no. Supplément
A four-field three-phase flow model with both miscible and immiscible components
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S251-S278

A three-phase flow model with hybrid miscibility constraints is proposed: three immiscible phases are considered (liquid water, liquid metal and gas) but the gaseous phase is composed with two miscible components (steam water and non-condensable gas). The modelling approach is based on the building of an entropy inequality for the system of partial differential equations: once an interfacial velocity is given by the user, the model is uniquely defined, up to some relaxation time scales, and source terms complying with the second principle of thermodynamics can then be provided. The convective part of the system is hyperbolic when fulfilling a non-resonance condition and classical properties are studied (Riemann invariants, symmetrization). A key property is that the system possesses uniquely defined jump conditions. Last, preservation of thermodynamically admissible states and pressure relaxation are investigated.

DOI : 10.1051/m2an/2020037
Classification : 76T30, 35Q35, 35L60
Keywords: Three-phase flow, entropy, jump conditions, miscible components 
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     title = {A four-field three-phase flow model with both miscible and immiscible components},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {S251--S278},
     year = {2021},
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     url = {https://www.numdam.org/articles/10.1051/m2an/2020037/}
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Hérard, Jean-Marc; Hurisse, Olivier; Quibel, Lucie. A four-field three-phase flow model with both miscible and immiscible components. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S251-S278. doi: 10.1051/m2an/2020037

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