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This work focuses on the development of a novel, strongly-coupled, second-order partitioned method for fluid–poroelastic structure interaction. The flow is assumed to be viscous and incompressible, and the poroelastic material is described using the Biot model. To solve this problem, a numerical method is proposed, based on Robin interface conditions combined with the refactorization of the Cauchy’s one-legged ‘ϑ-like’ method. This approach allows the use of the mixed formulation for the Biot model. The proposed algorithm consists of solving a sequence of Backward Euler–Forward Euler steps. In the Backward Euler step, the fluid and poroelastic structure problems are solved iteratively until convergence. Then, the Forward Euler problems are solved using equivalent linear extrapolations. We prove that the iterative procedure in the Backward Euler step is convergent, and that the converged method is stable when ϑ ∈ [1/2, 1]. Numerical examples are used to explore convergence rates with varying parameters used in our scheme, and to compare our method to a monolithic method based on Nitsche’s coupling approach. [ABSTRACT FROM AUTHOR]

This paper presents analytical formulations for systematically deriving the solutions of Biot’s poroelasticity in saturated multilayered media of either full-space or halfspace extents. The number of the saturated multilayer media is either n + 2 for full-space extent or n + 1 for halfspace extent, where n is a positive or zero integer. The applied loadings include the internal forces and liquid source for full-space and both internal and external loadings for halfspace region with eight cases of four boundary conditions. The mathematical tools for the formulations are classical and include the two-dimensional Fourier transform, the Hankel transform, Laplace transform as well as linear algebra. The solutions are expressed in matrix forms and each matrix is explicitly expressed with clear physical meaning and well-defined elements. The matrix solutions in the Fourier and Laplace transform domains are axially symmetric about the vertical axis. The internal and boundary conditions can be four-dimensional and the matrix solutions in the physical domain are also four-dimensional. [ABSTRACT FROM AUTHOR]

The present study investigates the transverse concentration distribution of a passive contaminant in an incompressible viscous fluid. The parallel plate device is filled with an anisotropic porous medium with boundary absorption at both the plates. Das et al. (Phys Fluids 36(2):023610, 2024) have considered a similar configuration in an oscillatory Couette flow and analyzed the solute dispersion based on the method of moments and finite difference discretization. They have suggested a control mechanism based on the anisotropic parameters on the growth of mean concentration. In the current study, we consider a combined Couette–Poiseuille device and develop an analytical solution using the small aspect ratio of the channel, ϵ . Further, we employ a multi-scale homogenization technique to derive the dispersion coefficient, mean concentration, and transverse concentration up to the third order, i.e. O (ϵ 3) . The study examines the effects of Darcy number, relative viscosity, and anisotropy parameters on the velocity profile, dispersion coefficient, as well as mean and transverse concentration distributions. The dispersion coefficient in an anisotropic medium increases to 76 % , and significantly enhances the solute dispersion over isotropic conditions. The transverse concentration variation of anisotropic medium changes by up to 80 % compared to isotropic conditions. Boundary absorption causes persistent transverse non-uniformity in concentration variation, shifting the peak downstream. When the absorption is off at one of the walls, overlapping occurs at the center. The peak transverse variation changes from a bimodal to a unimodal distribution. These findings enhance the understanding of solute dispersion in enhanced oil recovery, particularly in anisotropic porous rock structures. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to determine the conditions necessary for existence of a solution to a problem involving fuel cells. In the first part, we present the model for a proton exchange membrane fuel cell (PEMFC) single cell and we clarify the interactions of the different components namely, velocity, pressure, density, temperature, and potential. The final mathematical model consists of the Stokes–Darcy system in the fluid-porous domain altogether with the heat, charge, and diffusion equations, which involve the Fourier, Ohm and Fick fluxes, the Dufour–Soret (or thermodiffusion effect), and Peltier–Seebeck (or thermoelectrical effect) cross effects, the Nernst–Einstein relation, and the Joule heating effect. We complete the quasilinear elliptic system by considering the Beavers–Joseph–Saffman condition on the fluid-porous interface, and a Butler–Volmer-type condition, under the presence of a known limiting current, on the membrane interface. The proof of existence of weak solutions relies on the Tychonoff fixed point theorem, by providing some regularity and some smallness conditions. We divide the actual system into two systems of equations and study them separately. The novelty of the present work is to establish quantitative estimates for improving the technical hypotheses and, in particular, the smallness conditions in the two-dimensional case. Indeed, the smallness conditions only can be explicit if quantitative estimates are established. To this aim, we also establish quantitative estimates for the Poincaré and Sobolev inequalities and for some trilinear terms. [ABSTRACT FROM AUTHOR]

