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We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the problem is nonlinear. We propose a discretization of this equation that combines Euler's implicit scheme in time and spectral methods in space. We prove optimal a priori error estimates and present some numerical experiments which confirm the interest of the discretization. [ABSTRACT FROM AUTHOR]

A third-order in time numerical IMEX-type algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors' knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes-Darcy system possessing its favorable efficiency, stability, and accuracy properties. [ABSTRACT FROM AUTHOR]

Flow through arrays of micropillar embedded inside microfluidic chip systems is important for various microfluidic devices. It is critical to accurately predict the mass flow rate through pillar arrays based on the pillar design. This work presents a dissipative particle dynamics (DPD) model to simulate a problem of flow across periodic arrays of circular micropillar and investigates the permeability of two types of micropillar arrays. The flow fields including horizontal and vertical velocity fields, the number density field, and the streamline of the flow are analyzed. The predicted solid volumes by the presented DPD simulation of both types of arrays are quite close to the actual counterparts. These quantitative agreements show usefulness and effectiveness of the DPD model in simulating arrays of micropillar. By comparing two types of micropillar arrangement patterns, we find that the arrangement pattern of micropillar does not have significant influence on the permeability of the array. [ABSTRACT FROM AUTHOR]

A stability analysis of linearized Rayleigh-Bénard convection in a densely packed porous layer was performed using a matrix differential operator theory. The boundary temperatures were assumed to vary periodically with time in a sinusoidal manner. The correction in the critical Darcy-Rayleigh number was computed and depicted graphically. It was shown that the phase difference between the boundary temperatures rather than the frequency of modulated temperatures decides the nature of influence of modulation on the onset of convection. Conclusions were drawn regarding the possible transitions from harmonic to subharmonic solutions. The results on the onset of thermally modulated convection in a rectangular porous enclosure were obtained using those on the modulated Darcy-Bénard convection. [ABSTRACT FROM AUTHOR]

This article deals with the discretization of hybrid dimensional Darcy flows in fractured porous media. These models couple the flow in the fractures represented as surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of gradient schemes which accounts for a large family of conforming and nonconforming discretizations. The vertex approximate gradient scheme and the hybrid finite volume scheme are extended to such models and are shown to verify the gradient scheme framework. Our theoretical results are confirmed by numerical experiments performed on tetrahedral, Cartesian and hexahedral meshes in heterogeneous isotropic and anisotropic porous media. [ABSTRACT FROM AUTHOR]

The present paper deals with the multiple solutions and their stability analysis of non-Newtonian micropolar nanofluid slip flow past a shrinking sheet in the presence of a passively controlled nanoparticle boundary condition. The Lie group transformation is used to find the similarity transformations which transform the governing transport equations to a system of coupled ordinary differential equations with boundary conditions. These coupled set of ordinary differential equation is then solved using the Runge- Kutta-Fehlberg fourth-fifth order (RKF45) method and the ode15s solver in MATLAB. For stability analysis, the eigenvalue problem is solved to check the physically realizable solution. The upper branch is found to be stable, whereas the lower branch is unstable. The critical values (turning points) for suction (0 < s < s) and the shrinking parameter (χ < χ < 0) are also shown graphically for both no-slip and multiple-slip conditions. Multiple regression analysis for the stable solution is carried out to investigate the impact of various pertinent parameters on heat transfer rates. The Nusselt number is found to be a decreasing function of the thermophoresis and Brownian motion parameters. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a model describing the global behavior of the two-phase incompressible flow in fractured porous media. The fractured medium is regarded as a porous medium consisting of two superimposed continua, a connected fracture system, which is assumed to be thin of order, wherebeing the relative fracture thickness, and an–periodic system of disjoint matrix blocks. We derive the global behavior of the fractured medium by passing to the limit as, taking into account that the permeability of the blocks is proportional to, while the permeability of the fractures is of order one and obtain the corresponding global–model, i.e. the homogenized model with the coefficients depending on the small parameter. In the–model, we linearize the cell problem in the matrix block and then by letting, we obtain the macroscopic model which does not depend onand, and is fully homogenized in the sense that all the coefficients are calculated in terms of given data and do not depend on the additional coupling or cell problems. [ABSTRACT FROM AUTHOR]

Peaceman's equivalent well-cell radius for 2D Cartesian grids has been generalized to 2D uniform Voronoi grids consisting of stretched hexagons in an isotropic medium. An analytical expression for the equivalent well-cell radius for infinitely fine grids is derived. The derivation is performed by comparison of analytical and numerical solution for boundary value problems with one or two wells. Since the well-cell radius varies slowly with the grid fineness, the found formula can be considered representative for all grid sizes. [ABSTRACT FROM AUTHOR]

