Abstract
We present two simple numerical methods to find the free boundary in one-phase Stefan problem. The work is motivated by the necessity for better understanding of the solution surface (temperatures) near the free boundary. We formulate a log-transform function with the unfixed and fixed free boundary that has Lipschitz character near free boundary. We solve the quadratic equation in order to locate the free boundary in a time-recursive way. We also present several numerical results which illustrate a comparison to other methods.
Highlights
The free boundary in a Stefan problem can give prediction of the boundary between two opposing materials
We present two simple numerical methods to find the free boundary in one-phase Stefan problem
We find the log-transform function with the unfixed and fixed free boundary to decide the free boundary by the Taylor series
Summary
The free boundary in a Stefan problem can give prediction of the boundary between two opposing materials. A boundary immobilization method (BIM), suggested by Landau [13], fixes the free boundary by using a transform method. The benefit of this function is its simple domain. The main contribution of this paper is the development of two simple numerical methods to find the free boundary in a time-recursive way. We exploit a log-transform function with the unfixed and fixed free boundary that has Lipschitz character which reduces the accumulating error of the solution surface near the free boundary.
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