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A boundary-integral equation method for free surface viscous flows

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Sommario

Si propone un metodo basato sulla soluzione di equazioni integrali di contorno per flussi viscosi con superficie libera. Tale metodo è applicato allo studio della convezione termocapillare ed al processo di formazione di una goccia, entrambi in condizioni di microgravità. La presenza dei termini non lineari nell'equazione di Navier-Stokes comporta un integrale di volume che viene approssimato mediante un processo di linearizzazione.

Risultati numerici per flussi termocapillari con superficie libera sia fissa che mobile sono confrontati con altri ottenuti in precedenza con un metodo alle differenze finite. Si presentano inoltre alcuni risultati preliminari sul problema della formazione della goccia ed in particolare l'evoluzione nel tempo della configurazione geometrica della superficie libera. Nei due casi si analizzano solo campi bidimensionali.

Summary

A boundary integral equation method is proposed for the solution of viscous recirculating flows with free surfaces. In particular the method is applied to thermocapillary convection and to drop formation, both in micro-gravity conditions, the latter to test its capability to handle real unsteady problems.

The presence of non linear terms in Navier-Stokes equations leads to a volume integral, which has to be approximated by a linearization procedure.

Several numerical results for thermocapillary flows, both with fixed and moving free surface, are discussed in comparison with previously obtained finite difference solutions. Some preliminary results, and in particular the time evolution of the free surface shape, are also presented for the drop formation problem. Only plane two dimensional fields are considered for both problems.

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Authors and Affiliations

  1. Dipartimento di Meccanica e Aeronautica, Università ≪La Sapienza≫ di Roma, Italy

    Shuyao Ma, Giorgio Graziani & Renzo Piva

Authors
  1. Shuyao Ma
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  2. Giorgio Graziani
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  3. Renzo Piva
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Additional information

In leave of absence from Tianjin University, China.

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Ma, S., Graziani, G. & Piva, R. A boundary-integral equation method for free surface viscous flows. Meccanica 19, 294–299 (1984). https://doi.org/10.1007/BF01556326

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  • DOI: https://doi.org/10.1007/BF01556326

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