In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time. The classical Stefan problem aims to describe the … See more The problem is named after Josef Stefan (Jožef Stefan), the Slovenian physicist who introduced the general class of such problems around 1890 in a series of four papers concerning the freezing of the ground and the … See more The one-dimensional one-phase Stefan problem The one-phase Stefan problem is based on an assumption that one of the material phases may be … See more The classical Stefan problem deals with stationary materials with constant thermophysical properties (usually irrespective of phase), a constant phase change temperature and, in the example above, an instantaneous switch from the initial temperature … See more 1. ^ Applied partial differential equations. Ockendon, J. R. (Rev. ed.). Oxford: Oxford University Press. 2003. ISBN 0-19-852770-5. OCLC 52486357.{{cite book}}: CS1 maint: others ( See more From a mathematical point of view, the phases are merely regions in which the solutions of the underlying PDE are continuous and differentiable up to the order of the PDE. In physical problems such solutions represent properties of the medium for each … See more Apart from modelling melting of solids, Stefan problem is also used as a model for the asymptotic behaviour (in time) of more complex problems. For example, Pego uses matched asymptotic expansions to prove that Cahn-Hilliard solutions for phase separation … See more • Free boundary problem • Olga Oleinik • Shoshana Kamin See more WebFeb 4, 2024 · On the two-phase fractional Stefan problem. Félix del Teso, Jørgen Endal, Juan Luis Vázquez. The classical Stefan problem is one of the most studied free boundary …
TWO PHASES STEFAN PROBLEM WITH SMOOTHED ENTHALPY
WebKey words. Stefan problem, phase change problems, enthalpy, convergence. AMS subject classi cations. 35B6, 65L20, 65N12, 80A20, 80A22. 1. Introduction The two-phase Stefan … WebThe two-phase Stefan problem in several space dimensions and with an enthalpy dependent source is studied here. Assuming that a strictly positive temperature is prescribed at the … green brown yarn
Stefan Problem - an overview ScienceDirect Topics
WebPrior to this study, much of the work on the inverse Stefan problem has been done for one-phase flow, see e.g. [5–10]. However, the literature on solving numerically the two-phase inverse Stefan problem is much more scarce, see [11–13]. A reason for this, as it has been pointed out earlier in the literature, is that standard direct problem ... WebSep 18, 2024 · Abstract. Artificial ground freezing (AGF) has historically been used to stabilize underground structure. Numerical methods generally require high computational … WebIn this paper, we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative procedure, which allows us to determine the position of the moving boundary. The presented method is an extension of … green brown white bathroom