Pseudospectral approximation in a parabolized Navier-Stokes code

A pseudospectral method which is a combination of a spectral method and a collocation method offers an alternative to finite difference and finite element methods for problems with complex geometries. Spectral methods have the potential of yielding high accuracy for a given number of spatial nodes or collocation points. In this thesis, a parabolized Navier-Stokes code known as the Air Force Wright Aeronautical Laboratories Parabolized Navier-Stokes Code (AFWAL PNS Code) has been modified to make it pseudospectral in the circumferential direction. This modification uses a Fourier spectral method to obtain an accurate solution. Numerical solutions of the three-dimensional parabolized Navier-Stokes equations were obtained for a shuttle-like geometry at Mach 7.4 at an angle of attack of 20 degrees for comparison of finite difference and spectral approximations in the' circumferential direction. These computations indicate that the spectral approximation required approximately 4% more computing time while achieving results essentially identical to a second-order finite difference scheme. The second-order accurate finite-difference terms on the left hand side of the solution algorithm in the AFWAL PNS Code are suspected of dominating the accuracy of the solution and causing the spectral approximation results to be less accurate than expected. The smoothing terms in the numerical algorithm also have an influence on the accuracy of a solution. Further study would be necessary to determine how to optimize the AFWAL PNS Code numerical algorithms to obtain the potential accuracy of the spectral technique.