Peaceman's equivalent well-cell radius for 2D square grids has been generalized to 2D grids consisting of regular hexagons. The development consists of the following steps. Firstly, the analytical solution for the pressure drop between injector and producer for wells in a seven-spot pattern is determined. Secondly, this solution is compared with the numerical solution on hexagonal grids for a sixth of a seven-spot pattern. Finally, the equivalent well-cell radius is calculated, and its asymptotic behavior for infinitely fine grids is derived. The results are valid for both steady-state and unsteady-state conditions. [ABSTRACT FROM AUTHOR]

In this paper, an incompressible couple stress fluid flow with magnetic field in a porous channel with expanding or contracting walls and slip boundary condition is considered. Lie group analysis and group invariant solutions are obtained, the governing equations are reduced to nonlinear ordinary differential equations. The resulting equations are solved analytically, also this equations are solved by using Adomian method. The graphs for the axial and the normal velocity components and the pressure distribution for different values of the physical and geometric parameters are plotted and discussed. Finally, the comparison between the analytic and Adomian methods is discussed. It is found that for no-slip case ϕ = 0 the fluid adheres to the walls and axial velocity is maximum at the center of the channel, also by increasing the slip parameter the velocity at the channel walls increases. However, it decreases at center of the channel by increasing slip parameter. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical model for a fully developed flow through a composite porous channel. The channel consists of a fluid layer sandwiched between two porous layers. A generalized Brinkman-extended Darcy model for the porous layers and Navier-Stokes equations for the fluid layer are used to investigate the flow in detail. The continuity of stress and velocity are used at the interface and no slip at the impermeable walls. We assume that the porous layers are anisotropic. Accordingly, $$\varphi $$ is taken as the angle between the horizontal direction and the principal axes with permeability $$K_{2}$$ or $$K_{4}$$ for the lower or upper porous layers considering the anisotropic nature of the porous medium. It is shown that the anisotropic permeability and orientation angle $$\varphi $$ have a strong effect on the fluid flow and skin friction. We present some important findings based on the response to variations in the anisotropy. [ABSTRACT FROM AUTHOR]

Oblique wave scattering by multiple porous, flexible barriers is studied in a two-layer fluid in both the cases of surface-piercing and bottom-standing partial barriers in water of finite depth. The mathematical problem is handled for a solution using a generalized orthogonal relation suitable for a two-layer fluid along with the least square approximation method for single and double barriers. Various characteristics of the eigensystem, including convergence of the eigenfunction expansions for the velocity potentials associated with surface gravity waves in two-layer fluid, are derived. Wave scattering by multiple barriers is studied using a wide-spacing approximation method and compared with the solution obtained through the least square approximation method in the case of double barriers. The effectiveness of the barrier system on wave scattering is analyzed in different cases by analyzing the scattering coefficients in surface and internal modes, surface and interface wave elevations, deflection of the flexible barriers under wave action, and wave loads on the barriers. It is observed that multiple zeros in wave reflections occur for waves in surface and internal modes for various values of nondimensional barrier spacing and an oblique angle of incidence. Further, the condition for Bragg resonance is derived in the case of multiple barriers in a two-layer fluid. In the case of wave scattering by double barriers, for certain combinations of barrier spacing and porous-effect parameter, optimum wave forces are exerted for the same angle of incidence. The findings of the present study are likely to play a significant role in the protection of marine facilities from wave action. [ABSTRACT FROM AUTHOR]

We consider the incompressible inhomogeneous Navier–Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance relation for this system holds for weak solutions if the velocity, density, and pressure belong to a range of Besov spaces of smoothness 1/3. A density-dependent version of the classical Kármán–Howarth–Monin relation is derived. [ABSTRACT FROM AUTHOR]

We consider nonlinear parabolic equations involving fractional diffusion of the form $${\partial_t u + {(-\Delta)}^{s} \Phi(u)= 0,}$$ with $${0 < s < 1}$$ , and solve an open problem concerning the existence of solutions for very singular nonlinearities $${\Phi}$$ in power form, precisely $${\Phi'(u)=c\,u^{-(n+1)}}$$ for some $${0 < n < 1}$$ . We also include the logarithmic diffusion equation $${\partial_t u + {(-\Delta)}^{s} \log(u)= 0}$$ , which appears as the case $${n=0}$$ . We consider the Cauchy problem with nonnegative and integrable data $${u_0(x)}$$ in one space dimension, since the same problem in higher dimensions admits no nontrivial solutions according to recent results of the author and collaborators. The limit solutions we construct are unique, conserve mass, and are in fact maximal solutions of the problem. We also construct self-similar solutions of Barenblatt type, which are used as a cornerstone in the existence theory, and we prove that they are asymptotic attractors (as $${t\to\infty}$$ ) of the solutions with general integrable data. A new comparison principle is introduced. [ABSTRACT FROM AUTHOR]

