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Stefan Problem (stefan + problem)

Distribution by Scientific Domains
Mathematics and Statistics71%

Selected Abstracts

Discontinuous Galerkin framework for adaptive solution of parabolic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007
Deepak V. Kulkarni
Abstract Non-conforming meshes are frequently employed in adaptive analyses and simulations of multi-component systems. We develop a discontinuous Galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non-conforming mesh interfaces. A benefit of the DG scheme is that it does not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. The salient features of the formulation are highlighted through an a priori analysis. When coupled with a mesh refinement scheme the DG formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems. We demonstrate our approach by analysing the Stefan problem of solidification. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Numerical approximation of a thermally driven interface using finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
P. Zhao
Abstract A two-dimensional finite element model for dendritic solidification has been developed that is based on the direct solution of the energy equation over a fixed mesh. The model tracks the position of the sharp solid,liquid interface using a set of marker points placed on the interface. The simulations require calculation of the temperature gradients on both sides of the interface in the direction normal to it; at the interface the heat flux is discontinuous due to the release of latent heat during the solidification (melting) process. Two ways to calculate the temperature gradients at the interface, evaluating their interpolants at Gauss points, were proposed. Using known one- and two-dimensional solutions to stable solidification problems (the Stefan problem), it was shown that the method converges with second-order accuracy. When applied to the unstable solidification of a crystal into an undercooled liquid, it was found that the numerical solution is extremely sensitive to the mesh size and the type of approximation used to calculate the temperature gradients at the interface, i.e. different approximations and different meshes can yield different solutions. The cause of these difficulties is examined, the effect of different types of interpolation on the simulations is investigated, and the necessary criteria to ensure converged solutions are established. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A phenomenon of waiting time in phase change problems driven by radiative heat transfer

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2009
A. Fasano
Abstract In the paper (J. Food Process Eng. 2008; in press) we emphasized that during a phase change process in which the heat input is driven by a radiation transfer mechanism, a peculiar phenomenon may occur, characterized by a temporary stop of the increase of the boundary temperature due to a sudden change of the heat transfer coefficient upon phase transition. This time interval is needed to allow the thermal properties of the surface to evolve toward a state that is compatible with the heat intake rate corresponding to the new phase. The occurrence of the waiting time is motivated and studied for a general one-dimensional Stefan problem. Then an application is presented to the much complicated problem considered in (J. Food Process Eng. 2008; in press), namely, the model for frying process. Copyright © 2008 John Wiley & Sons, Ltd. [source]

An analytical and numerical study of the Stefan problem with convection by means of an enthalpy method

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2001
E. Casella1
Abstract In this paper, we consider a theoretical and numerical study of the Stefan problem with convection, described by the Navier,Stokes equations with no-slip boundary conditions. The mathematical formulation adopted is based on the enthalpy method. The existence of a weak solution is proved in the bidimensional case. The numerical effectiveness of the model considered is confirmed by some numerical results. Copyright © 2001 John Wiley & Sons, Ltd. [source]

On the numerical approach of the enthalpy method for the Stefan problem

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004
Khaled Omrani
Abstract In this article an error bound is derived for a piecewise linear finite element approximation of an enthalpy formulation of the Stefan problem; we have analyzed a semidiscrete Galerkin approximation and completely discrete scheme based on the backward Euler method and a linearized scheme is given and its convergence is also proved. A second-order error estimates are derived for the Crank-Nicolson Galerkin method. In the second part, a new class of finite difference schemes is proposed. Our approach is to introduce a new variable and transform the given equation into an equivalent system of equations. Then, we prove that the difference scheme is second order convergent. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source]