A variational formulation based on velocity and stress is developed for linear fluid–structure interaction problems. The well-posedness and energy stability of this formulation are established. A hybridizable discontinuous Galerkin method is employed to discretize the problem. An hp-convergence analysis is performed for the resulting semi-discrete scheme. The Crank–Nicolson method is used for temporal discretization, and the convergence properties of the fully discrete scheme are examined. Numerical experiments are presented to validate the theoretical results and demonstrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This article presents a mathematical model addressing a scenario involving a hybrid nanofluid flow between two infinite parallel plates. One plate remains stationary, while the other moves downward at a squeezing velocity. The space between these plates contains a Darcy-Forchheimer porous medium. A mixture of water-based fluid with gold (Au) and silicon dioxide (SiO2) nanoparticles is formulated. In contrast to the conventional Fourier's heat flux equation, this study employs the Cattaneo-Christov heat flux equation. A uniform magnetic field is applied perpendicular to the flow direction, invoking magnetohydrodynamic (MHD) effects. Further, the model accounts for Joule heating, which is the heat generated when an electric current passes through the fluid. The problem is solved via NDSolve in MATHEMATICA. Numerical and statistical analyses are conducted to provide insights into the behavior of the nanomaterials between the parallel plates with respect to the flow, energy transport, and skin friction. The findings of this study have potential applications in enhancing cooling systems and optimizing thermal management strategies. It is observed that the squeezing motion generates additional pressure gradients within the fluid, which enhances the flow rate but reduces the frictional drag. Consequently, the fluid is pushed more vigorously between the plates, increasing the flow velocity. As the fluid experiences higher flow rates due to the increased squeezing effect, it spends less time in the region between the plates. The thermal relaxation, however, abruptly changes the temperature, leading to a decrease in the temperature fluctuations. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates the two-grid stabilized lowest equal-order finite element method for the time-independent dual-permeability-Stokes model with the Beavers-Joseph-Saffman-Jones interface conditions. This method is mainly based on the idea of combining the two-grid and the two local Gauss integrals for the dual-permeability-Stokes system. In this technique, we use a difference between a consistent mass matrix and an under-integrated mass matrix for the pressure variable of the dual-permeability-Stokes model using the lowest equal-order finite element quadruples. In the two-grid scheme, the global problem is solved using the standard P 1 - P 1 - P 1 - P 1 finite element approximations only on a coarse grid with grid size H. Then, a coarse grid solution is applied on a fine grid of size h to decouple the interface terms and the mass exchange terms for solving the three independent subproblems such as the Stokes equations, microfracture equations, and the matrix equations on the fine grid. On the other hand, microfracture and matrix equations are decoupled through the mass exchange terms. The weak formulation is reported, and the optimal error estimate is derived for the two-grid schemes. Furthermore, the numerical results validate that the two-grid stabilized lowest equal-order finite element method is effective and has the same accuracy as the coupling scheme when we choose h = H 2 . [ABSTRACT FROM AUTHOR]

