Singularity Problem for One-Dimensional Steady-State Gas Dynamics Problems

One-dimensional gas dynamics models are used to analyze flows whose parameters depend on a single spatial variable. Such models quickly and accurately predict changes in flow parameters. In the stationary case, such flows are described by ordinary differential equations. At velocities close to the sonic speeds, the flow can pass through the speed of sound, i.e., pass through a critical point. From a mathematical point of view, it is a question of occurrence of a singularity. The presence of a singularity causes difficulties in obtaining the solutions. The study considers a method for overcoming these difficulties using examples of flow in a channel of an arbitrary cross-section in the presence of friction, heat and mass transfer.