A new residual-based variational multiscale (RBVMS) formulation for incompressible turbulent flows is proposed that is suitable for discretization using divergence-conforming B-splines. The proposed methodology results in a pointwise satisfaction of the zero-divergence constraint on the discrete velocity field. The velocity fine scales are residual-driven and constructed in a manner that is consistent with the divergence-free constraint on the discrete velocity solution. The resulting formulation is tested on laminar-and turbulent-flow benchmark problems showing excellent stability and accuracy characteristics in both regimes.
In van Opstal et al. (Comput Mech 50:779-788, 2012) airbag inflation simulations were performed where the flow was approximated by Stokes flow. Inside the intricately folded initial geometry the Stokes assumption is argued to hold. This linearity assumption leads to a boundary-integral representation, the key to bypassing mesh generation and remeshing. It therefore enables very large displacements with near-contact. However, such a coarse assumption cannot hold throughout the domain, where it breaks down one needs to revert to the original model. The present work formalizes this idea. A model adaptive approach is proposed, in which the coarse model (a Stokes boundary-integral equation) is locally replaced by the original high-fidelity model (Navier-Stokes) based on a-posteriori estimates of the error in a quantity of interest. This adaptive modeling framework aims at taking away the burden and heuristics of manually partitioning the domain while providing new insight into the physics. We elucidate how challenges pertaining to model disparity can be addressed. Essentially, the solution in the interior of the B T. M. van Opstal coarse model domain is reconstructed as a post-processing step. We furthermore present a two-dimensional numerical experiments to show that the error estimator is reliable.
A fluid-structure interaction technique for the simulation of inflatable structures is introduced. The presented finite-element/boundary-element (FEBE) technique couples an isogeometric finite element discretization of a flexible shell structure with an isogeometric boundary element discretization of a Stokes fluid. This technique was introduced in [10] for planar problems and extended to 3D in [11]. One of the marked advantages of this approach is the contact mechanism, lubrication, which is an inherent attribute of the flow model. Its role in preventing contact was theoretically substantiated, but only demonstrated in the planar setting. In the present work, we demonstrate the effectiveness of the contact mechanism in the isogeometric and three-dimensional setting, discussing various aspects pertaining to the accurate resolution of the traction responsible for contact prevention.An extensive body of literature already covers the interface of the fields of fluidstructure interaction and contact mechanics. If the problem under consideration requires that the gap between two contact surfaces may vanish, an interface tracking technique may be applied, sometimes locally [5, 19], e.g. [3, 7, 21]. If however, a problem allows for a finite gap to be maintained between the contacting surfaces, Arbitrary Lagrangian-Eulerian [4] and Space-time [18] techniques can been used to compute problems as challenging as the disreefing of parachute clusters [15,16,17] and 1000 spheres falling through a tube [6]. In this work a finite (but arbitrarily small) gap will likewise be maintained in contact regions.The target application for the current approach is inflatable structures. These typically undergo large deformations with ubiquitous self-contact during the inflation process, which often starts from a complex, folded initial configuration. Correct simulation is contingent to the resolution of every single contact mode throughout the
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