TY - JOUR
T1 - A three-level finite element method for the instationary incompressible Navier-Stokes equations
AU - Gravemeier, Volker
AU - Wall, Wolfgang A.
AU - Ramm, Ekkehard
PY - 2004/4/16
Y1 - 2004/4/16
N2 - We present a two- and a three-level finite element method for the numerical simulation of incompressible flow governed by the Navier-Stokes equations. Within the theoretical framework of the variational multiscale method and exploiting the concept of residual-free bubbles we propose a separation of three different scale groups, namely large (resolved) scales, small (resolved) scales, and unresolved scales. The resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches. The dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm. The proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method. It is supposed to be the basic scheme also for turbulent flow in a subsequent study.
AB - We present a two- and a three-level finite element method for the numerical simulation of incompressible flow governed by the Navier-Stokes equations. Within the theoretical framework of the variational multiscale method and exploiting the concept of residual-free bubbles we propose a separation of three different scale groups, namely large (resolved) scales, small (resolved) scales, and unresolved scales. The resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches. The dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm. The proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method. It is supposed to be the basic scheme also for turbulent flow in a subsequent study.
KW - Incompressible Navier-Stokes equations
KW - Residual-free bubbles
KW - Subgrid viscosity
KW - Three-level finite element method
KW - Variational multiscale method
UR - http://www.scopus.com/inward/record.url?scp=2042524350&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2003.12.027
DO - 10.1016/j.cma.2003.12.027
M3 - Article
AN - SCOPUS:2042524350
SN - 0045-7825
VL - 193
SP - 1323
EP - 1366
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 15-16
ER -