An immersed boundary method for a contractile elastic ring in a three-dimensional Newtonian fluid.

*(English)*Zbl 1383.76363Summary: In this paper, we present an immersed boundary method for modeling a contractile elastic ring in a three-dimensional Newtonian fluid. The governing equations are the modified Navier-Stokes equations with an elastic force from the contractile ring. The length of the elastic ring is time dependent and the ring shrinks with time because of its elastic nature in our proposed model. We dynamically reduce the number of Lagrangian boundary points when the distance between adjacent points is too small. This point-deleting algorithm helps keep the number of immersed boundary points in a single Cartesian mesh grid from becoming too high. We perform numerical experiments with various initial configurations of the contractile elastic ring, and numerical simulations to investigate the effects of the parameters are also conducted. The numerical results show that the proposed method can model and simulate the time-dependent contractile elastic ring in a three-dimensional Newtonian fluid.

Reviewer: Reviewer (Berlin)

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

##### Keywords:

immersed boundary method; contractile elastic ring; Navier-Stokes equation; multigrid method
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\textit{S. Lee} et al., J. Sci. Comput. 67, No. 3, 909--925 (2016; Zbl 1383.76363)

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