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- W2024761396 abstract "This two-part paper treats the numerical approximation of atrickyquadratic eigenvalue problem arising from the followinggeneralization of the classical Taylor-Couette problem: A viscousincompressible fluid occupies the region between arigid inner cylinder and a deformable outer cylinder, which we take to be a nonlinearly viscoelastic membrane. The inner cylinder rotates at a prescribed angularvelocity ω, driving the fluid, which in turn drives the deformable outercylinder. The motion of the outer cylinder is not prescribed, butresponds to the forces exerted on it by the moving fluid.A steady solution of this coupled fluid-solid system, analogous to the Couette solution of the classical problem, can be found analytically.Its linearized stability is governed by a non-self-adjoint quadratic eigenvalue problem.In Part I, we give a careful formulation of the geometrically exact problem.We compute the eigenvalue trajectories in the complex planeas functions of ω by using a Fourier-finite element method.Computational results show that the steady solution loses its stabilityby a process suggestive of a Takens-Bogdanov bifurcation. In Part II we proveconvergence of the numerical method." @default.
- W2024761396 created "2016-06-24" @default.
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- W2024761396 date "2009-01-01" @default.
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- W2024761396 title "A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part I: Formulation, Analysis, and Computations" @default.
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- W2024761396 doi "https://doi.org/10.3934/cpaa.2009.8.123" @default.
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