03-43
Finite Element Error Analysis and Implementation of a Variational Multiscale Method for the Navier-Stokes Equations
Preprint series: 03-43, Preprints
- MSC:
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract: The paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space $L^H$ for the velocity deformation tensor and a turbulent viscosity $\u_T$. The connection of this method to the standard formulation of a VMS is explained. A finite element error analysis for the velocity is presented. It is shown that the constants in the error estimate, in particular in the dominating exponential factor, depend in general on a reduced Reynolds number. It is studied under which conditions on $L^H$, the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier-Stokes equations. Numerical tests with the Smagorinsky LES model for $\u_T$ are presented which show that the VMS behaves as expected if $L^H$ is varied.
Keywords: Variational multiscale method, finite element method, error analysis, Navier-Stokes equations
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.