A Finite Element Variational Multiscale Method for the Navier--Stokes Equations
Volker John, Songül Kaya · SIAM Journal on Scientific Computing · 2005
This 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. The conditions on L H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier--Stokes equations are studied. Numerical tests with the Smagorinsky large eddy simulation model for $ u_T$ are presented.