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Conservation form, in general non steady coordinates, of the Navier-Stokes equations and boundary conditions for a moving boundary problem

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Sommario

Il sistema completo di equazioni di Stokes-Navier e di condizioni al contorno per due fluidi immiscibili separati da una superficie di interfaccia incognita e mobile nel tempo, viene espresso in forma conservativa e con riferimento ad un sistema mobile di coordinate generalizzate in cui la superficie di interfaccia coincide con uno dei piani coordinati. Le equazioni vengono ricavate, al limite per piccole velocità relative, dal corrispondente sistema che regola il moto nell'ambito della meccanica relativistica: questo metodo appare diretto ed appropriato in particolare per la derivazione delle condizioni al contorno su una superficie mobile.

Viene infine discussa la possibile applicazione del metodo per trattare tipi differenti di superfici di discontinuità in un campo fluido.

Summary

The conservative form of the complete set of Navier-Stokes equations and boundary conditions for the flow field of two immiscible fluids separated by a moving interface of unknown shape, is obtained with reference to a boundary fitted system of non steady general coordinates. The method applied in this paper to obtain the set of equations as the limit, in the case of small relative velocities, of the corresponding set in the frame of relativistic fluid mechanics, seems particularly direct and appropriate to express the boundary conditions on the moving interface. The immediate extension of the method to treat different kinds of interfaces of discontinuity is also discussed.

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References

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  1. Istituto di Macchine e Tecnologie Meccaniche, Facoltà di Ingegneria, Roma

    M. Strani

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  1. M. Strani
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Strani, M. Conservation form, in general non steady coordinates, of the Navier-Stokes equations and boundary conditions for a moving boundary problem. Meccanica 18, 8–15 (1983). https://doi.org/10.1007/BF02156095

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  • DOI: https://doi.org/10.1007/BF02156095

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