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<p>In this paper, we have developed a novel technique for solving 2D moving boundary problems showing the melting of a solid material. The complete analysis is presented in a non-dimensional form. The approximation of non-dimensional temperature is considered a linear combination of a 2D Legendre wavelet with the Gaussian function. Using the Galerkin method, the moving boundary problem of partial differential equations is converted into a system of linear parametric equations in which the number of equations is more than the number of unknown variables. We have used the singular value decomposition (SVD) method to solve this problem. Picard's iteration process is applied to determine the moving front. To validate our approach, we plotted figures between the errors obtained from the model equations. The impact of the Fourier number, Biot number, Kirpichev number, Predvoditelev number, and space coordinate on the moving front are briefly discussed.</p>

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SVD Galerkin Method in 2D Moving Boundary Problem of Heat Transfer

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Subrahamanyam Upadhyay,
  • Hasim Khan,
  • Vikas Chaurasiya,
  • Abhinav Goel,
  • Harpreet Kaur,
  • Priti Sharma

摘要

In this paper, we have developed a novel technique for solving 2D moving boundary problems showing the melting of a solid material. The complete analysis is presented in a non-dimensional form. The approximation of non-dimensional temperature is considered a linear combination of a 2D Legendre wavelet with the Gaussian function. Using the Galerkin method, the moving boundary problem of partial differential equations is converted into a system of linear parametric equations in which the number of equations is more than the number of unknown variables. We have used the singular value decomposition (SVD) method to solve this problem. Picard's iteration process is applied to determine the moving front. To validate our approach, we plotted figures between the errors obtained from the model equations. The impact of the Fourier number, Biot number, Kirpichev number, Predvoditelev number, and space coordinate on the moving front are briefly discussed.