An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing
In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of the problem, we present three schemes based on diff...
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| Format: | Article |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1924 |
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| author | Vasily Vasil’ev Maria Vasilyeva |
| author_facet | Vasily Vasil’ev Maria Vasilyeva |
| author_sort | Vasily Vasil’ev |
| collection | DOAJ |
| description | In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of the problem, we present three schemes based on different smoothing of the sharp phase change interface. We propose the method using smooth coefficient approximation based on the analytical smoothing of discontinuous coefficients through an error function with a given smoothing interval. The second method is based on smoothing in one spatial interval (cell) and provides a minimal length of smoothing calculated automatically for the given values of temperatures on the mesh. The third scheme is a convenient scheme using a linear approximation of the coefficient on the smoothing interval. The results of the numerical computations on a model problem with an exact solution are presented for the one-dimensional formulation. The extension of the method is presented for the solution of the two-dimensional problem with numerical results. |
| first_indexed | 2024-03-10T15:09:25Z |
| format | Article |
| id | doaj.art-d29eb1cdce9c4e058128d76cdb6179cf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:09:25Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d29eb1cdce9c4e058128d76cdb6179cf2023-11-20T19:29:12ZengMDPI AGMathematics2227-73902020-11-01811192410.3390/math8111924An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient SmoothingVasily Vasil’ev0Maria Vasilyeva1Multiscale model reduction Laboratory, North-Eastern Federal University, 677007 Yakutsk, RussiaMultiscale model reduction Laboratory, North-Eastern Federal University, 677007 Yakutsk, RussiaIn this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of the problem, we present three schemes based on different smoothing of the sharp phase change interface. We propose the method using smooth coefficient approximation based on the analytical smoothing of discontinuous coefficients through an error function with a given smoothing interval. The second method is based on smoothing in one spatial interval (cell) and provides a minimal length of smoothing calculated automatically for the given values of temperatures on the mesh. The third scheme is a convenient scheme using a linear approximation of the coefficient on the smoothing interval. The results of the numerical computations on a model problem with an exact solution are presented for the one-dimensional formulation. The extension of the method is presented for the solution of the two-dimensional problem with numerical results.https://www.mdpi.com/2227-7390/8/11/1924heat transferStefan problemphase changenumerical methodcoefficient smoothingfinite element method |
| spellingShingle | Vasily Vasil’ev Maria Vasilyeva An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing Mathematics heat transfer Stefan problem phase change numerical method coefficient smoothing finite element method |
| title | An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing |
| title_full | An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing |
| title_fullStr | An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing |
| title_full_unstemmed | An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing |
| title_short | An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing |
| title_sort | accurate approximation of the two phase stefan problem with coefficient smoothing |
| topic | heat transfer Stefan problem phase change numerical method coefficient smoothing finite element method |
| url | https://www.mdpi.com/2227-7390/8/11/1924 |
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