Inviscid and viscous flow computations by means of a lambda methodology: a review

The present paper provides a review of the more important results obtained by the author, sometimes with co-authors, solving inviscid and viscous compressible flows by means of a lambda methodology. In particular, an implicit numerical algorithm, called fast solver, has always been applied. This methodology separately integrates the compatibility conditions, written in terms of generalized Riemann variables, along appropriate bicharacteristic lines. The multi-dimensional flow problem is, thus, reduced to a sequence of simple quasi one-dimensional problems. The merits of this approach are demonstrated by means of the application of the method to the solution of three dimensional (3-D) subsonic and transonic inviscid flows, of two-dimensional (2-D) and 3-D viscous flows and of the 2-D flow around a vertical axis wind turbine. In the transonic case the shock wave is computed by means of a shock fitting technique, which enforces the proper shock jumps by an explicit use of the Rankine-Hugoniot equations; in the wind turbine case the blades are represented in a time-averaged sense by means of an actuator porous cylinder, having the turbine radius. The results are then compared with other numerical results and with experimental results.