Solutions of the compressible Navier-Stokes equations using the integral method

The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.