Implicit upwind methods for the compressible Navier-Stokes equations

A c lass of implici t upwind-d i fferencing met hods for the compressibl e Navier-Stokes equaci ons i s des cr i bed and app l ied. The methods are based on the use of l ocal eigenvalues or wave speeds to control spat i al d ifferencing of inviscid terms and are a imed at i ncreasing the level of accuracy and stability achievable in computation. Tec hniques for accelerating the rate of convergence to a s teady-sta te so l ution are also used. Applications to invi sc i d and viscous transonic flows are discussed and compared with o ther methods and experi mental measurements . I t i s s hown that accurate and eff i cient t ransonic airf o i l calculations can be mad e on the Crayl computer i n l ess than 2 min.