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

2009 ◽  
Vol 215 (4) ◽  
pp. 1609-1621 ◽  
Author(s):  
S.L. Mitchell ◽  
M. Vynnycky
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
One Dimensional ◽  
Stefan Problems ◽  
Difference Methods

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 523-527 ◽  
Author(s):  
James Caldwell ◽  
Svetislav Savovic´ ◽  
Yuen-Yick Kwan
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Finite Difference Methods ◽  
Melting Process ◽  
Time Dependent ◽  
One Dimensional ◽  
Stefan Problems ◽  
Finite Difference Solution ◽  
Very High

The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However, very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.

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