Niels Bohr Institutet > Kalender - det sker på NBI > 2010 > Master Thesis by Jan V...

Master Thesis by Jan Valentin

On the Spectral Method

This master thesis defense focuses on the spectral method for modeling turbulent flow past an object. The Darcy term is applied to control the boundaries of the object for the purpose of showing that the method might be used for topology optimization. The thesis is mainly theoretical and so symmetries, conservation laws and the energy budget are deduced for the compressible Navier-Stokes flow, with good results.

Amongst these results, it is shown that helicity is in fact conserved for compressible flows for the viscosity going to zero.

Some numerical modeling, using sine transforms, are conducted, where the theory, in addition, is used to verify the results. The simulations are programmed in Java and uses parallel methods on multi-pc systems. The resulting energy spectra and flow plots of the simulations indicate some correctness of the model, but it is concluded that more powerful numerical methods must be taken into use to conduct further research.