On propagation of 2D nonlinear density waves
Abstract:
Two-dimensional nonlinear density waves in a large-scale infinitesimal
gaseous medium with neglected selfgravity are considered. In terms of the
radially expanding features in the central disc of the Galaxy a reduced
model of axially symmetric density perturbations in a rotating disc is
investigated. Analytical estimations on the amplitude decay rate are
obtained, while integrating the governing hydrodynamical PDEs along the
characteristic curves. For nonsymmetric 2D propagation, we propose a
modified method of characteristics as an adaptive mesh approach that
incorporates straightforward treatment of the most critical integration
regions, such as of discontinuities and shock fronts.