Variational multiscale methods for incompressible flows

The numerical simulation of incompressible flow governed by the Navier-Stokes equations requires to deal with subgrid phenomena. Particularly in turbulent flows, the scale spectra are notably widened and need to be handled adequately to get a reasonable numerical solution. Separating the complete scale range into subranges enables a different treatment of any of these subranges. In the brevity of this paper, the idea and applications of two methods are sketched. In the corresponding talk, we will present the general framework of a two- and a three-scale separation of the incompressible Navier-Stokes equations based on the variational multiscale method as proposed in [9] and [3]. In a two-scale separation, resolved and unresolved scales are distinguished, and in a three-scale separation, large resolved scales, small resolved scales, and unresolved scales are differentiated. After having presented the general framework, three different approaches to numerical realizations will be addressed (i.e., a global, a local, and a new residual-based approach). A comprehensive overview may be found in [6].     «

The numerical simulation of incompressible flow governed by the Navier-Stokes equations requires to deal with subgrid phenomena. Particularly in turbulent flows, the scale spectra are notably widened and need to be handled adequately to get a reasonable numerical solution. Separating the complete scale range into subranges enables a different treatment of any of these subranges. In the brevity of this paper, the idea and applications of two methods are sketched. In the corresponding talk, we wil...     »