A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived a posteriori error estimator for the velocity and pressure error in $$L^{2}$$ -norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator. [ABSTRACT FROM AUTHOR]

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]

The thermal radiation energy is the clean energy with a much lower environmental impact than the conventional energy. The objective of the present work is to investigate theoretically the effect of copper nanoparticles and carbon nanotubes (CNTs) in the presence of base fluid (water) with the variable stream condition due to the thermal radiation energy. Single-walled carbon nanotubes (SWCNTs) in the presence of base fluid flow over a porous wedge play a significant role compared to those of copper nanoparticles on absorbing the incident solar radiation and transiting it to the working fluid by convection. [ABSTRACT FROM AUTHOR]

A kinetically-based system of equations for three-phase porous media flow simulation is considered. A simple case with the following assumptions is discussed: phase transitions are absent, phases do not dissolve and do not mix, the rock compressibility is negligible. Such systems are under consideration in applied problems when the pressure changes slightly and thermal processes are absent, for example, in environmental problems. The continuity equation is modified via introduction of the regularizing term and the second-order time derivative. Due to conversion to the hyperbolic type the corresponding difference equation stability is improved. An explicit algorithm is developed and adapted to high-performance computing systems. High parallelization efficiency is achieved on a classical cluster as well as on a hybrid cluster with graphics accelerators. [ABSTRACT FROM AUTHOR]

A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics. [ABSTRACT FROM AUTHOR]

A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated. [ABSTRACT FROM AUTHOR]

In this paper, we present a reduced model of methane hydrate formation in variable salinity conditions, with details on the equilibrium phase behavior adapted to a case study from Ulleung Basin. The model simplifies the comprehensive model considered by Liu and Flemings using common assumptions on hydrostatic pressure, geothermal gradient, and phase incompressibility, as well as a simplified phase equilibria model. The two-phase three-component model is very robust and efficient as well as amenable to various numerical analyses, yet is capable of simulating realistic cases. We compare various thermodynamic models for equilibria as well as attempt a quantitative explanation for anomalous spikes of salinity observed in Ulleung Basin. [ABSTRACT FROM AUTHOR]

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and distance, and of vanishing viscosity. Under suitable conditions on the particle size, particle distance, and viscosity, we prove that solutions of the Navier-Stokes system in the perforated domain converges to solutions of the Euler system, modeling inviscid, incompressible flow, in the full plane. That is, the flow is not disturbed by the porous medium and becomes inviscid in the limit. Convergence is obtained in the energy norm with explicit rates of convergence. [ABSTRACT FROM AUTHOR]

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the global well-posedness of the 3D incompressible critical dissipative porous media equation with small initial data in the Triebel-Lizorkin space $F^{s}_{p,q}(\mathbb{R}^{3})$. By a pointwise exponential decay estimate on the Poisson semigroup $e^{-t\nu\sqrt{-\Delta}}$ and the Fourier localization technique, we generalize the global well-posedness in the Sobolev spaces $H_{p}^{s}(\mathbb{R}^{3})=F^{s}_{p,2}(\mathbb{R}^{3})$ and $H^{s}(\mathbb {R}^{3})=F^{s}_{2,2}(\mathbb{R}^{3})$ into the general Triebel-Lizorkin spaces $F^{s}_{p,q}(\mathbb{R}^{3})$ with $s>\frac{3}{p}$, $p, q\in (1,\infty)$. [ABSTRACT FROM AUTHOR]

We analyze evolution of the interface between immiscible fluids of different densities in porous media. The fluids can be compressible ( CO or natural gases) or incompressible (oil, water). We rigorously prove that, if the heavier fluid is on the top and there are no sink or source, a tip of the interface will move in the direction of the gravity (if the tip is directed toward the bottom) or the buoyancy (if the tip is directed toward the top).We also showhowthe sink/source influence propagation of the interface and provide numerical examples. [ABSTRACT FROM AUTHOR]

In this short note, we study the stability of flows of a fluid through porous media that satisfies a generalization of Brinkman's equation to include inertial effects. Such flows could have relevance to enhanced oil recovery and also to the flow of dense liquids through porous media. In any event, one cannot ignore the fact that flows through porous media are inherently unsteady, and thus, at least a part of the inertial term needs to be retained in many situations. We study the stability of the rest state and find it to be asymptotically stable. Next, we study the stability of a base flow and find that the flow is asymptotically stable, provided the base flow is sufficiently slow. Finally, we establish results concerning the uniqueness of the flow under appropriate conditions, and present some corresponding numerical results. [ABSTRACT FROM AUTHOR]

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are $${C^{\infty}}$$ on $${(0,T)\times \mathbb{R}^{N}}$$ for any $${T > 0}$$ . Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to $${\mu(\rho)=\rho^{\alpha}}$$ with $${\alpha > 1}$$ . Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density $${\rho_{0}}$$ . [ABSTRACT FROM AUTHOR]

