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An adaptive remeshing strategy for flows with moving boundaries and fluid – structure interaction. (English) Zbl 1194.76140

Summary: The primary objective of this work is to extend the capability of the arbitrary Lagrangian-Eulerian (ALE)-based strategy for solving fluid – structure interaction problems. This is driven by the fact that the ALE mesh movement techniques will not be able to treat problems in which fluid – structure interface experiences large motion. In addition, for certain problems the need arises to capture accurately flow features, such as a region with high gradients of the solution variables. This can be achieved by incorporating an adaptive remeshing procedure into the solution strategy.
The fluid flow is governed by the incompressible Navier-Stokes equations and modelled by using stabilized low order velocity pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. The flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics. For temporal discretization of both fluid and solid bodies, the discrete implicit generalized-\(\alpha\) method is employed. The resulting strongly coupled set of nonlinear equations is then solved by means of a novel partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates full linearization of the overall incremental problem.
Within the adaptive solution strategy, the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required. The adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field. For the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross-sections. To be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution. The numerical examples demonstrate the robustness and efficiency of the methodology.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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