A quasi-conservative coin lambda formulation

Abstract

INTRODUCTION The present paper is concerned with the numerical simulation of transonic inviscid flows. Among the several numerical methods developed for such computations, the so-called lambda formulation (e.g., Ref. I) has several, very desirable features. In order to enhance the accuracy of this formulation, Moretti et al.(e.g., Ref. 2) have developed a very accurate numerical scheme, while Dadone and Napolitano /3/ have shown that a significant improvement is obtained by employing a perturbative formulation. The classical lambda formulation has its drawbacks when transonic flows have to be computed: the supersonic region is decoupled from the shocked subsonic one, once the shock wave is established. On the contrary such a coupling is allowed by the "flux difference splitting" methodologies, by splitting the waves containing a "sonic point". By inserting such a basic mechanism into the classical lambda formulation, Dadone and Magi /4/ obtained a modified lambda formulation, characterized by a supersonic flow region coupled with the shocked subsonic one and apt to compute transonic flows with weak shocks. The present paper provides the extension of the previous quasi conservative methodology to higher shock strengths, by modifying the correction terms used in the shock transition region. Moreover, a COIN variant is presented which has been obtained by modifying the perturbative formulation /3/. Transonic flows can thus be accurately and efficiently computed.