A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case | Zendy

Graziano Guerra | Zendy; Rinaldo M. Colombo | Zendy

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A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case

Author(s) -

Graziano Guerra,

Rinaldo M. Colombo

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016.11.313

Subject(s) - compressibility , limit (mathematics) , isentropic process , compressible flow , mathematical analysis , infinity , physics , computation , convergence (economics) , mathematics , space (punctuation) , dimension (graph theory) , coupling (piping) , classical mechanics , mechanics , materials science , computer science , pure mathematics , algorithm , economics , metallurgy , economic growth , operating system

We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we present the proof of rigorous convergence for the fully non--linear compressible to incompressible limit of the coupled dynamics of the two fluids. A linear example is considered in detail, where fully explicit computations are possible.

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