Refine
Year of publication
- 2014 (3) (remove)
Language
- English (3)
Is part of the Bibliography
- yes (3)
Keywords
- low-dimensional models (2)
- nonlinear dynamical systems (2)
- shear layers (2)
- Graph rewriting (1)
- Model transformation (1)
- Tool survey (1)
- Transformation tool contest (1)
Model transformation is one of the key tasks in model-driven engineering and relies on the efficient matching and modification of graph-based data structures; its sibling graph rewriting has been used to successfully model problems in a variety of domains. Over the last years, a wide range of graph and model transformation tools have been developed all of them with their own particular strengths and typical application domains. In this paper, we give a survey and a comparison of the model and graph transformation tools that participated at the Transformation Tool Contest 2011. The reader gains an overview of the field and its tools, based on the illustrative solutions submitted to a Hello World task, and a comparison alongside a detailed taxonomy. The article is of interest to researchers in the field of model and graph transformation, as well as to software engineers with a transformation task at hand who have to choose a tool fitting to their needs. All solutions referenced in this article provide a SHARE demo. It supported the peer-review process for the contest, and now allows the reader to test the tools online.
We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337-355) and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e. g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.