Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations

Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly in solutions multidimensional Euler equations. In this paper we study the convergence first-order finite volume method based on exact Riemann solver complete Specifically, derive entropy inequality prove consistency numerical method. Passing limit, show weak strong identify their limit. The results presented spiral, Kelvin-Helmholtz Richtmyer-Meshkov problem are consistent with our theoretical analysis.