We introduce a simple hyperbolic system of three equations, in one space dimension, which models a fluid flow through a porous medium. The model also allows for phase transitions of the fluid: both liquid and vapor phases may be present as well as mixtures of them. At last, an equilibrium pressure makes metastable states possible. The porous medium is modeled by a damping term that depends on the phase and is linear in the velocity. First, we give some necessary conditions in order that two end-states can be joined by a traveling wave. Then, we provide several sufficient conditions which yield the existence and uniqueness of traveling waves in many different situations. We also verify some structural properties of the model, which imply the global existence of smooth solutions for states close to the stable-liquid or stable-vapor regions.
A hyperbolic model for phase transitions in porous media
CORLI, Andrea;
2014
Abstract
We introduce a simple hyperbolic system of three equations, in one space dimension, which models a fluid flow through a porous medium. The model also allows for phase transitions of the fluid: both liquid and vapor phases may be present as well as mixtures of them. At last, an equilibrium pressure makes metastable states possible. The porous medium is modeled by a damping term that depends on the phase and is linear in the velocity. First, we give some necessary conditions in order that two end-states can be joined by a traveling wave. Then, we provide several sufficient conditions which yield the existence and uniqueness of traveling waves in many different situations. We also verify some structural properties of the model, which imply the global existence of smooth solutions for states close to the stable-liquid or stable-vapor regions.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
