Pseudospectral Method for Transonic Flows Around an Airfoil

摘要

This investigation attempted to construct a pseudospectral scheme that is highly accurate and competitive in computational efficiency with existing finite difference or finite volume methods. A hybrid scheme using spectral decomposition in the direction along the airfoil surface and a finite difference scheme in the other direction was found to be capable of resolving shock waves in one grid. Several filters have been studied. A low-pass filter in the spectral space was not able to stabilize the computation without seriously affecting the shock resolution. An algebraic filter that averages the flow variables around a grid point was capable of stabilizing the computations and maintaining the sharpness of the shock wave. The residue of the scheme did not decrease with time. The number of supersonic points in the flow field was taken as an indicator of convergence. Attempts to find another form of error norm were not successful. An explicit full spectral scheme studied with a Chebyshev polynomial expansion required excessive computing time and would not be competitive with a finite volume calculation using a dense grid.