This paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large-eddy simulation. The analysis is based on EDQNM closure theory, and is applied to the LES of decaying isotropic turbulence. First, the effects of finite-differencing truncation error, aliasing error and the dynamic Smagorinsky model are independently considered. The time-evolution of kinetic energy and spectra predicted by the analysis are compared to actual LES using the Navier-Stokes equations, and good agreement is obtained. The analysis is then extended to simultaneously consider all sources of error in a second-order discretely energy conserving, central-difference LES solver. Good agreement between the analysis and actual LES is obtained. The analysis is used to compare the contribution of the subgrid model to that of numerical errors, and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors. The proposed one-dimensional EDQNM-LES model shows potential as a more general tool for the analysis of numerical error, and SGS model in simulations of turbulent flow.
Bibliographical noteFunding Information:
This work was supported by the Department of Energy under the Stanford ASC alliance, and the Air Force Office of Scientific Research under grant FA9550-04-1-0341. Computer time was provided by the Minnesota Supercomputing Institute, the San Diego Supercomputer Center, and the National Center for Supercomputing Applications.
- EDQNM theory
- Large eddy simulation
- Numerical error