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Vortices are important features in vector fields that show a swirling behavior around a common core. The concept of a vortex core line describes the center of this swirling behavior. In this work, we examine the extension of this concept to 3D second-order tensor fields. Here, a behavior similar to vortices in vector fields can be observed for trajectories of the eigenvectors. Vortex core lines in vector fields were defined by Sujudi and Haimes to be the locations where stream lines are parallel to an eigenvector of the Jacobian. We show that a similar criterion applied to the eigenvector trajectories of a tensor field yields structurally stable lines that we call tensor core lines. We provide a formal definition of these structures and examine their mathematical properties. We also present a numerical algorithm for extracting tensor core lines in piecewise linear tensor fields. We find all intersections of tensor core lines with the faces of a dataset using a simple and robust root finding algorithm. Applying this algorithm to tensor fields obtained from structural mechanics simulations shows that it is able to effectively detect and visualize regions of rotational or hyperbolic behavior of eigenvector trajectories.

Direct Numerical Simulations of premixed combustion produce terabytes of raw data, which are prohibitively large to be stored, and have to be analyzed and visualized. A simultaneous and integrated treatment of data storage, data analysis and data visualization is required. For this, we introduce a sparse representation tailored to DNS data which can directly be used for both analysis and visualization. The method is based on the observation that most information is located in narrow‐band regions where the chemical reactions take place, but these regions are not well defined. An approach for the visual investigation of feature surfaces of the scalar fields involved in the simulation is shown as a possible application. We demonstrate our approach on multiple real datasets.

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The impact of the collision model employed when simulating fully resolved particles interacting in a fluid is investigated in the present study. We are using for this purpose a p seudo-spectral in compressib le Direct Numerical Simulation (DNS) code based on the Navier-Stokes equation as well as a Lattice-Boltzmann Method (LBM), developed in our group and coupled with the direct-forcing Immersed Boundary Method (IBM) to describe the particles. Most of the corresponding literature assumes that the collision model does not have a significant impact on the flow field. Additionally, the impact of the collision model on the particle trajectories has not been analyzed in a systematic manner. Thus, by using the DNS solver, four different collision models (velocity barrier, repulsive potential force, lubrication barrier and hard-sphere model) have been employed in order to examine consequences for particle behavior and turbulence structure. It was found that the particle motion and turbulence statistics are qualitatively similar for all models. However, noticeable quantitative differences appear concerning the turbulent dissipation rate. In the LBM section two different types of repulsive-force collision model are selected and their effect on a 2D fluid-particle interaction is investigated. Furthermore, other factors affecting performance of the LB-IBM solver, like the forcing scheme will be discussed.