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This paper presents the general purpose framework Peano for the solution of partial differential equations (PDE) on adaptive Cartesian grids. The strict structuredness and inherent multilevel property of these grids allows for very low memory requirements, efficient (in terms of hardware performance) implementations of parallel multigrid solvers on dynamically adaptive grids, and arbitrary spatial dimensions. This combination of advantages distinguishes Peano from other PDE frameworks. We describe shortly the underlying octree-like grid type and its most important properties. The main part of the paper shows the framework concept of Peano and the implementation of a Navier-Stokes solver as one of the main currently implemented application examples. Various results ranging from hardware and numerical performance to concrete application scenarios close the contribution.

Social scientists have criticised computer models of pedestrian streams for their treatment of psychological crowds as mere aggregations of individuals. Indeed most models for evacuation dynamics use analogies from physics where pedestrians are considered as particles. Although this ensures that the results of the simulation match important physical phenomena, such as the deceleration of the crowd with increasing density, social phenomena such as group processes are ignored. In particular, people in a crowd have social identities and share those social identities with the others in the crowd. The process of self categorisation determines norms within the crowd and influences how people will behave in evacuation situations. We formulate the application of social identity in pedestrian simulation algorithmically. The goal is to examine whether it is possible to carry over the psychological model to computer models of pedestrian motion so that simulation results correspond to observations from crowd psychology. That is, we quantify and formalise empirical research on and verbal descriptions of the effect of group identity on behaviour. We use uncertainty quantification to analyse the model's behaviour when we vary crucial model parameters. In this first approach we restrict ourselves to a specific scenario that was thoroughly investigated by crowd psychologists and where some quantitative data is available: the bombing and subsequent evacuation of a London underground tube carriage on July 7th 2005.Comment: accepted by Safety Science, 34 pages (incl. bibliography

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The directed transport of microparticles depending on their size is the basis for particle sorting methods that are of utmost importance in, for example, life sciences. A drift ratchet is a Brownian motor that allows for such a directed transport. Hereby, the particle motion is induced by a combination of the Brownian motion and asymmetries stemming, for example, from the domain's geometry, electrical fields, or transient pressure boundary conditions. We simulate a particular drift ratchet which consists of a matrix of pores with asymmetrically oscillating diameter wherein a fluid with suspended particles is pumped forward and backward, and where the particles' longterm transport direction depends on their size. Thus, this setup allows for continuous and parallel particle separation, which has been shown experimentally. However, for a deeper understanding and for an optimized parameters' choice, further investigations, i.e., simulations, are necessary. In this paper, we present first results achieved with our parallel three-dimensional simulation codes applied to a still simplified scenario. This simplification is necessary to isolate different phenomena (e.g., asymmetries and Brownian motion) to check their relevance for the particle transport. The simulation codes are based on (adaptive) Cartesian grids in combination with finite volume and finite element discretizations. Cartesian grids allow for a very efficient implementation of the solver algorithms and an efficient balanced parallelization via domain decomposition. The achieved simulation results show the effectiveness of our approach and give some strong hints on a directed particle transport already with the simplified model we used here.

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In order to predict the turbulent transport in magnetic fusion experiments, global (i.e., full-torus) gyrokinetic simulations are often carried out. In this context, one frequently encounters situations in which the plasma temperature varies by large factors across the radial simulation domain. In grid-based Eulerian codes, this enforces the use of a very large number of grid points in the two-dimensional velocity space, and, thus, an enormous computational effort. To minimize the computational requirements, one may employ block-structured grids, adapted to the radial changes of the temperature. As the block-structured grids rely on a general approach, they can be applied to different Eulerian gyrokinetic implementations. In this paper, we explain the construction and implementation of such grids in the gyrokinetic code GENE, F. Jenko et al. (2000), and present corresponding simulation results.