A variational multiscale stabilized formulation for the incompressible Navier-Stokes equations
Abstract
This paper presents a variational multiscale residual-based stabilized finite element method for the incompressible Navier-Stokes equations. Structure of the stabilization terms is derived based on the two level scale separation furnished by the variational multiscale framework. A significant feature of the new method is that the fine scales are solved in a direct nonlinear fashion, and a definition of the stabilization tensor τ is derived via the solution of the fine-scale problem. A computationally economic procedure is proposed to evaluate the advection part of the stabilization tensor. The new method circumvents the Babuska-Brezzi (inf-sup) condition and yields a stable formulation for high Reynolds number flows. A family of equal-order pressure-velocity elements comprising 4-and 10-node tetrahedral elements and 8- and 27-node hexahedral elements is developed. Convergence rates are reported and accuracy properties of the method are presented via the lid-driven cavity flow problem.
- Publication:
-
Computational Mechanics
- Pub Date:
- July 2009
- DOI:
- 10.1007/s00466-008-0362-3
- Bibcode:
- 2009CompM..44..145M
- Keywords:
-
- Multiscale finite element methods;
- Navier–
- Stokes equations;
- Convergence rates;
- Equal order interpolation functions;
- Tetrahedral elements;
- Hexahedral elements