A Benchmark Solution for Infiltration and Adsorption of Polluted Water Into Unsaturated–Saturated Porous Media

We discuss the numerical modeling of the infiltration of contaminated water into unsaturated porous media. A system with contaminant transport, dispersion, and adsorption is considered. The mathematical model for unsaturated flow is based on Richards nonlinear and degenerate equation. Nonlinear adsorption is represented by adsorption isotherms and kinetic rates. An accurate numerical method is constructed in 1D which can be a good candidate for the solution of inverse problems to determine model parameters in the adsorption part of the model. Our numerical solution is based on the method of lines (MOL method) where space discretization leads to the corresponding system of ODEs. We substantially use the numerical modeling of interfaces, separating fully saturated, partially saturated, and dry zones in the underground. Finally, in a series of numerical experiments and in comparisons with HYDRUS (?imunek et al., The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably/saturated media, version 2.0, Rep. IGWMC-TPS-70, 202 pp., Int. Groundwater Model. Cent., Colo. Sch of Mines, Golden, Colo), we demonstrate the effectiveness of our method.     

Letter to the Editor: Comments on the Paper “Inertia Effects in High-Rate Flow Through Heterogeneous Porous Media” by M. Fourar, R. Lenormand, M. Karimi-Fard, and R. Horne, Transport in Porous Media, DOI 10.1007/s11242-004-6800-6, 2005

In a recent article, Fourar et al. (Transp Porous Med, 2005, doi:10.1007/s11242-004-6800-6) analyzed the effect of heterogeneity in the permeability distribution on Forchheimer flow in porous media. They derived expressions to calculate the effective inertial coefficient in serial layers, parallel layers, and two-dimensional correlated media. Here, we highlight an inconsistency in their first-order expression for serial layers and extend their findings by providing closed-form expressions for the effective inertial coefficient in the case of a lognormal permeability distribution.     

Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang

A paper, “Dynamics of the general Lorenz family,” was published in the journal Nonlinear Dynamics. The authors investigate the general Lorenz family $\dot{x} = a(y-x)$ , $\dot{y} = dx + cy - xz$ , $\dot{z} = -bz + xy $ , considering that it contains four independent parameters. However, we show that, generically (for c≠0), this family is equivalent to the Lorenz system and, thus, the results they provide for the general Lorenz family are easily obtained from the corresponding results on the Lorenz system. Moreover, in the case c=0, it is sufficient to consider a two-parameter system.     

Reply to Comments by Veling on “A Semi-Analytical Solution for Large-Scale Injection-Induced Pressure Perturbation and Leakage in a Laterally Bounded Aquifer–Aquitard System” by Zhou,Birkholzer, and Tsang

Transport in Porous Media -     

Comment on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work” by A. Barletta and D. A. Nield,Transport in Porous Media,DOI 10.1007/s11242-008-9320-y, 2009

In a recent article by Barletta and Nield (Transport in Porous Media, DOI , 2009), the title problem for the fully developed parallel flow regime was considered assuming isoflux/isothermal wall conditions. For the limiting cases of the forced and the free convection, analytical solutions were reported; for the general case, numerical solutions were reported. The aim of the present note is (i) to give an analytical solution for the full problem in terms of the Weierstrass elliptic P-function, (ii) to illustrate this general approach by two easily manageable examples, and (iii) to rise a couple of questions of basic physical interest concerning the interplay between the viscous dissipation and the pressure work. In this context, the concept of “eigenflow” introduced by Barletta and Nield is discussed in some detail.     

Comments on the Paper “Non-Darcian Forced-Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium” by O. Aydin and A. Kaya,Transport in Porous Media,doi:10.1007/s11242-007-9200-x, 2008

In a very recent paper by Aydin and Kaya (Transp. Porous Media (to appear), 2008) the combined effects of viscous dissipation and surface mass flux on the forced-convection boundary-layer flow was considered. However, as the present Note shows, the thermal boundary condition imposed at the outer edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are in error.     

From the Highly Compressible Navier–Stokes Equations to Fast Diffusion and Porous Media Equations,Existence of Global Weak Solution for the Quasi-Solutions

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 \({\rho_{0}}\).     

Comments on “Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk by M. S. Alam,S. M. Chapal Hossain,M. M. Rahman [Meccanica (2014) 49:2439–2451]”

In this letter, we submit our comments on recently published paper titled “Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk by Alam et al. (Meccanica 49: 2439–2451, 2014)”. Authors of this paper have attempted to present similarity solutions in the paper. We comment in this letter is that the similarity transformations considered in Alam et al. (Meccanica 49: 2439–2451, 2014) are not correct and thus results are leading to invalid conclusions.     

Comments on Reply to Comments on “Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid Over a Flat Plate Embedded in a Porous Medium”

This note is a comment on the reply by Aydin and Kaya (Transp Porous Media (to appear), 2008b) to comments by Rees and Magyari (Transp Porous Media (to appear), 2008) on an article by Aydin and Kaya (Transp Porous Media (to appear), 2008a) concerning the combined effects of viscous dissipation and surface mass flux on the forced convection boundary-layer flow in a saturated porous medium modeled by the Brinkman equation. It is argued that the statements by Rees and Magyari are in fact appropriate. The thermal boundary condition imposed at the edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are inconsistent with the physics of the situation. The attempts of Aydin and Kaya to justify their paper are flawed by an inappropriate assumption and calculations with an insufficiently large parameter.     

Further Comments on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work”

This note is concerned with the assertion of Barletta and Nield (2009a) that “a fluid with a thermal expansion coefficient greater than that of a perfect gas (β > β _perfect gas) is of marginal or no interest in the framework of convection in porous media”, and that for a remark of Magyari (Transp. Porous Media, 2009) about the forced convection eigenflow solutions, the circumstance β > β _perfect gas does not represent “a sound physical basis”. Here, it is shown, however, that these assertions are in contradiction with the experimentally measured values of β for important technical fluids as e.g., air, nitrogen, carbon dioxide, and ammonia where, in the temperature range between −20 and +100°C, just the inequality β > β _perfect gas holds.     

A Comment on “On Magneto Convection in a Mushy Layer” by D. N. Riahi

The impracticality of MHD convection in a porous medium is further clarified.     

Comments on “Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization”

This paper explores a nonlinear Cournot oligopoly with n firms displaying general isoelastic demand. The marginal profits-based gradient rule and the expectation rule Local Monopolistic Approximation were employed in two Cournot oligopoly games. Nash equilibrium stability analysis is carried out on each of the two games to throw light on the effects of demand elasticity and other parameters on the dynamics of the game. Our results show that the influence of demand elasticity on stability depends on firms’ expectation rules.     

Comments on “Modeling of Nuclear Species Diffusion Through Cement-Based Materials” by Wattez et al. (2013)

We propose a simpler alternative to Wattez et al.’s method for the exploitation of tritiated water diffusion tests in cement-based materials.     

Comments on “Confluent edge conditions for the electromagnetic wave at the edge of a wedge bounded by material sheets” by Mithat Idemen

It is pointed out some inaccuracies in Idemen’s method [Idemen (2000, 2011)] while having investigated electromagnetic field near the edge of a resistive half-plane. The limiting for the field expansion only to the first power of logarithmic function is not valid and rigorously leads to the trivial solution. It is needed to include the logarithmic functions to the field expansion in any cases when among the solutions of the characteristic equation there are roots that differ from one another by any integer.