper FE-mesh in the fluid domain of the RVE, we introduce a fictitious elastic solid in the pores; however, the adopted variational setting ensures that the fictitious material does not obscure the motion of the (physical) solid skeleton. For the subsequent numerical evaluation of the RVE-response, hyperelastic properties are assigned to the solid material, whereas the fluid motion is modeled as incompressible Stokes’ flow. Variationally consistent homogenization of the standard first order is adopted. The homogenization is selective in the sense that the resulting macroscale (upscaled) porous media model reminds about the classical one for a quasi-static problem with displacements and pore pressure as the unknown macroscale fields. Hence, the (relative) fluid velocity, i.e. seepage, “lives” only on the subscale and is part of the set of unknown fields in the RVE-problem. As to boundary conditions on the RVE, a mixture of Dirichlet and weakly periodic conditions is adopted. In the numerical examples, special attention is given to an evaluation of the Biot coefficient that occurs in classical phenomenological models for porous media. [ABSTRACT FROM AUTHOR]

Porous horizontal layers are considered. A class of non-constant porous throughflows, 2D in vertical planes, is obtained. The global stability conditions and the 'cold convection instability' conditions are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we study the macroscopic modeling of a steady fluid flow in an ɛ-periodic medium consisting of two interacting systems: fissures and blocks, with perme-abilities of different order of magnitude and with the presence of flow barrier formulation at the interfacial contact. The homogenization procedure is performed by means of the two-scale convergence technique and it is shown that the macroscopic model is a one-pressure field model in a one-phase flow homogenized medium. [ABSTRACT FROM AUTHOR]