INSTABILITIES OF STATIONARY INVISCID COMPRESSIBLE FLOW AROUND AN AIRFOIL

In this paper we numerically solve the stationary inviscid flow around an airfoil, Using the second-order explicit Runge-Kutta method in com bination with the MUSCL scheme and the minmod limiter, we do not obtai n a machine accurate solution. This has already been observed in liter ature and is explained by the non-differentiability of the minmod limi ter. An analysis of the limiter shows that it is possible to obtain a machine accurate solution with an asymmetric minmod limiter if an impl icit scheme with low CFL number is used. For higher CFL number the con vergence rate of this scheme increases considerably at the expense of a strong increase in the final residual level, A further study of the differences reveals that the steady state obtained with the implicit m ethod is In fact unstable and can only be found due to the dissipation present in the implicit method. In this paper we give some evidence t hat the stall in convergence with the explicit method might be caused by a physical instability in the wake behind the airfoil. This instabi lity is also predicted by linear stability theory and confirmed by a g rid refinement study. (C) 1997 Academic Press.