Title | Investigation of difference methods for solving the problem of thermal conductivity with phase transitions |
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Authors | N. Y. Kudryashova^{1}, Y. V. Pervuhina^{2}^{1}Penza state university ^{2}Production Association «Estech» |

Annotation | The paper presents a physical and mathematical model of the laser welding process of two metal plates in the form of rectangular parallelepipeds of the same thickness, which are joined by the sides. When implementing this model, a three-dimensional difference scheme was constructed for a three-dimensional heat equation with phase transitions. A numerical method is presented that allows to decompose it into a chain of three one-dimensional difference schemes. An algorithm for finding the depth of the formed steam channel is given. Numerical modeling of all considered methods for solving the problem of thermal conductivity with phase transitions is carried out. |

Keywords | Stefan's problem, interphase boundary, laser welding, difference scheme |

Citation | Kudryashova N. Y., Pervuhina Y. V. ''Investigation of difference methods for solving the problem of thermal conductivity with phase transitions'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 96-100. Available at: https://conf.svmo.ru/files/2023/papers/paper14.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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