Special Aspects of Hybrid Kinetic-Hydrodynamic Model When Describing the Shape of Shockwaves

摘要

A mathematical model of the flow of a polyatomic gas containing a combination of the Navier-Stokes-Fourier model (NSF) and the model kinetic equation of polyatomic gases is presented. At the heart of the hybrid components is a unified physical model, as a result of which the NSF model is a strict first approximation of the model kinetic equation. The model allows calculations of flow fields in a wide range of Knudsen numbers (Kn), as well as fields containing regions of high dynamic nonequilibrium. The boundary conditions on a solid surface are set at the kinetic level, which allows, in particular, to formulate the boundary conditions on the surfaces absorbing or emitting gas. The hybrid model was tested. The example of the problem of the shock wave profile shows that up to Mach numbers M ≈ 2 the combined model gives smooth solutions even in those cases where the sewing point is in a high gradient region. For the Couette flow, smooth solutions are obtained at M = 5, Kn = 0.2. A model effect was discovered: in the region of high nonequilibrium, there is an almost complete coincidence of the solutions of the kinetic region of the combined model and the "pure" kinetic solution.