Construction of edge-based 1-exact schemes for solving the Euler equations on hybrid unstructured meshes

In this paper, 1-exact vertex-centered finite-volume schemes with an edge-based approximation of fluxes are constructed for numerically solving hyperbolic problems on hybrid unstructured meshes. The 1-exactness property is ensured by introducing a new type of control volumes, which are called semitransparent cells. The features of a parallel algorithm implementing the computations using semitransparent cells on modern supercomputers are described. The results of solving linear and nonlinear test problems are given.