A perturbative lambda formulation

This paper provides a new perturbative lambda formulation for the numerical solution of compressible flows. The time-dependent Euler equations are recast into compatibility equations for perturbative bicharacteristic variables that are the differences between the standard Riemann variables and those corresponding to an appropriate steady incompressible flow. In this way, the geometry-induced gradients are accounted for by the incompressible flow solution and the smooth correction accounting for compressibility effects is solved accurately even on a coarse mesh. The new perturbative lambda equations for two-dimensional homentropic flows are provided in a general orthogonal curvilinear coordinate system and solved numerically by means of an alternating direction implicit method. Results are presented for flow past a NACA 0012 airfoil that demonstrate the remarkable accuracy of the proposed methodology.