A stabilized finite element procedure for turbulent fluid–structure interaction using adaptive time–space refinement

Abstract

SUMMARYThis paper presents our e ort to addressing uid-structure interaction (FSI) problems by means of computational mechanics. A stabilized ÿnite element formulation is used to solve the incompressible Navier-Stokes equations written in primitive variables. The structure is modelled using rigid-body dynamic equations solved using a Runge-Kutta method. The distinctive feature of our approach is the combination of large eddy simulation (LES)-based on implicit turbulence modelling-with time-space adaptive techniques in arbitrary Lagrangian Eulerian co-ordinates (ALE). Three representative numerical examples are presented. The ÿrst one is the simulation of turbulent vortex shedding around a ÿxed obstacle, comparing our two-dimensional (2D) LES results with experiments and more reÿned threedimensional (3D) numerical solutions. The second example presents an ALE computation with moving boundaries, where we were able to detect the lock-in phenomenon for an oscillating cylinder driven by periodic vortex shedding. Our ÿnal example is the FSI problem associated to the ow around a dominant central span section of the Rio-Niterà oi bridge, where we compare our results with experiments performed in a wind tunnel.

Dynamic subscales in the finite element approximation of thermally coupled incompressible flows

“…Any finite-difference scheme can now be applied to discretize in time both in Equations (7)- (9) and (13)- (15). Obviously, space-time finite-element discretizations are also possible.…”

“…A third and final possibility that can be considered to integrate (13)- (15) in time is a combination of exact integration and approximation of the stabilization parameters and residuals at t n+ . If this approximation is done, the equations for the velocity and temperature subscales are…”

Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modeling

“…In [2] the possibility to model turbulence using only numerical ingredients within the variational multiscale context is fully and successfully exploited. The role of numerical stabilization terms to model turbulence had also been envisaged in [12,15], for example. For similar ideas using other numerical formulations, see [4,25] and references therein.…”

Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier–Stokes Equations with Numerical Subgrid Scale Modeling

“…This approach, known as direct numerical simulation, requires in dimension 3 O(Re 2,25 ) mesh nodes. Unsurprisingly, this dimension is also related to the dimension of the continuous global attractor (see [13,17,31]). The memory usage grows so fast with respect to Re that DNS computations are unaffordable in most industrial applications, even at moderate Reynolds numbers.…”

“…It is also possible to bound the H 1 (Ω)-norm of the fluid velocity, which, together with the Rellich-Kondrachov theorem, allows to prove that any fluid velocity orbit converges to a finite dimensional set, the socalled global attractor, as the time variable goes to infinity (see [16,31]). Fractal and Hausdorfd dimensions of the global attractor have been estimated using Lyapunov exponents in dimension 2 and 3 [13,17].…”