Reactive Flows in Deformable , Complex Media 2411 Workshop : Reactive Flows in Deformable , Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today. Mathematics Subject Classification (2010): 35, 65, 74, 76. Introduction by the Organisers The focus of this meeting was on mathematical models, the analysis and discretization of flow and reactive transport models in deformable and complex (porous) media. It aimed at identifying relevant mathematical challenges connected with such issues and the underlying applications. This required the active participation of scientists with various expertise, willing to collaborate and exchange ideas in a common mathematical language. Therefore the participants had a broad and heterogeneous expertise, covering fields of mathematics (analysis, numerical methods), (geo-)physics, and environmental engineering. The workshop was attended by 48 scientists from 10 countries, including 5 young scientists supported by the ”Oberwolfach Leibniz Graduate Students” Programme. One of the participants, Prof. Todd Arbogast, was awarded the Simons Visiting 2410 Oberwolfach Report 43/2014 Professorship. This supported his visits to the universities in München (TU), Bergen and Eindhoven. The programme included 28 lectures on the mathematical analysis, upscaling, numerical simulation and scientific computing of processes in complex (porous) media, some of them having a survey character. The talks addressed the workshop theme from various viewpoints: • Mathematical methods, with subtopics in homogenization and multiscale analysis; • Discrete representations, including (mixed and conformal) finite elements and finite volume methods, in a multi-scale context; • Heterogeneous solvers, including domain decomposition methods and multilevel solvers; • Advanced applications, dealing with subsurface processes and biological systems. The organizers would like to acknowledge the involvement of Florin Adrian Radu (Bergen), who initiated the organisation of this workshop. The meeting atmosphere was very inspiring and collegial, with many discussions and promising initiatives. Needless to say, in achieving this the professional support offered kindly by the MFO was invaluable. All participants have experienced the hospitality and the wonderful conditions offered in Oberwolfach, and expressed the wish to come back. Next to them, the organizers are expressing the gratitude for this fantastic opportunity. Acknowledgement: The MFO and the workshop organizers would like to thank the National Science Foundation for supporting the participation of junior researchers in the workshop by the grant DMS-1049268, “US Junior Oberwolfach Fellows”. Moreover, the MFO and the workshop organizers would like to thank the Simons Foundation for supporting Todd Arbogast in the “Simons Visiting Professors” program at the MFO. Reactive Flows in Deformable, Complex Media 2411 Workshop: Reactive Flows in Deformable, Complex Media