In this work, we extend recent research on the fully mixed virtual element method based on Banach spaces for the stationary Boussinesq equation to suggest and analyze a new mixed-virtual element technique for the stationary generalized Boussinesq equations, where viscosity and thermal conductivity are temperature-dependent. Besides the original thermo-fluid variables, the pseudostress and vorticity tensors of the fluid and the pseudoheat vector of the thermal system are introduced as auxiliary unknowns, and the incompressibility condition is then used to remove the pressure, which is later computed using a postprocessing formula. The resulting highly coupled formulation is then written equivalently as uncoupled problems thanks to a fixed-point strategy, so that the classical Banach Theorem, combined with the corresponding Babuška–Brezzi theory, the Banach–Nečas–Babuška Theorem, smallness-of-data assumptions, and a slight higher-regularity assumption for the exact solution, are employed to establish the unique solvability of the continuous formulation. The virtual element discretization of the uncoupled problems is based on the H (div 6 / 5) - and H (div 6 / 5) -conforming virtual element techniques. The discrete analysis is conducted in a similar manner by establishing the discrete inf-sup condition and using the discrete versions of the aforementioned theorems to demonstrate the existence of the discrete solution and derive its stability estimates. In addition, a priori error estimates are established by utilizing the Céa estimate and a suitable assumption on data for all variables in their natural norms showing an optimal rate of convergence. Finally, several numerical examples are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics. [ABSTRACT FROM AUTHOR]

This paper presents the INM RAS–MSU land surface scheme, extracted from the INM RAS Earth system model into an independent software complex and supplemented with several modules to reproduce new components and processes of the Earth system. The resulting software product is referred to as TerM (Terrestrial Model). The physical and mathematical foundations of the model, the main features of the software implementation, and examples of applications in reproducing components of the terrestrial hydrological and carbon cycles are briefly outlined. Separating the land surface block into a standalone software complex significantly saves computational resources when assessing the impact of global and regional climate changes on natural resources (including hydrological ones), ecosystem dynamics, and emissions of climate-relevant substances with high spatial detalization. Within the TerM modelling complex, the development, validation, and calibration of new parameterizations of physical and biogeochemical processes are being conducted in an autonomous mode for subsequent implementation into the full INM RAS Earth system model. [ABSTRACT FROM AUTHOR]

We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and p-adic spatial variable, which can be seen as non-Archimedean counterparts of the fractional porous medium equation. In this case, we face the problem that a p-adic ball is simultaneously open and closed, thus having an empty boundary. To address this issue, we use the algebraic structure of the field of p-adic numbers and apply the Pontryagin duality theory to construct the appropriate fractional Sobolev type spaces. We prove the existence and uniqueness results for the corresponding nonlinear equation and define an associated nonlinear semigroup. [ABSTRACT FROM AUTHOR]

In this paper, we prove that stochastic porous media equations over σ -finite measure spaces (E , B , μ) , driven by time-dependent multiplicative noise, with the Laplacian replaced by a self-adjoint transient Dirichlet operator L and the diffusivity function given by a maximal monotone multi-valued function Ψ of polynomial growth, have a unique solution. This generalizes previous results in that we work on general measurable state spaces, allow non-continuous monotone functions Ψ , for which, no further assumptions (as e.g. coercivity) are needed, but only that their multi-valued extensions are maximal monotone and of at most polynomial growth. Furthermore, an L p (μ) -Itô formula in expectation is proved, which is not only crucial for the proof of our main result, but also of independent interest. The result in particular applies to fast diffusion stochastic porous media equations (in particular self-organized criticality models) and cases where E is a manifold or a fractal, and to non-local operators L, as e.g. L = - f (- Δ) , where f is a Bernstein function. [ABSTRACT FROM AUTHOR]

We establish a framework for the existence and uniqueness of solutions to stochastic nonlinear (possibly multi-valued) diffusion equations driven by multiplicative noise, with the drift operator L being the generator of a transient Dirichlet form on a finite measure space (E , B , μ) and the initial value in F e ∗ , which is the dual space of an extended transient Dirichlet space. L and F e ∗ replace the Laplace operator Δ and H - 1 , respectively, in the classical case. This framework includes stochastic fast diffusion equations, stochastic fractional fast diffusion equations, the Zhang model, and applies to cases with E being a manifold, a fractal, or a graph. In addition, our results apply to operators - f (- L) , where f is a Bernstein function, e.g., f (λ) = λ α or f (λ) = (λ + 1) α - 1 , 0 < α < 1 . [ABSTRACT FROM AUTHOR]

