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arXiv · 1810.08817

Existence of a weak solution to the fluid-structure interaction problem in 3D

Srđan Trifunović·Ya-Guang Wang
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Abstract

We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a generalization of Kirchhoff, von K\'arm\'an and Berger plate models. The fluid and the structure are fully coupled via kinematic and dynamic boundary conditions. The existence of a weak solution is obtained by designing a hybrid approximation scheme that successfully deals with the nonlinearities of the system. We combine time-discretization and operator splitting to create two sub-problems, one piece-wise stationary for the fluid and one in the Galerkin basis for the plate. To guarantee the convergence of approximate solutions to a weak solution, a sufficient condition is given on the number of time discretization sub-intervals in every step in a form of dependence with number of the Galerkin basis functions and nonlinearity order of the plate equation.

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Srđan Trifunović, Ya-Guang Wang. 2018-10-20. Existence of a weak solution to the fluid-structure interaction problem in 3D. https://arxiv.org/abs/1810.08817

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