Solving incompressible or compressible Navier-Stokes equations using Chebyshev or Fourier collocation spectral methods (Fortran)

In this project, a chebyshev collocation spectral method is applied to the incompressible Navier-Stokes (NS) equations based on the artificial compressibility to simulate incompressible fluid flows. Temporal terms are also discretized using high-order explicit Runge-Kutta methods. For compressible fluid flows, a fourier collocation spectral method is used. The quadrature points and basis functions are different in these two methods. Some of the results are presented in following.