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Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method

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Abstract

In this paper, we consider the inverse one-phase one-dimensional Stefan problem to study the thermal processes with phase change in a moving boundary problem and calculate the temperature distribution in the given domain, as well as approximate the temperature and the heat flux on a boundary of the region. For this problem, the location of the moving boundary and temperature distribution on this curve are available as the extra specifications. First, we use the Landau’s transformation to get a rectangular domain and then apply the Crank–Nicolson finite-difference scheme to discretize the time dimension and reduce the problem to a linear system of differential equations. Next, we employ the radial basis function collocation technique to approximate the spatial unknown function and its derivatives at each time level. Finally, the linear systems of algebraic equations constructed in this way are solved using the LU factorization method. To show the numerical convergence and stability of the proposed method, we solve two benchmark examples when the boundary data are exact or contaminated with additive noises.

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Authors and Affiliations

  1. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    Yasaman Lotfi & Kourosh Parand

  2. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    Kourosh Parand & Jamal Amani Rad

  3. Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

    Kamal Rashedi

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  1. Yasaman Lotfi
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  2. Kourosh Parand
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  3. Kamal Rashedi
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  4. Jamal Amani Rad
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Correspondence to Jamal Amani Rad.

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Lotfi, Y., Parand, K., Rashedi, K. et al. Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method. Engineering with Computers 37, 461–475 (2021). https://doi.org/10.1007/s00366-019-00835-9

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