A DAE approach to similarity solutions of unsteady fluid flows: An application case study

This note presents a discussion on the singularity crossing phenomenon (also known as sonic transition) of the unsteady fluid flows in gravitational fields with singularities. The systems of differential-algebraic equations that result from the similarity treatment in the unsteady fluid flow applications exhibit the singularity induced bifurcation phenomenon typical for the steady-state quasilinear or semi-explicit differential-algebraic equations in circuits, MHD, gas dynamics and other areas.