An embedded mesh method in a multiple material ALE

Abstract

A new approach for treating the mechanical interactions of overlapping finite element meshes is presented. Referred to as embedded mesh methods here, these overlapping mesh methods typically include a foreground solid mesh and a background Euler fluid grid or solid mesh. A number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface. Lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable. Several Lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid-structure interaction type problems. In addition, details regarding implementation in a two-step, multi-material, Arbitrary Lagrangian Eulerian (ALE) code are presented. Example problems demonstrate convergence and applicability to a range of problems. In particular, the fluid-structure interaction examples focus on blast applications.

Parallel adaptive fluid–structure interaction simulation of explosions impacting on building structures

“…While the utilization of an Eulerian fluid mesh with embedded boundary capability is nowadays frequently employed for FSI simulations with large structural motions, cf. (Wang et al, 2012;Zhao et al, 2008;Puso et al, 2012), we enhance its accuracy independent of a particular scheme by combining it with dynamic adaptation of the fluid mesh. Unique to our approach, we additionally employ recursive fluid time step refinement and the specially extended FSI coupling algorithms have been described.…”

Fluid–Structure Interaction Model of a Percutaneous Aortic Valve: Comparison with an In Vitro Test and Feasibility Study in a Patient-Specific Case

“…More details about this method can be found in references. 15,28 The fluid parts consist of a control volume (fluid domain), inlet and outlet parts. Since in the in vitro experiment the bottom of the compartment is fixed and fluid has no influence on the bottom during testing cycles, only the structural parts over the bottom of the compartment were immersed in the fluid domain.…”

Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid–thin structure interaction analysis, with application to heart valve modeling

“…Stability of such a discretization (in the steady or rigid-structure limits) would be more difficult to establish a priori , but preliminary numerical tests (omitted from this work for brevity) suggest that it is a practical option, so long as the elements of Λ H are coarse enough relative to the fluid discretization. An empirical comparison of Lagrangian and Eulerian constructions of Lagrange multiplier discrete spaces for non-boundary-fitted numerical methods was performed in [24], with the conclusion that the Eulerian (or, in the terminology of [24], “background”) construction was much more stable, but the cited study did not consider the possibility of radically-coarsened Lagrangian (“foreground”) constructions, which are enabled without loss of accuracy by accounting for (but stabilizing) fine scales of the Lagrange multiplier.…”