On a Lagrangian-Eulerian method calculation of unsteady flows compressible media

In this paper, a numerical method for calculating two-dimensional flows in Eulerian coordinates is implemented, which is based on an explicit Lagrangian-Eulerian difference scheme. The calculation of each time step is carried out in two stages. At the Lagrangian stage, a difference scheme based on the Kuropatenko method is used, which has zero energy dissipation on smooth solutions and minimal distraction on strong discontinuities. At the Eulerian stage, the mesh is rebuilded and all the parameters of the substance are recalculated from the old mesh to the new one in accordance with the laws of conservation of mass, momentum and energy. The developed numerical algorithm has shown its operability when tested on tasks having an analytical or reference solution.