TY - JOUR
T1 - A multi-scale formulation for compressible turbulent flows suitable for general variational discretization techniques
AU - Bos, van der, F.
AU - Vegt, van der, J.J.W.
AU - Geurts, B.J.
PY - 2007
Y1 - 2007
N2 - Based on the recently introduced variational multi-scale (VMS) approach to large-eddy simulation (LES) as introduced in [T.J.R. Hughes, L. Mazzei, K.E. Jansen, Large eddy simulation and the variational multiscale method, Comput. Visual. Sci. 3 (2001) 47-59; S.S. Collis, Monitoring unresolved scales in multiscale turbulence modeling, Phys. Fluids 13 (6) (2001) 1800-1806], we present a VMS formulation which can be used in the simulation of compressible flows. Special attention is given to obtain a VMS formulation which is suitable for complex flow domains and general variational discretization techniques. A generalization of the Favre-averaging procedure is introduced such that the formulation resembles the Favre-filtered Navier-Stokes equations traditionally used in LES of compressible flow, and no explicit subgrid terms arise in the continuity equation. Also, we show that with the use of discretization methods other than Fourier-spectral methods the VMS-projection no longer commutes with differentiation. This results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to LES. [All rights reserved Elsevier]
AB - Based on the recently introduced variational multi-scale (VMS) approach to large-eddy simulation (LES) as introduced in [T.J.R. Hughes, L. Mazzei, K.E. Jansen, Large eddy simulation and the variational multiscale method, Comput. Visual. Sci. 3 (2001) 47-59; S.S. Collis, Monitoring unresolved scales in multiscale turbulence modeling, Phys. Fluids 13 (6) (2001) 1800-1806], we present a VMS formulation which can be used in the simulation of compressible flows. Special attention is given to obtain a VMS formulation which is suitable for complex flow domains and general variational discretization techniques. A generalization of the Favre-averaging procedure is introduced such that the formulation resembles the Favre-filtered Navier-Stokes equations traditionally used in LES of compressible flow, and no explicit subgrid terms arise in the continuity equation. Also, we show that with the use of discretization methods other than Fourier-spectral methods the VMS-projection no longer commutes with differentiation. This results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to LES. [All rights reserved Elsevier]
U2 - 10.1016/j.cma.2006.12.005
DO - 10.1016/j.cma.2006.12.005
M3 - Article
SN - 0045-7825
VL - 196
SP - 2863
EP - 2875
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 29-30
ER -