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**Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monte-Ampère equation.**
*(English)*
Zbl 1141.76043

Summary: We review some recent applications of operator-splitting methods. We show that these methods are well-suited to the numerical solution of outstanding problems from various areas in mechanics, physics and differential geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and elliptic real Monge-Ampère equation. The results of numerical experiments illustrate the capabilities of these methods.

### MSC:

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

76M10 | Finite element methods applied to problems in fluid mechanics |

76T99 | Multiphase and multicomponent flows |

76D45 | Capillarity (surface tension) for incompressible viscous fluids |

65N99 | Numerical methods for partial differential equations, boundary value problems |

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\textit{R. Glowinski} et al., Japan J. Ind. Appl. Math. 25, No. 1, 1--63 (2008; Zbl 1141.76043)

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### References:

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