The paper describes the numerical scheme of new type for the solving of nonlinear hyperbolic systems of PDEs. The main advantage of this scheme is the ability to efficiently compute the non-stationary problems with different scales. The tools for its construction include conventional Godunov approach, TVD principles and specific switching mechanism, which allows performing the calculations with respect to explicit or implicit pattern depending on the flow structure. The numerical computation of the swirled flow with the aid of first order scheme is demonstrated as an example. The effective calculation of the subtle structures of such flow demonstrates the relevance of presented schemes construction method.

Mathematical modelling in actual problems of science and technics