Title | Application of the LU-SGS method for solving unsteady gas dynamics problems using implicit schemes |
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Authors | R. V. Zhalnin^{1}, I. S. Kazakova^{1}^{1}National Research Ogarev Mordovia State University |

Annotation | The article presents an overview of methods for developing the computational algorithm for solving one-dimensional Euler system of gas dynamics equations. Bases of the algorithm are implicit Godunov scheme, LU-SGS solver and minmod limiter. The article presents results of approbation of the algorithm on serie of one-dimensional problems, namely order of accuracy of the realized scheme and profiles of gas dynamics parameters. It was also demonstrated probability of application of the LU-SGS solver on two-dimensional problems by solving model tests. |

Keywords | Euler equations of gas dynamics, implicit Godunov scheme, Lax-Friedrichs fluxes, minmod limiter, LU-SGS method, Riemann problem. |

Citation | Zhalnin R. V., Kazakova I. S. ''Application of the LU-SGS method for solving unsteady gas dynamics problems using implicit schemes'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 14-18, 2022). Saransk: SVMO Publ, 2022. - pp. 89-99. Available at: https://conf.svmo.ru/files/2022/papers/paper14.pdf. - Date of access: 24.07.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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