TY - JOUR
T1 - Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems
AU - Mitchell, S. L.
AU - Vynnycky, M.
PY - 2009/10/15
Y1 - 2009/10/15
N2 - 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.
AB - 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.
KW - Boundary immobilization
KW - Crank-Nicolson scheme
KW - Keller box scheme
KW - Starting solutions
KW - Stefan problem
UR - http://www.scopus.com/inward/record.url?scp=70450144252&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2009.07.054
DO - 10.1016/j.amc.2009.07.054
M3 - Article
AN - SCOPUS:70450144252
SN - 0096-3003
VL - 215
SP - 1609
EP - 1621
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 4
ER -