A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation. (English) Zbl 1104.74026
To examine the interaction of incompressible viscous fluid and elastic body, the authors develop a new monolithic (fully-coupled, simultaneous or direct) approach based on the fluid pressure Poisson equation (PPE). In two variants of the suggested method the fluid pressure is derived implicitly by solving PPE for fluid-structure interaction (FSI) so as to satisfy the incompressibility constraint, and other unknown variables are derived partially explicitly or fully explicitly. The method has the following advantages: 1) the number of degrees of freedom of the equations to be solved is reduced; 2) the condition on the coefficient matrix of PPE for FSI is insensitive to inhomogeneity of material properties; 3) the coefficient matrix of PPE for FSI becomes symmetric and positive definite. For taking into account the deformable fluid-structure interface, the authors use arbitrary Euler-Lagrange method in finite element formulation for incompressible viscous fluid. Two applications of the proposed method are given.
Reviewer: Peter A. Velmisov (Ul’yanovsk)
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
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