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Application of viscous-filled nodal completely sonservative difference schemes to the gas dynamics equations in Euler variables on the Soda problem

TitleApplication of viscous-filled nodal completely sonservative difference schemes to the gas dynamics equations in Euler variables on the Soda problem
AuthorsM. E. Ladonkina1, 2, Y. A. Poveschenko1, 2, H. Z.1, 2
1Keldysh Institute of Applied Mathematics of RAS
2Moscow Institute of Physics and Technology
AnnotationFor the equations of gas dynamics in Euler variables, a family of two-layer time-dependent completely conservative difference schemes (CCDS) with time weights defined in space is created. Considerable attention is paid to the application of methods of constructing regularized flows of mass, momentum and internal energy preserving the properties of CCDS of this class on the classical Sod problem, to the analysis of their amplitude and the possibility of their use on non-uniform meshes. The constructed scheme has second-order accuracy and is realized by simple iterative processes. Methods and programs based on the constructed scheme for shock wave tube problems are developed. The developed program has high accuracy, even with large meshes. Testing of the classical Soda problem is performed to confirm the effectiveness of the developed scheme and methods.
KeywordsCompletely conservative difference scheme, method of reference operators, gas dynamics, Sod problem
CitationLadonkina M. E., Poveschenko Y. A., H. Z. ''Application of viscous-filled nodal completely sonservative difference schemes to the gas dynamics equations in Euler variables on the Soda problem'' [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. 129-134. Available at: https://conf.svmo.ru/files/2023/papers/paper19.pdf. - Date of access: 04.03.2024.