In order to participate in the seminar, on June 25 after 4:45 pm (UTC+7) you should connect to the Zoom conference via the following link or manually using the Zoom conference ID 897 7646 2466 and password 549526.The system of equations of gas dynamics (Euler's equations) is constituted by integral conservation laws, which in the regions of smoothness of the solution are reduced to a system of quasilinear partial differential equations of hyperbolic type. Among the methods for the numerical solution of these equations, difference schemes that are based on the stream form of writing difference equations (the finite volume method) and the problem of discontinuity decay as a method for calculating fluxes are currently most widely used (S. K. Godunov, 1959). Since the publication of the basic technique, the method of S. K. Godunov was significantly improved and generalized to other classes of problems described by conservation laws. In all these algorithms, known as "Godunov type schemes", the hyperbolicity of conservation laws is hidden in the Hugoniot relations, or their simplified analogs (Ph. Roe), and the fact of the existence of characteristics, as the most significant sign of hyperbolicity, was not used in any way.
Another approach to the numerical solution of equations of the laws of conservation of hyperbolic type (the CABARET scheme) is also based on the flow form of writing the difference equations, however, to calculate the flows, not the decay of the discontinuity is used, but the characteristic form of the original equations. The flows are formed on the basis of local Riemann invariants (quasi-invariants) determined by the approximation of the characteristic shape within each space-time computational cell. The term "CABARET scheme" is a designation of a whole class of conservative-characteristic (KX) difference schemes for systems of hyperbolic equations loaded (perturbed) by integral and differential operators of higher orders. The CABARET scheme can be considered as an alternative to the S. K. Godunov.
The report is devoted to a brief review of the history of the development of CH, an analysis of their features and examples of use in problems of aeroacoustics, hydrogen safety and computational oceanology.
