Accurate and efficient solutions of compressible internal flows

The present paper applies a new 'perturbative lambda formulation' to one-dimensional and two-dimensional compressible internal flows. The lambda Euler equations are recasted in terms of perturbation-type variables, which are the difference between the usual characteristic (Riemann) variables and those corresponding to an appropriate incompressible flow. In this way the geometry-induced gradients are accounted for by the incompressible flow solution and the rather smooth correction, due to the compressibility effects, can be solved accurately even on a very coarse mesh. The perturbative equations are provided for the cases of one-dimensional and two-dimensional flows and are solved numerically by means of a fully implicit and an alternating direction implicit method, respectively. The accuracy and efficiency of the proposed approach is demonstrated by means of a few example-applications.