In this paper, an adaptive time filter algorithm with different subdomain variable time steps for super-hydrophobic proppants based on the 3D unsteady-state triple-porosity Stokes model is proposed and analyzed. The main feature of this algorithm is the use of two different time steps in two different subdomains. Specifically, a larger step size is used in a porous medium region with a smaller flow velocity, and a smaller step size is used in a free-flow region. In addition, the central advantage of this algorithm is that it combines the advantages of a time filter algorithm and variable time steps in different subdomains, and constructs a corresponding adaptive algorithm to further improve computational efficiency. The stability and second-order convergence of the algorithm are established, and its performance is validated through numerical experiments. [ABSTRACT FROM AUTHOR]

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]

In the present paper, double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we find that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined. [ABSTRACT FROM AUTHOR]

Within this work, we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder. We provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure, stresses, and elastic displacement. We obtain the solution by performing a Laplace transform on the governing equations, which are those of Biot's poroelasticity in cylindrical polar coordinates. We enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time domain. The sensitivity analysis is then carried out, considering only the derived pressure solution. This analysis finds that the time t, Biot's modulus M, and Poisson's ratio v have the highest influence on the pressure whereas the initial value of pressure P0 plays a very little role. [ABSTRACT FROM AUTHOR]

By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise, we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary conditions. Consequently, the expected ergodicity for this turbulence model is established. [ABSTRACT FROM AUTHOR]

In this work, we present the construction of two distinct finite element approaches to solve the porous medium equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous Galerkin method. In the second approach, we introduce additional potential and velocity variables to rewrite the PME into a system of equations, for which we construct a mixed finite element method. Both approaches are first-order accurate, mass conserving, and proved to be unconditionally energy stable for their respective energies. The mixed approach is shown to preserve positivity under a CFL condition, while a much stronger property of unconditional bound preservation is proved for the log-density approach. A novel feature of our schemes is that they can handle compactly supported initial data without the need for any perturbation techniques. Furthermore, the log-density method can handle unstructured grids in any number of dimensions, while the mixed method can handle unstructured grids in two dimensions. We present results from several numerical experiments to demonstrate these properties. [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]

This study explores the effects of a first-order slip boundary condition on the magnetohydrodynamic flow and heat transfer in a Casson-based hybrid nanofluid containing copper oxide (CuO) and graphite oxide (GO) nanoparticles in methanol (CH 3 OH) . To address the critical need in advanced cooling and thermal management, the research delves into the complexities of thermal radiation, viscous dissipation, and Joule heating. To ensure comprehensive validation and robustness of the findings, we employed both the bvp4c and Keller–Box numerical methods, each chosen for its strengths in different aspects of the model problem. This dual-method approach, detailed in our comparative analysis section, enhances the scientific rigor of our results. Using an effective similarity transformation, complex governing equations are transformed into a manageable set of ordinary differential equations, which are then numerically solved. Our findings reveal that hybrid nanofluids offer enhanced thermal properties and flow adjustability compared to single-nanoparticle fluids, with significant impacts of radiation and magnetic field on the thermal boundary layer. These insights not only advance theoretical knowledge but also have substantial practical applications in fields such as medical sciences, opto- electronics, and energy systems, establishing a new benchmark in fluid dynamics and materials science for thermal management technologies. [ABSTRACT FROM AUTHOR]

On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution. [ABSTRACT FROM AUTHOR]

A combined hybrid mixed and hybridizable discontinuous Galerkin method is formulated for the flow and transport equations. Convergence of the method is obtained by deriving optimal a priori error bounds in the L 2 norm in space. Since the velocity in the transport equation depends on the flow problem, the stabilization parameter in the HDG method is a function of the discrete velocity. In addition, a key ingredient in the convergence proof is the construction of a projection that is shown to satisfy optimal approximation bounds. Numerical examples confirm the theoretical convergence rates and show the efficiency of high order discontinuous elements. [ABSTRACT FROM AUTHOR]

