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 $\lambda$ of vapor in the fluid. The equation governing the time evolution of $\lambda$ 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 $\lambda$ 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.
Solutions for a hyperbolic model of multi-phase flow
CORLI, Andrea
2013
Abstract
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 $\lambda$ of vapor in the fluid. The equation governing the time evolution of $\lambda$ 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 $\lambda$ 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.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
