Medial symmetry type graphs

A $k$-orbit map is a map with its automorphism group partitioning the set of flags into $k$ orbits. Recently $k$-orbit maps were studied by Orbani\' c, Pellicer and Weiss, for $k \leq 4$. In this paper we use symmetry type graphs to extend such study and classify all the types of $5$-orbit maps, as well as all self-dual, properly and improperly, symmetry type of $k$-orbit maps with $k\leq 7$. Moreover, we determine, for small values of $k$, all types of $k$-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest

Map operations and k-orbit maps

AbstractA k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k⩽4. “Hurwitz-like” upper bounds for the cardinality of the automorphism groups of 2-orbit and 3-orbit maps on surfaces are given. Furthermore, we consider effects of operations like medial and truncation on k-orbit maps and use them in classifying 2-orbit and 3-orbit maps on surfaces of small genus

Investigation of vortex shedding from an airfoil by CFD simulation and computer-aided flow visualization

The article presents an experimental and numerical study of vortex generation and shedding from a NACA 4421 airfoil at low Reynolds number. The experiment was conducted in a low-speed wind tunnel by flow visualization. A high-speed camera was used to record flow structures at the airfoil trailing edge. The recorded images were processed with an in-house developed software based on the advection-diffusion equation to compute instantaneous 2D velocity fields. These results were compared with results of the CFD simulation which employed the scale-adaptive simulation (SAS) turbulence modelling. The SST-SAS model produced finer and less stable turbulent structures compared to an URANS simulation with the SST model. Time-averaged velocities and frequency spectra for the both models are in good agreement, but variability of flow in both time and frequency domain is higher in case of the SST-SAS model. Velocity fields computed on the basis of visualization show generally acceptable agreement with the CFD results. Higher errors occur in areas of unperturbed smoke trails and areas of high velocity gradients, however, the vortex shedding frequency is captured with excellent agreement to the experiment