This study examines the behavior of an unsteady magnetohydrodynamic Casson fluid past over an exponentially accelerated vertical plate in a rotating system. The flow is driven by the combined effects of thermal radiation, heat source/sink, chemical reaction and Hall current taken into account. The non-dimensional equations governing the system are solved using the Laplace transform technique, yielding expressions that offer insights into velocity, temperature and concentration profiles. The axial velocity decreases with increasing thermal radiation and chemical reaction, while it increases with Casson and heat source/sink. The current findings are compared with previous studies, revealing substantial agreement. Additionally, the study examines skin friction, heat transfer and mass transfer rates. The insights gained from the heat transport processes have implications across various applications in cooling systems, aerospace engineering and energy storage technologies. The results of this study have direct relevance in engineering applications and are determined analytically. [ABSTRACT FROM AUTHOR]

The key interest in this paper to examine the heat and mass transport nature of Ti6Al4V–H20 based nanofluid flow and its interaction with a strong magnetic field. In this study significances of Hall current, magneto and thermo diffusions on the flow behavior are included. The induced magnetic field (IMF) and its consequences on the flow-field are also examined. The non-dimensional flow model is solved analytically by use of perturbation method. In order to scrutinize the effects of relevant flow parameters to the flow nature, the numerical values of flow behaviors corresponds to these parameters are depicted, and graphically and tabuly presented. This kind of a study has significant applications in nano science to explore the heat and mass transport characteristic of electrically conducting nanofluids. An important result noted from this study that, on incrementing the volumetric concentration of nanoparticles in the fluid employing resistance force which cause to reduce the flow velocity and enhance the temperature. The mass diffusion factor grows the flow velocity while it reduces the IMF along the main flow. A key fact noted that Hall current generates IMF by modifying the existing magnetic field. [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]

In this paper, the rotational pressure-correction schemes for the closed-loop geothermal system are developed and analyzed. The primary benefit of this projection method is to replace the incompressible condition. The system is considered consisting of two distinct regions, with the free flow region governed by the Navier–Stokes equations and the porous media region governed by Darcy’s law. At the same time, the heat equations are coupled with the flow equations to describe the heat transfer in both regions. In the closed-loop geothermal system, the rotational pressure-correction schemes are used for the Navier–Stokes equations in the free flow region, and the direct decoupled scheme is used for the other equations. Besides, the stability of the proposed methods is proved. Finally, the high efficiency and applicability of the decoupled scheme are verified by 2D/3D numerical experiments. [ABSTRACT FROM AUTHOR]

We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves the computational efficiency. The construction and the convergence proof are based on the connection to a differential equation with two time delays, namely one and two times the step size. Numerical experiments confirm the theoretical results and indicate the applicability to higher-order schemes. [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]

In two-dimensional bounded Lipschitz domains, we analyze a convective Brinkman–Forchheimer problem on the weighted spaces H 0 1 (ω , Ω) × L 2 (ω , Ω) / R , where ω belongs to the Muckenhoupt class A 2 . Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm à la Céa under the assumption that Ω is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform. [ABSTRACT FROM AUTHOR]

AbstractThis article analyses the flow across a moving surface using the magnetohydrodynamic (MHD) Williamson fluid model in detail, accounting for the effects of diffusion, nonlinear convection, and variable thermal conductivity. The heat transmission within the system is impacted by the changing thermal conductivity, which can also significantly alter the flow behavior. The effects of the moving surface on flow forms in porous media are explained here using the Darcy model. The similarity transformations are used to convert the underlying nonlinear partial differential equations into a collection of ordinary differential equations. The work uses a numerical RK4 technique to examine the complex incompressible fluid flow behavior on a moving surface. The study’s conclusions provide insight into the intricate flow patterns and shear layer forms brought on by the interaction of fluid and surface motion while taking varied thermal conductivity into account. The findings give important information for the design and optimization of engineering applications involving changeable thermal characteristics and advance our understanding of fluid dynamics in geophysical and atmospheric systems. Physical descriptions are used to depict how flow parameters behave in relation to velocity, temperature, and concentration distributions. [ABSTRACT FROM AUTHOR]

