ZAMM · Z. Angew. Math. Mech. 94, No. 7 – 8, 559 (2014) / DOI 10.1002/zamm.201400559

Editorial

Deformation and transport phenomena in porous media

Published online 1 July 2014

Wolfgang Ehlers, Rainer Helmig, and Christian Rohde

Universitat Stuttgart, Stuttgart Research Centre for Simulation Technology (SimTech)

Since its beginnings in the mid nineteenth century, the investigation of deformation and flow in porous media has emergedto one of the major fields in continuum-mechanical and mathematical porous media research. Based on theoretical researchin the framework of “Rational Continuum Mechanics” in the sixties and seventies of the last century, porous media ap-proaches have been based on superimposed but interacting continua stemming from the idea of a virtual averaging of theunderlying microstructure. Proceeding from this idea, a variety of analytical and numerical studies has been carried out byengineers and mathematicians, basically subdivided in two major groups, solid- and fluid-mechanical researchers. Whilethe first group has been approaching porous media from the solid deformation side coupling the pore-fluid flow throughinteraction forces driven by the solid deformation, the second group investigated the flow and transport behaviour of singleand multiphasic fluids in rigid solid skeletons based on driving forces such as those initiated by pressure gradients.

Modern approaches in porous media research combine the solid-deformation aspect with multiphasic and multi-com-ponent flow and transport phenomena. Furthermore, many applications require further multifield couplings to account fore. g. temperature, radiative, or electro-chemical effects. Yet another challenge is the passage from the classical assumptionof a simple homogeneous porous media to more heterogeneous material structures of all kinds. The variety of applicationsof extended porous media approaches includes classical applications in geotechnical and hydraulical engineering. Howeverit extends by now to sophisticated problems in e. g. soft- and hard-tissue biomechanics, biological cell dynamics, or coupledtransport phenomena in fuel cells to name just a few.

This special issue puts the focus on some of the described modern trends in porous media research. It covers modelling,analysis and numerical topics from the mathematical and the engineering perspective. The contributions emerged fromlectures delivered at the occasion of the Workshop “Flow and Deformation in Porous Media: Modelling, Analysis, Simula-tion”, which has been held under the auspices of the DFG-Cluster of Excellence “Simulation Technology” in Freudenstadt,Germany, 14–15 March 2012. The scientific submissions can be sorted into two groups. The first group emphasizes theinteraction of complex flow properties with solid-deformation aspects and multifield couplings, the second one deals morewith the effects of heterogeneity.

The issue starts with the paper of Bluhm, Bloßfeld, and Ricken. They propose a mathematical model and associatednumerical simulations for phase transition in porous media under freezing-thawing load conditions. Rigorous upscaling forchemically reactive flows at rough boundaries is the content of Kumar, van Helvoort, and Pop. The next paper by Ratzand Schweizer addresses the old question how to include hysteretic effects into the modelling of capillary pressure forRichards and two-phase flow. Finally, Ricken et al. discuss the interaction of energetic, flow and solid deformation effectson the complex example of methane oxidation in landfill cover layers.

The second round of papers on heterogeneous porous media is opened by Eymard, Guichard, Herbin, and Massonwho present a unifying convergence analysis for the class of so-called gradient schemes. This class contains conformingand mixed finite elements as well as the mimetic mixed hybrid family. Complex flow and mechanical effects of liquefactionphenomena in fluid-saturated soil with heterogeneous microstructure are studied by Ehlers, Schenke, and Markert. Mostnotably they consider the soil matrix as an elasto-plastic material interacting with the fluid flow. Andreianov, Brenner,and Cances suggest a scheme to approximate in multiple space dimensions the vanishing capillarity limit in heterogeneoustwo-phase flow. A new transmission condition to model oil trapping is introduced. Also the last contribution by Kisslingand Karlsen considers a vanishing capillarity limit in heterogeneous media. They analyse the effect of spatial heterogeneityin the presence of rate- dependent dynamical models for the capillary pressure.

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