A Buffered Fourier Spectral Method for Non-periodic Pde

Standard Fourier spectral method can be used to solve a lot of problems with periodic boundary conditions. However, for non-periodic boundary condition problems, standard Fourier spectral method is not efficient or even useless. This work has developed a new way to use Fourier spectral method for non-periodic boundary condition problems. First, the original function is normalized and then a smooth buffer polynomial is developed to extend the normalized function domain. The new function will be smooth and periodic with both function values and derivatives, which is easy to be treated by standard FFT for high resolution. This method has obtained high order accuracy and high resolution with a penalty of 25% over standard Fourier spectral method, as shown by our examples. The scheme demonstrates to be robust. The method will be further used for simulation of transitional and turbulent flow.