The time-dependent electrophoresis of an infinitely cylindrical particle in an electrolyte solution, saturated in a charged porous medium after the sudden application of a transverse or tangential step electric field, is investigated semi-theoretically with an arbitrary double-layer thickness in an arbitrary direction relative to the cylinder. The time-dependent modified Brinkman equation with an electric force term, which governs the fluid flow field, is used to model the porous medium and is solved by using the Laplace transform technique. Explicit formulas, for the time-dependent electrophoretic velocity of the cylindrical particle in Laplace's transform domain, have been derived for both axially and transversely when the uniform electric fields are imposed. They can also be linearly superimposed for an arbitrarily oriented relative to the electric field. Semi-analytical results for the electrophoretic velocities are presented as functions of the dimensionless elapsed time, the ratio of the particle radius to the Debye length, the particle-to-medium density ratio, and the permeability parameter of the porous medium. The results demonstrate, in general, that the growth of the electrophoretic velocities with the time scale are more slower for high permeability, and the effect of the relaxation time for unsteady electrophoresis is found to be negligible, regardless of the thickness of the double layer, the relative mass density or the permeability of the medium. The normalized transient electrophoretic velocities exhibit a consistent upward trend as the ratio of the particle radius to the Debye screening length increases. Conversely, they display a consistent downward trend as the particle-to-fluid density ratio increases, while all other parameters remain constant. The effect of the relaxation time for the transient electrophoresis is much more important for a cylindrical particle than for a spherical particle due to its smaller specific surface area. [ABSTRACT FROM AUTHOR]

A novel method is presented for explicitly solving inhomogeneous initial-boundary-value problems (IBVPs) on the half-line for a well-known coupled system of evolution partial differential equations. The so-called double-diffusion model, which is based on a simple, yet general, inhomogeneous diffusion configuration, describes accurately several important physical and mechanical processes and thus emerges in miscellaneous applications, ranging from materials science, heat-mass transport and solid–fluid dynamics, to petroleum and chemical engineering. For instance, it appears in nanotechnology and its inhomogeneous version has recently appeared in the area of lithium-ion rechargeable batteries. Our approach is based on the extension of the unified transform (also called the Fokas method), so that it can be applied to systems of coupled equations. First, we derive formally effective solution representations and then justify a posteriori their validity rigorously. This includes the reconstruction of the prescribed initial and boundary conditions, which requires careful analysis of the various integral terms appearing in the formulae, proving that they converge in a strictly defined sense. The novel solution formulae are also utilized to rigorously deduce the solution's regularity properties near the boundaries of the spatiotemporal domain. In particular, we prove uniform convergence of the solution to the data, its rapid decay at infinity as well as its smoothness up to (and beyond) the boundary axes, provided certain data compatibility conditions at the quarter-plane corner are satisfied. As a sample of important applications of our analysis and investigation of the boundary behavior of the solution and its derivatives, we both prove a novel uniqueness theorem and construct a 'non-uniqueness counterexample'. These supplement the preceding 'constructive existence' result, within the framework of well-posedness. Moreover, one of the advantages of the unified transform is that it yields representations which are defined on contours in the complex Fourier λ -plane, which exhibit exponential decay for large values of λ . This important characteristic of the solutions is expected to allow for an efficient numerical evaluation; this is envisaged in future numerical-analytic investigations. The new formulae and the findings reported herein are also expected to find utility in the study of questions pertaining to well-posedness for nonlinear counterparts too. In addition, our rigorous approach can be extended to IBVPs for other significant models of mathematical physics and potentially also to higher-dimensional and variable-coefficient cases. [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]

