This Special Issue of the Journal Applicable Analysis contains a set of contributions based on talks delivered at the conference ‘Numerical and Mathematical Modeling of Flow and Transport in Porous Media’ http://nm2porousmedia.math.pmf.unizg.hr/ which was held in Dubrovnik, Croatia from 29 September to 3 October 2014. This Conference was jointly organized by the Department of Mathematics of the University of Zagreb (Croatia), the Applied Mathematics Laboratory of the University of Pau & CNRS UMR 5142 (France).
The aim of the conference was to bring together researchers, scientists, engineers, and students to exchange and share their experiences, new ideas, and research results about modeling, analysis and simulation of flow and transport in porous media and application to problems including subsurface hydrology, petroleum exploration, contaminant remediation, carbon sequestration, and nuclear waste storage. This conference contained 7 invited talks and 36 contributed talks and 7 posters. It was attended by 63 participants from 31 different countries: Albania, Algeria, Austria, Belgium, Canada, Croatia, Czech Republic, Denmark, France, French Guiana, Germany, India, Israel, Italy, Japan, Mexico, Morocco, The Netherlands, Norway, Russia, Kingdom of Saudi Arabia, Slovakia, South Korea, Spain, Sweden, Switzerland, Tunisia, Turkey, United Kingdom, USA, and Venezuela.
This Special Issue of the Journal Applicable Analysis contains 9 contributions corresponding to a part of the talks delivered at the conference. In selecting these papers, we followed the regular refereeing procedure. We would like to thank the authors for the effort in preparing their contributions and for meeting the deadlines. We would like to thank those whom we asked for their help in reviewing these papers. We also would like to thank Robert P. Gilbert and Yongzhi Steve Xu the Editors-in-Chief of the Journal Applicable Analysis for offering us the possibility to publish this Special Issue.
This Special Issue focuses on Mathematical and Numerical Analysis of Flow and Transport in Porous Media. The contribution includes work on an Upscaling nonlinear adsorption in periodic porous media – homogenization approach; On the localization of solutions of doubly nonlinear parabolic equations with nonstandard growth in filtration theory; A non-homogeneous Riemann solver for shallow water equations in porous media; An upwind finite volume method on non-orthogonal quadrilateral meshes for the convection–diffusion equation in porous media; Nitsche’s extended finite element method for a fracture model in porous media; Nematodynamics and random homogenization; Generalized multiscale finite element methods for problems in perforated heterogeneous domains; A fully homogenized model for incompressible two-phase flow in double porosity media; Upscaling of an immiscible non-equilibrium two-phase flow in double porosity media.
We would like to thank the members of the organizing committee for their active role in the organization. Last, but not least, we want to acknowledge all participants for their contribution and efforts in making the conference an interesting, pleasant, and successful event.
Brahim Amaziane
University of Pau & CNRS, France
[email protected] Jurak
University of Zagreb, Croatia
[email protected]