Stability in the Stefan problem with surface tension (I)
نویسندگان
چکیده
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension also known as the Stefan problem with Gibbs-Thomson correction.
منابع مشابه
Development of a phase change model for volume-of-fluid method in OpenFOAM
In this present study, volume of fluid method in OpenFOAM open source CFD package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. This model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. Both phases (liquid-va...
متن کاملStability in the Stefan problem with surface tension (II)
Continuing our study of the Stefan problem with surface tension effect, in this paper, we establish sharp nonlinear stability and instability of steady circles. Our nonlinear stability proof relies on an energy method along the moving domain, and the discovery of a new ‘momentum conservation law’. Our nonlinear instability proof relies on a variational framework which leads to the sharp growth ...
متن کاملA study of a Stefan problem governed with space–time fractional derivatives
This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...
متن کاملStability of Equilibria for the Stefan Problem With Surface Tension
We characterize the equilibrium states for the two-phase Stefan problem with surface tension and with or without kinetic undercooling, and we analyze their stability in dependence of physical and geometric quantities.
متن کاملMorphological Instability of Similarity Solution to the Stefan Problem with Undercooling and Surface Tension
This paper concerns morphological stability of a similarity solution to the Stefan problem with surface tension and initial supercooling. The linear stability analysis shows that for a nonzero surface tension each perturbation mode with a nonzero wave number is stable. However, the solution is unstable with respect to perturbations with a zero wave number limit point in their Fourier spectrum. ...
متن کامل