scholarly journals Lack of BV bounds for approximate solutions to a two‐phase transition model arising from vehicular traffic

2020 ◽  
Vol 43 (18) ◽  
pp. 10381-10390
Author(s):  
Mohamed Benyahia ◽  
Massimiliano D. Rosini
Keyword(s):  
Phase Transition ◽  
Approximate Solutions ◽  
Transition Model ◽  
Vehicular Traffic ◽  
Two Phase

WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS

2006 ◽  
Vol 16 (04) ◽  
pp. 559-586 ◽  
Author(s):  
MICHEL FRÉMOND ◽  
ELISABETTA ROCCA
Keyword(s):  
Phase Transition ◽  
Balance Equation ◽  
Strain Tensor ◽  
Absolute Temperature ◽  
Phase System ◽  
Transition Model ◽  
Well Posedness ◽  
State Variables ◽  
Two Phase ◽  
Two Phases

The paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. The state variables are the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved.

scholarly journals A hyperbolic phase-transition model coupled to tabulated EoS for two-phase flows in fast depressurizations

2021 ◽  
Vol 371 ◽  
pp. 110954
Author(s):  
M. De Lorenzo ◽  
Ph. Lafon ◽  
M. Pelanti ◽  
A. Pantano ◽  
M. Di Matteo ◽  
...  
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Two Phase Flows ◽  
Two Phase

scholarly journals A General Phase Transition Model for Vehicular Traffic

2011 ◽  
Vol 71 (1) ◽  
pp. 107-127 ◽  
Author(s):  
S. Blandin ◽  
D. Work ◽  
P. Goatin ◽  
B. Piccoli ◽  
A. Bayen
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Vehicular Traffic ◽  
General Phase

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

GLOBAL EXISTENCE FOR PHASE TRANSITION PROBLEMS VIA A VARIATIONAL SCHEME

2004 ◽  
Vol 01 (04) ◽  
pp. 747-768
Author(s):  
CHRISTIAN ROHDE ◽  
MAI DUC THANH
Keyword(s):  
Phase Transition ◽  
Surface Tension ◽  
Initial Data ◽  
Time Discretization ◽  
Approximate Solutions ◽  
Implicit Time ◽  
Time Step ◽  
Dynamical Phase Transition ◽  
Transition Dynamics ◽  
Variational Scheme

We construct approximate solutions of the initial value problem for dynamical phase transition problems via a variational scheme in one space dimension. First, we deal with a local model of phase transition dynamics which contains second and third order spatial derivatives modeling the effects of viscosity and surface tension. Assuming that the initial data are periodic, we prove the convergence of approximate solutions to a weak solution which satisfies the natural dissipation inequality. We note that this result still holds for non-periodic initial data. Second, we consider a model of phase transition dynamics with only Lipschitz continuous stress–strain function which contains a non-local convolution term to take account of surface tension. We also establish the existence of weak solutions. In both cases the proof relies on implicit time discretization and the analysis of a minimization problem at each time step.

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