This program simulates incompressible flow in a spherica gap based on a pseudo-spectral technique developed by G. Dumas. The technique relies on the use of special divergence-free test functions that vanish on the boundary to eliminate pressure from the set of unknown variables. The time-evolution is performed in spectral space which has fewer degrees of freedom than the physical space. Nevertheless, every time-step requires transforming back to physical space but this cab be performed efficiently by the Fourier Transform routine FFTW3.
The program is implemented with FORTRAN in the file main.f90 and relies on the following libraries:
- FFTW3 (http://www.fftw.org/)
- SHTns (https://bitbucket.org/nschaeff/shtns/src/master/)
- lapack (https://www.netlib.org/lapack/)
The program is compiled with the command make and generates the executable main which can be run with the command ./main. Although, before compliling, one must ensure that the path to the libraries in the makefile are set correctly.
A report of the theoretical basis and the implemntation can be found in the file report.pdf.