Peer-Reviewed Journal Details
Mandatory Fields
Mitchell, SL; Vynnycky, M
Applied Mathematics And Computation
Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems
Optional Fields
Stefan problem Boundary immobilization Starting solutions Keller box scheme Crank-Nicolson scheme BALANCE INTEGRAL METHOD MOVING BOUNDARY-PROBLEMS NUMERICAL-SOLUTION BOX SCHEMES SOLIDIFICATION
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. (C) 2009 Elsevier Inc. All rights reserved.
Grant Details