An implicit lambda scheme

Abstract

This paper is concerned with the numerical simulation of transonic inviscid flows. The unsteady Euler equations are written in characteristi c-type variables, discretized in time, and solved by means of an implicit technique or an alternating direction implicit technique, for one- and two-dimensional flows, respectively, so that only block-tridiagonal systems have to be solved at each time level. The present method has been successfully applied to one-dimension al transonic internal flows and two-dimensional transonic external flows within the framework of thin airfoil theory, and can be generalized to transonic two- and three-dimensional flows for arbitrary geometries. In all computed cases the present technique has proved itself reliable and about one order of magnitude more efficient than its well-known explicit counterpart.