Recent Developments in Spectral Element Simulations of Moving-Domain Problems

On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems

“…The stabilization method is based on the approximate deconvolution model with relaxation term (ADM-RT) method used for the large-eddy simulation of transitional flows (Schlatter, Stolz & Kleiser 2004, 2006 and has been validated with channel flows and flow over wings in Negi et al (2018). Moving boundaries are treated using the ALE formulation (Ho & Patera 1990, 1991 and the fluid and structural equations are coupled using the Green's function decomposition approach whereby the geometrical nonlinearity is evaluated explicitly via extrapolation, while the added-mass effects are treated implicitly (Fischer, Schmitt & Tomboulides 2017). In addition, we have also implemented a fully implicit fixed-point nonlinear iteration method (Küttler & Wall 2008) for coupling of the fluid and structural equations.…”

Stability and transition in pitching wings

“…For the partitioned time marching algorithms, the coupling between the two systems is non trivial since both systems affect the dynamic behavior of each other. In the current work the fluid-structure coupling is performed using the Green's function approach recently developed by Fischer et al (2017). It is a semi-implicit technique which allows for a fully-implicit treatment of the added-mass effects while explicitly treating the geometric non-linearities.…”

“…The approach builds on the results of Causin et al (2005) where the authors identified the added-mass effects as a linear phenomenon. Fischer et al (2017) incorporate the added-mass effects into the solution of the coupled problem through a Stokes update step. Unlike a fully implicit method like fixed-point iterations with relaxation (Küttler & Wall 2008), the Green's function approach is iteration free at the cost of an added Stokes solve.…”

“…The method can easily be extended to structures where multiple degrees of freedom of the structure are active, with each active degree of freedom requiring a Stokes solve. The method has been tested even for a zero mass solid and presents no numerical difficulties (Fischer et al 2017). The validation of the implementation is done for an oscillating cylinder at Re = 100 with a solid to fluid density ratio of ρ s /ρ f = 10.…”

“…The cylinder motion is modeled using a spring-mass system with a spring natural frequency of f = 0.167. The same case considered in Fischer et al (2017) and also in the works of Prasanth & Mittal (2008). Figure 2.4 shows the time variation of the vertical position of the oscillating cylinder.…”