Computational Methods for Problems in Aerodynamics and Large Space StructuresUsing Parallel and Vector Architectures

摘要

The objective of our research was to design a computer code capable of simulatinginteractions between complicated flows and shock waves. It is possible to completely overcome the Gibbs phenomenon from the approximation (or signal processing) point of view. The main theoretical breakthrough has been the observation that the Gibbs phenomenon does not apply to moments of the approximated function. These moments are obtained with high accuracy. The only remaining difficulty is the accurate reconstruction of a given function from its moments. We have suggested and tested several different methods. Computationally the above ideas are carried out as low-pass filters. We have proved that when a discontinuous signal is being evolved in time by a linear system of hyperbolic equations, the moments are obtained with spectral accuracy. An essentially non-oscillatory spectral method is developed for the numerical simulations of non-linear equations. Cell Averages techniques are developed for Fourier and Chebyshev Spectral methods. This techniques is crucial for modern shock capturing techniques. (JHD)