A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method.

DOI10.1016/S0096-3003(02)00846-9zbMath1034.65070MaRDI QIDQ1417002

Selcuk Kutluay, Alaattin Esen

Publication date: 18 December 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical examplesmoving boundary problemStefan problemfinite differenceEnthalpy methodHopscotch technique

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Free boundary problems for PDEs (35R35) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20)

Related Items (14)

A modified variable time step method for solving ice melting problem ⋮ Behavior of the solution of a Stefan problem by changing thermal coefficients of the substance ⋮ Numerical study of solid-liquid phase change by phase field method ⋮ The method of approximate fundamental solutions (MAFS) for Stefan problems for the sphere ⋮ On the Adomian decomposition method for solving the Stefan problem ⋮ Valuation of the American put option as a free boundary problem through a high-order difference scheme ⋮ The method of approximate fundamental solutions (MAFS) for Stefan problems ⋮ Ablative degradation of cryogenic thermal protection and fuel boil-off: improvement of using graded density insulators ⋮ An instantaneous semi-Lagrangian approach for boundary control of a melting problem. ⋮ An accurate numerical solution for the transient heating of an evaporating spherical droplet ⋮ A meshless method for one-dimensional Stefan problems ⋮ Numerical solutions of the one-phase classical Stefan problem using an enthalpy Green element formulation ⋮ Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems ⋮ Numerical schemes for one-dimensional Stefan-like problems with a forcing term

Uses Software

• Hopscotch

Cites Work

• Accurate solutions of moving boundary problems using the enthalpy method
• A Galerkin method for Stefan problems
• A new look at the heat balance integral method
• A variable time step Galerkin method for a one-dimensional Stefan problem
• The numerical solution of one-phase classical Stefan problem
• TWO METHODS FOR THE NUMERICAL SOLUTION OF MOVING-BOUNDARY PROBLEMS IN DIFFUSION AND HEAT FLOW
• A Method for Calculating Solutions of Parabolic Equations with a Free Boundary
• An efficient implementation of the enthalpy method
• A Comparative Study of Numerical Methods for Moving Boundary Problems
• Hopscotch: a Fast Second-order Partial Differential Equation Solver
• A Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue
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