Collapsing and Explosion Waves in Phase Transitions with Metastability, Existence, Stability and Related Riemann Problems
نویسنده
چکیده
Collapsing waves were observed numerically before and were used to explain the ring formations in dynamic flows involving phase transitions with metastability. In this paper, necessary and sufficient conditions for collapsing type of waves to exist are given. The conditions are that the wave speed of the collapsing wave is not less than a number and is supersonic on both sides of the wave. Existence and non-existence conditions for the explosion waves are also found. The stability of these waves are studied numerically. Although there are infinitely many collapsing (or explosion) waves for a fixed downstream state, the collapsing (or explosion) wave appeared in the solution of Riemann problem is numerically verified to be the one with the slowest speed. Although a Riemann problem in the zero viscosity limit may have two solutions, one with, the other without, a collapsing (or explosion) wave, from the vanishing viscosity point of view, the one with a collapsing (or explosion) wave is numerically verified to be admissible.
منابع مشابه
Wave Interactions in Suliciu Model for Dynamic Phase Transitions
Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states, the solution may be constructed from the Riemann solutions, with each two adjacen...
متن کاملA Numerical Study of Riemann
A numerical study of the isothermal fluid equations with a nonmonotone equation of state (like that of van der Waals) and with viscosity and capillarity terms is presented. This system is ill-posed (i.e., elliptic in x vs. t) in some regions of state space and well-posed (i.e., hyperbolic) in other regions. Thus, it may serve as a model for describing dynamic phase transitions. Numerical comput...
متن کاملMultidimensional Stability of Subsonic Phase Transitions in a Non-Isothermal Van Der Waals Fluid
We show the multidimensional stability of subsonic phase transitions in a non-isothermal van der Waals fluid. Based on the existence result of planar waves in our previous work [1], a jump condition is posed on non-isothermal phase boundaries which makes the argument possible. Stability of planar waves both in one dimensional and multidimensional spaces are proved.
متن کاملShock-Induced Martensitic Phase Transitions I: Critical Stresses, Two-wave Structures, Riemann Problems
We consider a class of shock-loading experiments which, as a result of solid-to-solid phase transitions, give rise to certain characteristic patterns consisting of two shock-like waves. We show that the single assumption that stresses in a phase cannot lie beyond the transition boundaries leads to a complete description of the observed phenomena. The model presented here is di erent from others...
متن کاملFree Energy Minimization by Simulated Annealing with Applications to Lithospheric Slabs and Mantle Plumes
An optimization algorithm based upon the method of simulated annealing is of utility in calculating equilibrium phase assemblages as functions of pressure, temperature, and chemical composition. Operating by analogy to the statistical mechanics of the chemical system, it is applicable both to problems of strict chemical equilibrium and to problems involving metastability. The method reproduces ...
متن کامل