This study presents a comprehensive mathematical framework that applies fluid dynamics to model the spatial spread of infectious diseases with low mortality rates. By treating susceptible, infected, and treated population densities as fluids governed by a system of partial differential equations, the study simulates the epidemic’s spatial dynamics. The Monotone Upwind Scheme for Conservation Laws is employed to enhance the accuracy of numerical solutions, providing a high-resolution approach for capturing disease transmission patterns. The model’s analogy between fluid flow and epidemic propagation reveals critical insights into how diseases disperse geographically, influenced by factors like human mobility and environmental conditions. Numerical simulations show that the model can predict the evolution of infection and treatment population densities over time, offering practical applications for public health strategies. Sensitivity analysis of the reproduction number highlights the influence of key epidemiological parameters, guiding the development of more efficient disease control measures. This work contributes a novel perspective to spatial epidemiology by integrating principles of fluid dynamics, aiding in the design of targeted interventions for controlling disease outbreaks.

In this research, we present a novel enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic (possibly discontinuous) diffusion problems on general meshes. We create a polygonal dual mesh T h ∗ and its submesh T h ∗ ∗ from a primal mesh T h in such a manner that a set number of adjacent tetrahedral elements of T h ∗ ∗ are united to form each dual control volume of T h ∗ , which corresponds to a primal vertex. The weak solution of the diffusion problem is approximated by the piecewise linear functions on the subdual mesh T h ∗ ∗ . In order to capture the local continuity of numerical fluxes across the interfaces, the proposed scheme gives the auxiliary face unknowns interpolated by the multi-point flux approximation. Moreover, the consistency, coercive, and convergence properties of the method are presented within a rigorous theoretical framework. Numerical results are carried out to highlight accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Surface-subsurface filtration transport with seawater intrusion phenomena are formulated and variationally analyzed, as coupled multimedia mixed pairs of free boundary interface problems. Physically, multidomain subsurface mixed velocity-pressure fractional Darcian flow models coupled with surface evolution Stokesian mixed flows are considered. Specifically, two-phase air-fresh water above the sea level and fresh water-seawater characterizations are considered. Internal boundary synchronizing transmission conditions of multidomain nonoverlapping decompositions are modeled in terms of variational Lagrangian dual subpotential maximal monotone inclusions. Similarly, filtration transport coupling interface transmission constraints are implemented by mass flux-velocity-pressure Lagrange dual multipliers as solutions of subpotential subdifferential equations. [ABSTRACT FROM AUTHOR]

A boundary value problem of Dirichlet-transmission type for the nonlinear Darcy–Forchheimer–Brinkman and Navier–Stokes equations in two adjacent bounded Lipschitz domains from R 3 has been studied. The existence and uniqueness of a weak solution in some Sobolev spaces is obtained using a layer potential approach and a fixed point theorem, when the boundary data are chosen in some L 2 -based Sobolev spaces and are suitable small. [ABSTRACT FROM AUTHOR]

Injectivity tests involve injecting fluid through wells into an oil reservoir to gather information about its parameters. This knowledge can be valuable for improving oil production. As such, several studies on injectivity tests in multilayered reservoirs have been conducted. Typically, these studies focus only on commingled systems, which are layers separated by impermeable barriers. The present work developed an analytical model in the Laplace space for multilayered reservoirs under injectivity tests, considering formation crossflow across all layers. The accuracy of the proposed solution was verified by comparing it with a finite difference flow simulator. The results from the analytical model and numerical data are consistently similar. Additionally, the analytical solution's data is used to estimate the reservoir's equivalent permeability, which yields satisfactory accuracy for all tested cases. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the effect of a vertical constant throughflow on convective instabilities in a horizontal layer of fluid-saturated bi-disperse porous medium heated from below. Via linear instability and nonlinear stability analyses of the throughflow solution, the linear and nonlinear critical Rayleigh numbers for convective instabilities have been determined and studied as functions of the strength of the throughflow. [ABSTRACT FROM AUTHOR]