A formulism of frequency-domainmass diffusion-waves in porousmedia is derived bymeans of Fourier transform. In analogy to conventional thermal-wave fields, internally consistent Green functions inCartesian coordinates for linearmass diffusion-waves is also presented for infinite, semiinfinite andfinite-size domains in three-dimensional spaces. TheGreen functions are utilized to analyze the resp...

We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and porousmedia flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness. We propose and analyze iterative methods to solve a conforming finite element appro...

1 Jagiellonian University, 31007 Krakow, Poland 2AGH University of Science and Technology, 30059 Krakow, Poland 3Applied Mathematics & Computational Science, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia 4Earth Science & Engineering and Center for Numerical PorousMedia, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, S...

according to the former researcher’s presented relations for flow through rock-fill porous media, the effects of physical characteristics was not studied separately. hence, due to the application of these relations, physical characteristics of porous materials effect must be investigated separately. in various constructed physical models of porous media, the effect of several variables such as ...

where D+ is the standard Caputo derivative with  < α ≤  and δ, γ are constants with δ > , γ > . Differential equations of fractional order have recently proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering. Indeed, we can findnumerous applications in viscoelasticity, electrochemistry, control, porousmedia, electromagnetism, etc. (see [...

We present a methodology to characterize a continuum-scale model of transport in porousmedia on the basis of pore-scale distributions of velocities computed in three-dimensional pore-space images. The methodology is tested against pore-scale simulations of flow and transport for a bead pack and a sandstone sample. We employ a double-continuum approach to describe transport inmobile and immobile...

In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solut...

We find that the thin double layer assumption, in which the thickness of the electrical diffuse layer is assumed small compared to the radius of curvature of a pore or throat, is valid in a capillary tubes model so long as the capillary radius is >200 times the double layer thickness, while the thick double layer assumption, in which the diffuse layer is assumed to extend across the entire pore...