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This chapter examines a linearly coupled fluid-poroelastic structure interaction (FPSI) system, where an incompressible viscous fluid (modeled by time-dependent Stokes equations) interacts with a multilayered poroelastic structure comprising a thin plate and a thick Biot medium. The coupling occurs across a fixed interface, with displacements approximated on fixed domains—valid for small deformations. Key coupling conditions include the Beavers-Joseph-Saffman condition, posing challenges for velocity trace regularity. Two scenarios are analyzed: Existence of weak, finite-energy solutions is proven using Rothe’s method and energy estimates, with compactness tools (e.g., Aubin-Lions lemma) for the nonlinear case. Uniqueness and strong solution criteria are also discussed.

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FPSI with Linear Coupling

  • 章节

  • 发表日期：

    2025年

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  • Sunčica Čanić,
  • Jeffrey Kuan,
  • Boris Muha,
  • Krutika Tawri

摘要

This chapter examines a linearly coupled fluid-poroelastic structure interaction (FPSI) system, where an incompressible viscous fluid (modeled by time-dependent Stokes equations) interacts with a multilayered poroelastic structure comprising a thin plate and a thick Biot medium. The coupling occurs across a fixed interface, with displacements approximated on fixed domains—valid for small deformations. Key coupling conditions include the Beavers-Joseph-Saffman condition, posing challenges for velocity trace regularity. Two scenarios are analyzed: Existence of weak, finite-energy solutions is proven using Rothe’s method and energy estimates, with compactness tools (e.g., Aubin-Lions lemma) for the nonlinear case. Uniqueness and strong solution criteria are also discussed.