Quality Criteria for Large Eddy Simulation - Turbulence Mechanics ...

CHAPTER 2. LITERATURE REVIEW 20
simulation has been attempted since the late nineteen nineties [Kravchenko
and Moin, 1997, Geurts and Frohlich, 2002]. It has been addressed by Celik
et al. [2005] through formulation of an index termed LES IQ, the LES index
of quality. Other studies by Klein [2005], Geurts [2005], Meyers et al. [2003]
and Celik [2005:2] have also attempted an estimation of the errors in LES
calculations.
The following taxonomy for obtaining error estimates [Roache, 1998,
Klein, 2005] has been employed for RANS simulations, but are also applicable
to LES.
1. Additional solutions of the governing equations on other grids
Grid refinement/coarsening
2. Additional solutions of the governing equations on the same grid
Higher/lower order accuracy solutions
3. Auxiliary PDE solutions on the same grid
Solution of an error equation
4. Auxiliary algebraic evaluations on the same grid; surrogate estimators
Non-conservation of higher order moments, grid adaptation methods,
convergence of higher order quadratures, etc.
The grids employed in LES of turbulent flows are just fine enough to re-
solve the important large flow structures. The numerical discretisation errors
on such grids can have considerable effects on the simulation results. These
numerical errors can be attributed to either truncation or aliasing. The trun-
cation errors result from the numerical evaluation of the derivatives, while
the aliasing errors result from the evaluation of nonlinear terms on a discrete
grid [Kravchenko and Moin, 1997]. Unlike truncation errors, aliasing errors