The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Mahir Hadžic - One of the best experts on this subject based on the ideXlab platform.
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global stability of steady states in the classical Stefan Problem for general boundary shapes
Philosophical Transactions of the Royal Society A, 2015Co-Authors: Mahir Hadžic, Steve ShkollerAbstract:The classical one-phase Stefan Problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperat...
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global stability and decay for the classical Stefan Problem
Communications on Pure and Applied Mathematics, 2015Co-Authors: Mahir Hadžic, Steve ShkollerAbstract:The classical one-phase Stefan Problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accom- plished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small tempera- tures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities. 1.1. The Problem formulation. We consider the Problem of global existence and asymptotic stability of classical solutions to the classical Stefan Problem describing the evolving free-boundary between the liquid and solid phases. The temperature of the liquid p(t,x) and the a priori unknown moving phase boundary ( t) must satisfy the following system of equations:
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global stability and decay for the classical Stefan Problem
arXiv: Analysis of PDEs, 2012Co-Authors: Mahir Hadžic, Steve ShkollerAbstract:The classical one-phase Stefan Problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities.
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orthogonality conditions and asymptotic stability in the Stefan Problem with surface tension
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Mahir HadžicAbstract:We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan Problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.
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stability in the Stefan Problem with surface tension i
Communications in Partial Differential Equations, 2010Co-Authors: Mahir Hadžic, Yan GuoAbstract: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.
Domingo A Tarzia - One of the best experts on this subject based on the ideXlab platform.
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an exact solution to a Stefan Problem with variable thermal conductivity and a robin boundary condition
Nonlinear Analysis-real World Applications, 2018Co-Authors: Andrea N Ceretani, Natalia N Salva, Domingo A TarziaAbstract:Abstract In this article it is proved the existence of similarity solutions for a one-phase Stefan Problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a generalized modified error function which is defined as the solution to a nonlinear ordinary differential Problem of second order. It is proved that the latter has a unique non-negative bounded analytic solution when the parameter on which it depends assumes small positive values. Moreover, it is shown that the generalized modified error function is concave and increasing, and explicit approximations are proposed for it. Relation between the Stefan Problem considered in this article with those with either constant thermal conductivity or a temperature boundary condition is also analysed.
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exact solution for a two phase Stefan Problem with variable latent heat and a convective boundary condition at the fixed face
Zeitschrift für Angewandte Mathematik und Physik, 2018Co-Authors: Julieta Bollati, Domingo A TarziaAbstract:Recently, in Tarzia (Thermal Sci 21A:1–11, 2017) for the classical two-phase Lame–Clapeyron–Stefan Problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction was obtained. Motivated by this article we study the two-phase Stefan Problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary Problem. We also consider the limit to our Problem when that coefficient goes to infinity obtaining a new free boundary Problem, which has been recently studied in Zhou et al. (J Eng Math 2017. https://doi.org/10.1007/s10665-017-9921-y).
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explicit solution for a Stefan Problem with variable latent heat and constant heat flux boundary conditions
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Natalia N Salva, Domingo A TarziaAbstract:Abstract In Voller, Swenson and Paola [V.R. Voller, J.B. Swenson, C. Paola, An analytical solution for a Stefan Problem with variable latent heat, Int. J. Heat Mass Transfer 47 (2004) 5387–5390], and Lorenzo-Trueba and Voller [J. Lorenzo-Trueba, V.R. Voller, Analytical and numerical solution of a generalized Stefan Problem exhibiting two moving boundaries with application to ocean delta formation, J. Math. Anal. Appl. 366 (2010) 538–549], a model associated with the formation of sedimentary ocean deltas is studied through a one-phase Stefan-like Problem with variable latent heat. Motivated by these works, we consider a two-phase Stefan Problem with variable latent of fusion and initial temperature, and constant heat flux boundary conditions. We obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary Problem for a semi-infinite material. Moreover, the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity.
Atusi Tani - One of the best experts on this subject based on the ideXlab platform.
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classical solvability of the two phase Stefan Problem in a viscous incompressible fluid flow
Mathematical Models and Methods in Applied Sciences, 2002Co-Authors: Yoshiaki Kusaka, Atusi TaniAbstract:In this paper we study the two-phase Stefan Problem for a viscous incompressible fluid which is a model of melting a solid to a liquid or of soldificating a liquid to a solid with a liquid flowing. The unique solvability is established in Holder spaces locally in time. The method of the proof is rather standard, however the result obtained is completely new: the existence in the Holder spaces with the same Holder exponents as the data and the uniqueness also in the same Holder spaces.
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on the classical solvability of the Stefan Problem in a viscous incompressible fluid flow
Siam Journal on Mathematical Analysis, 1999Co-Authors: Yoshiaki Kusaka, Atusi TaniAbstract:This paper is devoted to the study of a solidification/melting process in the case where the fluid is flowing. Such a phenomenon is described by the Stefan Problem with transport terms in the equation of the temperature distribution and the initial-boundary value Problem for the incompressible Navier--Stokes equations. The existence of the classical solution is proved locally in time.
Adriana C Briozzo - One of the best experts on this subject based on the ideXlab platform.
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non classical Stefan Problem with nonlinear thermal coefficients and a robin boundary condition
Nonlinear Analysis-real World Applications, 2019Co-Authors: Adriana C Briozzo, Maria F NataleAbstract:Abstract A non-classical one dimensional Stefan Problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x = 0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x = 0 . Existence of a similarity type solution is obtained and the asymptotic behaviour of free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.
Jinzi Mac Huang - One of the best experts on this subject based on the ideXlab platform.
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a stable and accurate scheme for solving the Stefan Problem coupled with natural convection using the immersed boundary smooth extension method
Journal of Computational Physics, 2021Co-Authors: Jinzi Mac Huang, Michael Shelley, David B SteinAbstract:Abstract The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale “stone forests” of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan Problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these Problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan Problem coupled to a fluid flow. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ-L scheme that provides stable evolution of the boundary. We demonstrate 3rd-order temporal and pointwise spatial convergence of the scheme for the classical Stefan Problem, and 2nd-order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments.
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a stable and accurate scheme for solving the Stefan Problem coupled with natural convection using the immersed boundary smooth extension method
arXiv: Fluid Dynamics, 2020Co-Authors: Jinzi Mac Huang, Michael Shelley, David B SteinAbstract:The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan Problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these Problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan Problem coupled to a fluid flow. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a {\theta}-L scheme that provides stable evolution of the boundary. We demonstrate third-order temporal and pointwise spatial convergence of the scheme for the classical Stefan Problem, and second-order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments.
