Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow.

*(English)*Zbl 1242.76372Summary: Coupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and moving boundaries. To investigate the possibility for future IB-LB coupled simulations of the heart flow dynamics, an IB-LB coupling scheme suitable for rapid boundary motion and large pressure gradient FSI is proposed, and the mitral valve jet flow considering the interaction of leaflets and fluid is simulated. After analyzing the respective concepts, formulae and advantages of the IB and LB methods, we first explain the coupling strategy and detailed implementation procedures, and then verify the effectiveness and second-order accuracy of the scheme by simulating a benchmark case, the relaxation of a stretched membrane immersed in fluid. After that, the diastolic filling jet flow between mitral leaflets in a simplified 2D left heart model is simulated. The model consists of the simplified transmitral passage of the heart and two curvilinear leaflets. In the simulation, the atrial and ventricular pressure histories of normal human are specified as boundary conditions, and the leaflets are treated as fibers that interact with the fluid to define their deformations and movements. The resulting opening and closing movements of the leaflets and the flow patterns of the filling jet are qualitatively reasonable and compare well with existing numerical and measured data. It is shown that this IB-LB coupling method is feasible for treating flexible boundary FSI problems with rapid boundary motion and large pressure gradient, the results of the mitral leaflet flow are valuable for understanding the transmitral FSI dynamics, and it is possible to simulate the more realistic 3D heart flow by the scheme in the future.

##### MSC:

76Z05 | Physiological flows |

76M28 | Particle methods and lattice-gas methods |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

92C10 | Biomechanics |

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

##### Keywords:

lattice Boltzmann method; immersed boundary method; fluid; structure interaction; mitral leaflet flow; coupling
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\textit{Y. Cheng} and \textit{H. Zhang}, Comput. Fluids 39, No. 5, 871--881 (2010; Zbl 1242.76372)

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