Implicit implementation of the AUSM + and AUSM + up schemes

Abstract

SUMMARYAt the University of Liverpool, the Helicopter Multi‐Block (HMB2) CFD code is used for studies of various subsonic and transonic flows. This paper presents the implicit implementation in HMB2 of the AUSM + and AUSM + up, with a fully analytical Jacobian, so that a wider range of Mach numbers can be modelled, including high‐speed flows. A description of the derivation of the analytical Jacobian is given in this paper along with an evaluation of the performance of the implicit schemes for different test cases, including turbulent flows. As examples of high‐speed flows of aerospace interest, a blunt body, a single cone, a shock wave/turbulent boundary‐layer interaction and the Orion spacecraft have been considered. For the transonic regime, the RAE2822 aerofoil and the ONERA M6 wing have been used as test cases. Finally, for low Mach flows, the S809 wind turbine aerofoil and the MEXICO project wind turbine blade have been chosen. The shear stress transport and κ– ω turbulence models have been employed for the turbulent cases. The proposed implicit implementation of the AUSM + and AUSM + up schemes proved to have good efficiency and robustness without affecting the reliability of the original schemes.Copyright © 2014 John Wiley & Sons, Ltd.