On phase space peculiarities of gas dynamics equations for a supersonic initial-boundary value problem
This paper contains results on phase space analysis of supersonic flow over rigid body initial-boundary value problem for gas dynamics equations in extreme turbulent regime. At first some characteristics of hyperbolic PDEs are described. The structure of the operator is shown and discontinuous solutions (shock waves, rarefaction waves and contact discontinuities) are presented. Then the theorem on impossibility of perturbation propagation over a stationary shock wave is proven. In order to investigate the phase space a detail description of high order numerical method is presented and extreme turbulent regime model is described. The numerical method is applied to the initial-boundary value problem. The fundamental result is the difference in phase space configuration from incompressible and weakly compressible flow equations. The separation of phase space is found alongside characteristic lines that confirms theorem results. Different bifurcation cascades are shown in different parts of spacial domain for a single initial-boundary value problem. Thus the infinite dimensional phase space for the given problem is a unity of infinite dimensional independent phase subspaces.