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.
Citation: Rinaldo M. Colombo, Graziano Guerra. A coupling between a non--linear 1D compressible--incompressible limit and the 1D --system in the non smooth case[J]. Networks and Heterogeneous Media, 2016, 11(2): 313-330. doi: 10.3934/nhm.2016.11.313
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Abstract
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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Rinaldo M. Colombo, Graziano Guerra. A coupling between a non--linear 1D compressible--incompressible limit and the 1D --system in the non smooth case[J]. Networks and Heterogeneous Media, 2016, 11(2): 313-330. doi: 10.3934/nhm.2016.11.313
Rinaldo M. Colombo, Graziano Guerra. A coupling between a non--linear 1D compressible--incompressible
limit and the 1D --system in the non smooth case[J]. Networks and Heterogeneous Media, 2016, 11(2): 313-330. doi: 10.3934/nhm.2016.11.313
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