Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems

Research output: Contribution to journalArticlepeer-review

Abstract

Although the numerical solution of one-dimensional phase-change, or Stefan, problems is well documented, a review of the most recent literature indicates that there are still unresolved issues regarding the start-up of a computation for a region that initially has zero thickness, as well as how to determine the location of the moving boundary thereafter. This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes. We demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used, and is numerically second-order accurate in both time and space, a point that has been consistently overlooked for this type of moving-boundary problem.

Original languageEnglish
Pages (from-to)1609-1621
Number of pages13
JournalApplied Mathematics and Computation
Volume215
Issue number4
DOIs
Publication statusPublished - 15 Oct 2009

Keywords

  • Boundary immobilization
  • Crank-Nicolson scheme
  • Keller box scheme
  • Starting solutions
  • Stefan problem

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