On the accuracy of the modified Godunov method with discontinuous time-dependent basis functions

Title	On the accuracy of the modified Godunov method with discontinuous time-dependent basis functions
Authors	I. D. Kochurova¹, M. Е. Ladonkina^{1, 2}, V. F. Tishkin² ¹MIPT ²Keldysh Institute of Applied Mathematics, KIAM
Annotation	The paper explores the modification of the Godunov method using discon- tinuous basis functions. Instead of applying the traditional procedure, these basis functions are used, which adapt to the solution of the problem. In case of a violation of the entropy inequality in a cell, the original method is locally translated into a first-order method on a grid that has been halved. The paper shows that this method can be used without limiting functions when solving problems that contain strong shock waves. The accuracy of the method is investigated by solving a problem involving a simple wave, until the gas dynamic functions become smooth.
Keywords	the Godunov method with discontinuous basis functions, Euler’s equations, the Godunov method, shock waves.
Citation	Kochurova I. D., Ladonkina M. Е., Tishkin V. F. ''On the accuracy of the modified Godunov method with discontinuous time-dependent basis functions'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 88-93. Available at: https://conf.svmo.ru/files/2024/papers/paper14.pdf. - Date of access: 03.12.2024.