332	RWTH Publication No: 47342        2011        IGPM332.pdf
TITLE	Adaptive Multiresolution Finite Volume Discretization of the Variational Multiscale Method. General Framework.
AUTHORS	Wolfgang Dahmen, Thomas Gotzen, Siegfried Müller, Roland Schäfer
ABSTRACT	In order to investigate turbulent phenomena in compressible flows the Variational Multiscale method is used. This method is usually applied to incompressible flows. In a first step, we derive the VMS method for the compressible Navier-Stokes equations. The resulting weak formulation of the flow equations is split into resolved and unresolved scales using multiresolution techniques based on biorthogonal wavelets. Since the in principle infinite-dimensional subspace of fluctuations is also discretized, it needs to be stabilized by additional dissipative terms. The compressible VMS method is then incorporated into an adaptive multiresolution finite volume solver, where grid adaptation is also performed by means of the multiresolution analysis.
KEYWORDS	Variational Multiscale Method, multiscale analysis, biorthogonal wavelets, finite volume scheme
PUBLICATION	General Framework, Sonderforschungsbereich / Transregio ... Annual Report 40, (2010)