
Finite element approximation of fluid structure interaction using TaylorHood and ScottVogelius elements
Vacek, Karel ; Sváček, P.
This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible NavierStokes equations written in the arbitrary EulerianLagrangian (ALE) formulation. The ALE mapping is constructed with the use of a pseudoelastic approach. The flow problem is numerically approximated by the finite element method (FEM). For discretization of the fluid flow, the results obtained by both the TaylorHood (TH) element and the ScottVogelius (SV) finite element are compared. The TH element satisfies the BabuškaBrezzi infsup condition, which guarantees the stability of the scheme. In the case of the SV element the mesh, that is created as a barycentric refinement of regular triangulation, is used to satisfy the BabuškaBrezzi condition. The numerical results for two benchmark problems are shown.

 

Numerical evaluation of massdiffusive compressible fluids flows models
Bodnár, Tomáš ; Fraunié, P.
This contribution presents first numerical tests of some recently published alternative models for solution of viscous compressible and nearly incompressible models. All models are solved by high resolution compact finite difference scheme with strong stability preserving RungeKutta time stepping. The two simple but challenging computational test cases are presented, based on the doubleperiodic shear layer and the KelvinHelmholtz instability. The obtained timedependent flow fields are showing pronounced shear and vorticity layers being resolved by the standard as well as by the new massdiffusive modified models. The preliminary results show that the new models are viable alternative to the well established classical models.

 

Hidden symmetry in turbulence and analytic study of shell models
Caggio, Matteo
This short communication concerns symmetries in developed turbulence and analytic study of shell models. However scaleinvariance is broken due to the intermittency phenomenon, is possible to established a hidden selfsimilarity in turbulent flows. Using a shell model, the author in [18] (see also [19]) addressed the problem deriving a scaling symmetry for the inviscid equations. Here, first we discuss the analysis presented in [18], then, from the mathematical perspective, we propose an analytic study for the shell model with the presence of the viscous terms. This brief paper should be understood as an introductory note to this new scaling symmetry with implications for mathematical analysis [5].
