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Application of the LU-SGS method for solving unsteady gas dynamics problems using implicit schemes

TitleApplication of the LU-SGS method for solving unsteady gas dynamics problems using implicit schemes
AuthorsR. V. Zhalnin1, I. S. Kazakova1
1National Research Ogarev Mordovia State University
AnnotationThe 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.
KeywordsEuler equations of gas dynamics, implicit Godunov scheme, Lax-Friedrichs fluxes, minmod limiter, LU-SGS method, Riemann problem.
CitationZhalnin 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: 30.11.2022.