Geodesic
Solutions for a hyperbolic model of multi-phase flow
Debora Amadori1 ; Andrea Corli2
1 Department of Engineering, Computer Science and Mathematics, University of L’Aquila, Italy
2 Department of Mathematics and Computer Science, University of Ferrara, Italy
ESAIM. Proceedings, Tome 40 (2013), pp. 1-15.

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We discuss a model for the flow of an inviscid fluid admitting liquid and vapor phases, as well as a mixture of them. The flow is modeled in one spatial dimension; the state variables are the specific volume, the velocity and the mass density fraction λ of vapor in the fluid. The equation governing the time evolution of λ contains a source term, which enables metastable states and drives the fluid towards stable pure phases. We first discuss, for the homogeneous system, the BV stability of Riemann solutions generated by large initial data and check the validity of several sufficient conditions that are known in the literature. Then, we review some recent results about the existence of solutions, which are globally defined in time, for λ close either to 0 or to 1 (corresponding to almost pure phases). These solutions possibly contain large shocks. Finally, in the relaxation limit, solutions are proved to satisfy a reduced system and the related entropy condition.
DOI : 10.1051/proc/201340001

Debora Amadori 1 ; Andrea Corli 2

1 Department of Engineering, Computer Science and Mathematics, University of L’Aquila, Italy
2 Department of Mathematics and Computer Science, University of Ferrara, Italy 
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Debora Amadori; Andrea Corli. Solutions for a hyperbolic model of multi-phase flow. ESAIM. Proceedings, Tome 40 (2013), pp. 1-15. doi : 10.1051/proc/201340001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201340001/

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