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Linear stability analysis of a collapsible channel flow
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DOI：10.1007/s10409-026-51244-x.png)
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Abstract
En 中文
Linear stability analysis, which evaluates a system’s behaviour near its steady state, is widely used to investigate stability in various dynamic systems. However, when applied to fluid-structure interaction systems with flexible interfaces, special consideration is required due to the complexity introduced by moving boundaries. In order to establish a theoretically rigorous and mathematically precise framework for linearising fluid-structure interaction systems characterised by flexible interfaces, this study develops a methodology that incorporates the contributions of flexible interfaces into the linearisation by applying a Taylor expansion about the system’s steady state. In addition, a widely adopted linearisation approach that approximates variables directly on the steady-state interface is also considered. We present a systematic comparison of these two linearisation methods in terms of their theoretical development and numerical results. In particular, we use a collapsible channel flow model as an illustrative example to examine these linearisation approaches for both flux-driven and pressure-driven systems. Our results show that both the Taylor-based mapping and direct mapping linearisation methods accurately predict the critical parameters characterising the system’s neutral stability. Moreover, the more rigorous Taylor-based linearisation captures perturbation flow field details that the simplified direct mapping approach fails to resolve. This improved resolution provides a more robust foundation for further investigation of perturbation mechanisms, such as perturbation energy analyses that require precise numerical evaluation of perturbation velocity and pressure.
Keywords:
Linear stability analysis
Fluid-structure interaction
Dynamical system
Eigenvalue analysis
Journal
A
IF:
4.6
Papers:
2.9K
Citations:
4.7K
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