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**Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface.**
*(English)*
Zbl 1180.76043

Summary: A new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free. The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time-step advancement. The primary dependent variables are the pressure and the velocity components. Also used is a set of marker particles which move with the fluid. The technique is called the marker and cell method. Some examples of the application of this method are presented. All nonlinear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired.

### MSC:

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

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

76B07 | Free-surface potential flows for incompressible inviscid fluids |

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\textit{F. H. Harlow} and \textit{J. E. Welch}, Phys. Fluids 8, 2182--2189 (1965; Zbl 1180.76043)

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### References:

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