О численной апробации одной энтропийно консервативной разностной схемы для уравнений газовой динамики
Using the linear theory of waves in a compressible atmosphere located in a gravitational field, we found a family of sound speed profiles for which the wavefield can be represented by a traveling wave with no reflection. The vertical flux of wave energy on these nonreflected profiles is retained, which proves that the energy transfer may occur over long distances.
We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system.