Numerical Simulation of Compressible Gas Flow in Flat Channels in the Narrow Channel Approximation

A compressible gas in plane channels of constant and variable cross sections is numerically simulated using two-dimensional parabolized Navier-Stokes equations. The system of equations is solved numerically using the narrow-channel approximation model. A number of transformations, such as nondimensionalization of the system of equations to reduce the given domain to a square and refinement of computational points with large gradients of gas-dynamic parameters, are described in detail. Pressure gradient is determined from the flow-rate conservation condition. An efficient method is given for simultaneously determining the pressure gradient and longitudinal velocity, followed by other gas-dynamic parameters of stability for subsonic and supersonic flows, as well as a method for determining the critical flow rate for solving Laval nozzle problems. The results of methodical calculations are presented to validate the calculation methodology and confirm the reliability of the results by comparing them with data obtained by other authors.