Adaptive, second-order, unconditionally stable partitioned method for fluid–structure interaction

We propose a novel, time adaptive, strongly-coupled partitioned method for the interaction between a viscous, incompressible fluid and a thin elastic structure. The time integration is based on the refactorized Cauchy’s one-legged ‘θ−like’ method, which consists of a backward Euler method using a θτ...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 393; p. 114847
Main Authors: Bukač, Martina, Trenchea, Catalin
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2022
Elsevier BV
Subjects:
Algorithms
Convergence
Equivalence
Fluid flow
Fluid-structure interaction
Incompressible flow
Incompressible fluids
Iterative methods
Partitioned method
Second-order accuracy
Time adaptivity
Time integration
Unconditional stability
Unconditional stability
Second-order accuracy
Fluid–structure interaction
Partitioned method
Time adaptivity
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:We propose a novel, time adaptive, strongly-coupled partitioned method for the interaction between a viscous, incompressible fluid and a thin elastic structure. The time integration is based on the refactorized Cauchy’s one-legged ‘θ−like’ method, which consists of a backward Euler method using a θτn-time step and a forward Euler method using a (1−θ)τn-time step. The bulk of the computation is done by the backward Euler method, as the forward Euler step is equivalent to (and implemented as) a linear extrapolation. The variable τn-time step integration scheme is combined with the partitioned, kinematically coupled β−scheme, used to decouple the fluid and structure sub-problems. In the backward Euler step, the two sub-problems are solved in a partitioned sequential manner, and iterated until convergence. Then, the fluid and structure sub-problems are post-processed/extrapolated in the forward Euler step, and finally the τn-time step is adapted. The refactorized Cauchy’s one-legged ‘θ−like’ method used in the development of the proposed method is equivalent to the midpoint rule when θ=12, in which case the method is non-dissipative and second-order accurate. We prove that the sub-iterative process of our algorithm is linearly convergent, and that the method is unconditionally stable when θ≥12. The numerical examples explore the properties of the method when both fixed and variable time steps are used, and in both cases shown an excellent agreement with the reference solution.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2022.114847