Instabilities of stationary inviscid compressible flow around an airfoil
The authors study the convergence behaviour of numerical solutions of the Euler equations for two-dimensional steady compressible flow around an airfoil section. Among other results, it is shown that machine-accurate solutions can be obtained with implicit time stepping by using the minmod limiter. In various test calculations the authors find that fast convergence to machine accuracy can be obtained by beginning the computation with a high CFL number, for which a threshold exists, and then by reducing it to smaller values. Additionally, in test computations with different limiter discretization schemes and grid sizes the authors show that the difference between the final residual levels obtained in the calculations is not caused by the minmod limiter but must be attributed to an instability of the flow itself. This result is confirmed with an analysis of the solution in the frame of linear stability theory. It could also be shown that the instability found in the mean flow is weak in its nature, so that the integral quantities as lift and drag are not affected within the engineering accuracy. On the whole, this is an interesting study of the aerodynamic stability problem with numerical tools.
scientific article; zbMATH DE number 1138378