Nonlinear instabilities and advantages of the completely conservative convective flux approximation in gas dynamic problems

This work is devoted to the study of emergence of nonlinear instabilities (i.e. instabilities due to nonlinear effects) in numerical gas modeling in that cases, when the linear analysis gives us the reason to consider chosen discretization as stable. The advantage of completely conservative flux approximation in comparison with conservative one is shown with the aid of analysis of particular solutions obtained here.