Abstract
The increasing capabilities of higher order methods used in computational
fluid dynamics enables the analysis of previously little understood phenomena. One such case is the intricate flow mechanism causing obstructive sleep
apnea. In working towards a better understanding of the flow mechanism,
a arbitrarily high order Discontinuous-Galerkin Immersed boundary method
has been developed for the 2D compressible Navier-Stokes equations. The
arbitrarily high order is achieved using a novel approach to the construction
of basis functions. The method is tested on the case of a flow over a circular
cylinder. Results are obtained which indicate that further investigation is
needed, but that the method is indeed capable of qualitatively reproducing
the expected behaviour.