Thermal and fluid flow effects during solidification in a rectangular enclosure
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...The instability, that develops as the depth of the moving boundary increases, was avoided with Gupta and Kumar’s method....
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...Gupta and Kumar [23] also modified the Douglas and Gallie’s method to solve the oxygen diffusion problem due to the absence of an explicit relationship between the velocity of the moving boundary and mass flux....
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...Gupta and Kumar [20] formulated the same set of finite difference equation as Douglas and Gallie but they used the Stefan condition to update the time step....
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...However, Gupta and Kumar [22], in a study of a convective boundary condition at the fixed end, found that Goodling and Khader’s method does not converge as the computation progresses in time....
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...The complications due to the non-uniform grid size around the moving boundary were avoided by the methods of Crank and Gupta [30], in which the entire uniform grid system moves with the velocity of the moving boundary....
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