Numerical solution of the incompressible Navier-Stokes equations by a three-level finite element method

This paper describes a three-level finite element method for solving the instationary incompressible Navier-Stokes equations. Separating large resolved scales, small resolved scales and unresolved scales enables us to deal with each of these scale groups differently. Whereas the computation of the large scales is performed using a standard Galerkin method, the small scales are resolved by approximate residual-free bubbles exploiting an elementwise submesh with respect to the original discretization. The unresolved scales are merely regarded in their dissipative effect on the small scales. A dynamic modeling process for this making use of an elementwise sub-submesh slightly finer than the submesh is incorporated as level 3 of the method. Currently, applications of this method to the numerical simulation of turbulent flows are underway.     «

This paper describes a three-level finite element method for solving the instationary incompressible Navier-Stokes equations. Separating large resolved scales, small resolved scales and unresolved scales enables us to deal with each of these scale groups differently. Whereas the computation of the large scales is performed using a standard Galerkin method, the small scales are resolved by approximate residual-free bubbles exploiting an elementwise submesh with respect to the original discretizat...     »