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model (DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density. [ABSTRACT FROM AUTHOR]

In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations. [ABSTRACT FROM AUTHOR]

In this work we present the construction of the Riemann solution for a system of two conservation laws representing displacement in immiscible three-phase flow. The porousmedium is initially filled with oil and small amounts of water and gas; then a fixed proportion of water and gas is injected. We use the wave curve method to determine the wave sequences in the Riemann solution for arbitrary initial and injection data in the above mentioned class. We show the L-stability of the Riemann solution with variation of data. We do not verify uniqueness of the Riemann solution, but we believe that it is valid. [ABSTRACT FROM AUTHOR]

Well-known results on the filtration laws for the Newtonian fluids, obtained by the homogenization technique, served as a motivation to derive similar, analogous counterparts for the specific type of a non-Newtonian fluid. We studied a stationary filtration of the polymer fluid (Ostwald-de Waele model) through the periodic porous medium. Dimensions in the periodic domain are controlled by the two small parameters, one representing the period and the other controlling the ratio of a solid region and a fluid region of the porous medium. We found the specific critical size of the obstacles representing the impermeable part for which homogenization of the nonlinear Stokes flow results in the nonlinear Brinkman-type law by means of-convergence. [ABSTRACT FROM AUTHOR]

An approximate solution to Richards' equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method (DTM) with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution. [ABSTRACT FROM AUTHOR]

The onset of periodic and aperiodic convection in a binary nanofluid saturated rotating porous layer is studied considering constant flux boundary conditions. The porous medium obeys Darcy's law, while the nanofluid envisages the effects of the Brownian motion and thermophoresis. The Rayleigh numbers for stationary and oscillatory convection are obtained in terms of various non-dimensional parameters. The effect of the involved physical parameters on the aperiodic convection is studied graphically. The results are validated in comparison with the published literature in limiting cases of the present study. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive multigrid conjugate gradient method is applied to the inversion of the space-dependent permeability function in a nonlinear diffusion equation, which plays an important role in promoting the permeability estimation within multiphase porous media flow. The forward problem is discretized using finite-difference methods and the estimation is formulated as a least-square minimization problem with a regularization term. Firstly, the conjugate gradient method for optimization is used to solve this parameter identification problem. Secondly, to reduce the amount of calculation, the idea of multigrid inversion and the necessary condition of 'the optimal solution should be the fixed point of multigrid inversion' is considered. Then, by combining the multigrid multiscale method with the conjugate gradient method, a new inversion method called the adaptive multigrid conjugate gradient method is designed. The results of numerical simulations indicate that the proposed method can effectively reduce the required computation burden and have good ability in anti-noise. [ABSTRACT FROM AUTHOR]

We study a porous medium equation with fractional potential pressure: ∂ t u = ∇ ⋅ ( u m − 1 ∇ p ) , p = ( − Δ ) − s u , for m > 1 , 0 < s < 1 and u ( x , t ) ≥ 0 . The problem is posed for x ∈ R N , N ≥ 1 , and t > 0 . The initial data u ( x , 0 ) is assumed to be a bounded function with compact support or fast decay at infinity. We establish existence of a class of weak solutions for which we determine whether the property of compact support is conserved in time depending on the parameter m , starting from the result of finite propagation known for m = 2 . We find that when m ∈ [ 1 , 2 ) the problem has infinite speed of propagation, while for m ∈ [ 2 , 3 ) it has finite speed of propagation. In other words m = 2 is critical exponent regarding propagation. The main results have been announced in the note [29] . [ABSTRACT FROM AUTHOR]

An algorithm to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure is proposed. The material interfaces are implicitly represented by level sets which are identified by applying regularization using total variation penalty terms. The inverse problem is solved iteratively and the extended finite element method is used for the analysis of the structure in each iteration. The formulation is presented for three-dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material sub-domains in the presence of higher noise levels. [ABSTRACT FROM PUBLISHER]

In this paper, we present a method for determining the sorption isotherm from experimental measurements. The sorption isotherm is not assumed to be a member of any specific finite dimensional class (e.g. Freundlich isotherm, Langmuir isotherm). Instead, an infinite-dimensional space of functions is considered with limited a priori assumptions (e.g. smoothness, monotonicity). Consequently, we face a more challenging problem compared to the finite-dimensional case, in which only few tuning parameters need to be determined. We consider the case of flow of the contaminated water into the unsaturated porous media sample; we assume that the data are collected at the outflow. The sorption isotherm is determined in an iterative way. We minimize the cost functional reflecting the discrepancy between measured and computed data. In doing so, we use the Gateaux differential to obtain the direction of descent. [ABSTRACT FROM PUBLISHER]