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An immersed boundary method for fluid-flexible structure interaction. (English) Zbl 1228.74105
Summary: An immersed boundary method for simulation of fluid – flexible structure interaction has been proposed. In the method, an efficient Navier – Stokes solver adopting the fractional step method and a staggered Cartesian grid system is used to solve the incompressible fluid motion in an Eulerian domain. On the other hand, a moving Lagrangian grid is used to discretize the structure domain, and the equation of structure motion is derived by the energy method and is solved by an iterative method. The fluid-structure interaction is formulated by an additional momentum forcing, which is obtained on the Lagrangian grid using the structure motion equation and is spread to the nearby Eulerian girds by applying a smoothed approximation of the Dirac delta function. In this way, the massive boundary is handled easily without any special treatment, while for the neutrally buoyant case our formulation becomes equivalent with previous ones. In the simulations, we mainly use small additional boundary mass toward biofluid applications. Three numerical examples are simulated: a lid-driven cavity with a deformable volume at the bottom, a swimming jellyfish and a deformable circular ring moving through a channel with contraction. The results are compared with those of previous studies and the theoretical solutions. The temporal and spatial convergence rates of the present method are specified. The tendency of the numerical solution as the additional boundary mass approaches zero is investigated.

##### MSC:
 74S20 Finite difference methods applied to problems in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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