We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu x . DuMu x is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMu x , version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

No abstract

EUVL, i.e. projection lithography, utilizing actmic wavelengths in the range of 21 1-13 nm, appears to be the natural extension of optical lithography into the NGL-regime. All-reflective imaging systems, utilizing aspherical, multilayer coated, near normal incidence mirrors with reflectivities around 70%, were designed to enable diffraction limited imaging from 7Onm down to 3Onm feature sizes at high throughput. However, diffraction limited performance of optical systems calls for surface figures of typically 2J50to 2/1OO. Considering the operation wavelength of 2l 1-13 nm, this demand corresponds to unprecedented requirements for figure metrology and fabrication technology. Simultaneously, low flare levels and high reflectivities of the mirrors have to be ensured for proper system operation. These properties are related to the substrate roughness in the mid spatial (typically ljim-lmm) and high spatial (typically <1 jim) frequency ranges respectively. Accordingly these quantities have to be generated and controlled on a few-A-level.In this paper, the metrology and fabrication concepts at CARL ZEISS will be reviewed. The present status in the fabrication of specific EUVL mirrors will be reported as well.

The injection of fluids into the subsurface takes place in the context of a variety of engineering applications such as geothermal power generation, disposal of wastewater, CO 2 storage and enhanced oil recovery. These technologies involve not only the underground emplacement of fluids in a geologic formation but also affect the stress state of these rocks. If the rock's strength is surpassed, these stress changes can even lead to failure. In this context, we present a conceptual approach to model fault reactivation in porous media. As a starting point for developing and implementing this approach, the already existing combined hydroand geomechanical model within the open-source simulator DuMu x was chosen. For the evaluation of shear slip on the fault plane, the classical Mohr-Coulomb failure criterion is used. Based on the energy balance from Kanamori (Earthquake thermodynamics and phase transformations in the earth's interior, international geophysics, vol 76. Academic Press, London, pp [293][294][295][296][297][298][299][300][301][302][303][304][305] 2001), where a slip event on fault is described as a transformation of elastic energy into seismic waves, heat and an amount of energy required to cause fracture, we interpret failure as a dissipation of elastic energy. Furthermore, seismic data allow to infer a constant stress drop over a wide range of scales (Abercrombie and Leary in Geophys Res Lett 20 (14): [1511][1512][1513][1514] 1993). These findings are incorporated into our model by altering the material properties during the slip event. In detail, the linear elastic material law is replaced by a visco-elastic behaviour, which reproduces the characteristics mentioned above. This, in turn, leads to additional displacements, which are interpreted as the slip on the fault plane. Our results indicate that this pragmatic approach is capable of modelling fault reactivation without resolving the fault as a discrete surface but as a elements representing a fault zone instead.