Implicit upwind methods for the compressible Navier-Stokes equations

A class of implicit upwind differencing methods for the compressible Navier-Stokes equations is described and applied. The methods are based on the use of local eigenvalues or wave speeds to control spatial differencing of inviscid terms and are aimed at increasing the level of accuracy and stability achievable in computation. Techniques for accelerating the rate of convergence to a steady state solution are also used. Applications to inviscid and viscous transonic flows are discussed and compared with other methods and experimental measurements. It is shown that accurate and efficient transonic airfoil calculations can be made on the Cray-l computer in less than 2 min.