An efficient ADI lambda formulation

This paper is concerned with the numerical simulation of compressible inviscid flows, by means of an accurate and efficient technique. The 'implicit lambda scheme', recently presented by the authors for the cases of quasi-one-dimensional flows and two-dimensional flows past thin airfoils, is generalized here to arbitrary two-dimensional geometries. Starting from the time-dependent Euler equations in vector form, simplified by assuming homentropic flow conditions, the lambda-formulation equations are derived for a general orthogonal coordinate system, linearized in time and solved by an alternating direction implicit method. Such a technique is very accurate, due to its use of characteristic-type variables and of upwind differences - which correctly take into account the direction of wave propagation - and efficient, insofar as it allows to overcome the CFL stability limitation of explicit methods, while requiring the solution of only block-tridiagonal systems. The importance of the choice of the computational grid and of the boundary conditions on the accuracy and, henceforth, on the efficiency of the calculations is analyzed in some detail. The merits of the present approach are demonstrated by means of a few applications.