model for the Lagrangian Averaged Navier-Stokes- equations
model for the Lagrangian Averaged Navier-Stokes- equations
Hongwu Z., K. Mohseni, and J. E. Marsden
in the
Lagrangian Averaged Navier-Stokes- (LANS-) equations
is derived. The incompressible Navier-Stokes equations are
Helmholtz-filtered at the grid and test filter levels. A Germano
type identity is derived by comparing the filtered subgrid scale
stress terms with those given in the LANS- equations.
Assuming a constant value of and by averaging in the
homogenous directions of the flow, a nonlinear equation for the
parameter is derived, which determine the variation of
in the non-homogeneous directions or in time. The resulting
nonlinear equation is then solved by an iterative technique, in
which the parameter is calculated during the simulation
instead of a pre-defined value. The dynamic LANS- model is
initially tested for the isotropic homogenous forced and decaying
turbulence, where the value of is constant over the
computational box while its variation in time is allowed. The
results of the dynamic LANS- simulations are compared with
the direct numerical simulations and with the LANS-
simulations with constant value of . It is found that the
total kinetic energy decay rate and the energy spectra are predicted
accurately by the dynamic LANS- equations. In order to
verify the applicability of the dynamic LANS- model in
spatially varying turbulent flow an a-priori test in a wall bounded
flow is performed. The parameter is found, as expected, to
change in the wall normal direction where the turbulent scales vary.
A correct behavior of the subgrid scale stress in the wall normal
direction is observed using the dynamic LANS- equations.
The current results show the first derivation and application of a
dynamic LANS- model in spatially varying turbulent flow.
