### Abstract

The subject of this paper is the flow of a viscous incompressible fluid in a region containing immersed boundaries which move with the fluid and exert forces on the fluid. An example of such a boundary is the flexible leaflet of a human heart valve. It is the main achievement of the present paper that a method for solving the Navier-Stokes equations on a rectangular domain can now be applied to a problem involving this type of immersed boundary. This is accomplished by replacing the boundary by a field of force which is defined on the mesh points of the rectangular domain and which is calculated from the configuration of the boundary. In order to link the representations of the boundary and fluid, since boundary points and mesh points need not coincide, a semi-discrete analog of the δ function is introduced. Because the boundary forces are of order h^{-1}, and because they are sensitive to small changes in boundary configuration, they tend to produce numerical instability. This difficulty is overcome by an implicit method for calculating the boundary forces, a method which takes into account the displacements that will be produced by the boundary forces themselves. The numerical scheme is applied to the two-dimensional simulation of flow around the natural mitral valve.

Original language | English (US) |
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Pages (from-to) | 252-271 |

Number of pages | 20 |

Journal | Journal of Computational Physics |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1972 |

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### ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational Physics*,

*10*(2), 252-271. https://doi.org/10.1016/0021-9991(72)90065-4