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Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. (English) Zbl 1173.74418
Summary: Within this paper the so-called artificial added mass effect is investigated which is responsible for devastating instabilities within sequentially staggered Fluid-structure Interaction (FSI) simulations where incompressible fluids are considered.
A discrete representation of the added mass operator \(\mathcal M_A\) is given and ‘instability conditions’ are evaluated for different temporal discretisation schemes. It is proven that for every sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable. The analysis is quite general and does not depend upon the particular spatial discretisation schemes used. However here special attention is given to stabilised finite elements employed on the fluid partition. Numerical investigations further highlight the results.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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