In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid–structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek–Hron benchmarks in two and three dimensions, and investigate timing and scalability results.

Exploiting high‐contrast Stokes preconditioners to efficiently solve incompressible fluid–structure interaction problems / Wichrowski, Michał; Krzyżanowski, Piotr; Heltai, Luca; Stupkiewicz, Stanisław. - In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. - ISSN 0029-5981. - (2023), pp. 1-25. [10.1002/nme.7350]

Exploiting high‐contrast Stokes preconditioners to efficiently solve incompressible fluid–structure interaction problems

Wichrowski, Michał
;
Heltai, Luca;
2023-01-01

Abstract

In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid–structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek–Hron benchmarks in two and three dimensions, and investigate timing and scalability results.
2023
1
25
https://arxiv.org/abs/2305.08986
Wichrowski, Michał; Krzyżanowski, Piotr; Heltai, Luca; Stupkiewicz, Stanisław
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/134050
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